- Email: [email protected]
Hadroproduction experiments for precise neutrino beam calculations
Physics Reports 433 (2006) 65 – 126 www.elsevier.com/locate/physrep
Hadroproduction experiments for precise neutrino beam calculations M. Bonesinia,∗ , A. Guglielmib a Sezione INFN Milano-Bicocca, Dipartimento di Fisica G. Occhialini, Piazza Scienza 3, Milano, Italy b Sezione INFN Padova, Dipartimento di Fisica G. Galilei, via Marzolo 8, Padova, Italy
Accepted 11 July 2006 editor: J.V. Allaby
Abstract The discovery of the neutrino oscillation pattern with solar and atmospheric neutrinos has stimulated systematic studies with long-baseline accelerator experiments. Precise neutrino beamline calculations have demonstrated the importance and paucity of existing hadroproduction data needed to shape the primary meson production in targets and tune available Monte Carlo codes for hadronic shower simulation. After a brief introduction to the physics of neutrino beams, available hadron production data will be reviewed with regards to their parametrization. Fast simulations based on such parameterizations and full Monte Carlo simulations of neutrino beamlines will then be illustrated. The prospective impact of new hadroproduction experiments, such as HARP at CERN and MIPP at Fermilab, will be shown together with some neutrino beamline simulations. © 2006 Elsevier B.V. All rights reserved. PACS: 13.15.+g; 13.60.Hb; 13.75.−n; 13.85.−t
Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Neutrino oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. The present generation of long-baseline neutrino oscillation experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Sub-leading → e oscillations: the future challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Neutrino beams at accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Conventional high energy muon neutrino beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Beam dump neutrino beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Neutrino beams at LHC and pp colliders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Beyond conventions: Neutrino Factories and BetaBeams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Medium term options: SuperBeams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. A review of hadroproduction data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Main characteristics of hadron production reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Requirements on hadroproduction data for the study of conventional beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1. A side remark about low energy beam dump and Neutrino Factory beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ∗ Corresponding author.
E-mail address: [email protected] (M. Bonesini). 0370-1573/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physrep.2006.07.004
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4.3. Low energy hadroproduction experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.4. High energy hadroproduction experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.4.1. A case study: the NA56/SPY experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5. Existing parameterizations of hadroproduction data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.1. Low energy parameterizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.2. High energy parameterizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.2.1. Atherton and Malensek parameterizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.2.2. The BMPT parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.3. Extrapolation to other energies and target materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.4. The MARS pion production model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6. Simulations of neutrino beamlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.1. Fast simulation programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.2. Full Monte Carlo neutrino beam calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.2.1. The Geant 3.21 and MARS simulation packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.2.2. The FLUKA Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.2.3. The GEANT4 simulation package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 7. Examples of flux computations for present and future neutrino beamlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 7.1. The CERN WANF neutrino beam: a case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 7.2. Simulation of the K2K beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 7.3. Simulation of the CNGS beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.4. Simulation of the NuMI beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7.5. Simulation of the Neutrino Factory beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 7.6. Simulation of low energy beam dump experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 8. New hadroproduction experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 8.1. The HARP experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 8.2. E907 (MIPP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 8.3. Future measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 9. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
1. Introduction A renewed interest in precise determination of crucial parameters of neutrino beams as absolute fluxes, energy shape distributions and flavor composition, has been triggered by the recent discovery of neutrino oscillations with solar and atmospheric neutrinos. This discovery has stimulated systematic studies with accelerator based experiments. The new long baseline oscillation experiments, such as ICARUS and OPERA at the CNGS at CERN, MINOS at NuMI at FNAL, K2K at KEK and T2K at JHF impose severe requirements for precise beam calculations with small systematic uncertainty. In addition new projects, such as the Neutrino Factory or the SuperBeams, are stimulating similar considerations. An essential point is the paucity of available hadroproduction data to be used to shape the primary meson production in targets or to tune the available Monte Carlo codes for hadronic showers simulation. After a brief introduction on the status of neutrino oscillations, the physics of neutrino beams will be briefly outlined, with emphasis on the hadroproduction data needed for their optimization and understanding. The prospective impact of new hadroproduction experiments, such as HARP at CERN PS and MIPP at Fermilab, for the understanding of K2K and MiniBooNE results will be shown. Some examples of neutrino beam simulation, with both a fast parameterized approach and a full Monte Carlo simulation, will then be illustrated. 2. Neutrino oscillations Oscillations between neutrinos of different flavor require the existence of a m = 0 term for the neutrino mass and flavor lepton number violation interaction which cannot be simply accommodated within the Standard Model (SM). In the standard scenario of three neutrino generations, the observed flavor oscillations in solar and atmospheric neutrinos can be described by a mixing matrix U which translates between mass (1 , 2 , 3 ) and flavor eigenstates (e , , ). Six independent parameters have to be experimentally measured: three mixing angles 12 , 13 and 23 , two mass-squared differences m212 and m223 , where m2ij = m2i − m2j , and a CP violating phase .
M. Bonesini, A. Guglielmi / Physics Reports 433 (2006) 65 – 126
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In vacuum the oscillation probability between two neutrino flavors , is given by P ( → ) = −4
jk
Re[W ] sin2
k>j
m2j k L 4E
±2
k>j
jk
Im[W ] sin2
m2j k L 2E
,
(1)
jk
where = e, , , j = 1, 2, 3 and the coefficients W are expressed in function of the mixing matrix elements Uj as
W = Uj U∗j U∗k Uk . The neutrino energy E and the baseline L (distance of the neutrino source from the detector), combined in the oscillation formula into the L/E ratio, are the relevant experimental parameters. Oscillations are perturbed if neutrinos propagate in matter [1], depending on the sign of m223 [2]. The measurement of this quantity can fix the ordering with which mass eigenstates are coupled to flavor eigenstates (neutrino mass hierarchy). Solar neutrino oscillations were observed in the Homestake [3], Gallex-GNO [4], SAGE [5], Super-Kamiokande [6] and SNO [7] experiments giving a convincing evidence of , appearance and a first precise determination of the solar oscillation parameters. A combined data analysis of solar neutrino experiments and of the KamLAND [8] long-baseline reactor experiment running at the solar m2 scale constrains the solar mixing angle and mass splitting −5 to |m212 | = 7.9+0.6 eV2 , tan 12 = 0.40+0.10 −0.07 [9]. −0.5 × 10 A clear signal of disappearance of atmospheric neutrinos and an anomalous value of the ratio of electron to muon neutrino events were reported by the Super-Kamiokande experiment [10], then confirmed by the Soudan2 [11] and Macro [12] experiments. Super-Kamiokande provided an indirect evidence of appearance excluding pure oscillations into sterile neutrinos at 99% C.L. [13,14]. As a result an almost pure → transition, connected with the m2 and m3 mass eigenstates, with parameters 1.5 × 10−3 eV2 < |m223 | < 3.4 × 10−3 eV2 , sin2 223 > 0.92 [15] at 90% C.L was found. A first confirmation has been obtained in the long-baseline experiment K2K which observed a disappearance in a 1.5 GeV neutrino beam sent to the Super-Kamiokande detector (L = 250 km), measuring 1.9 × 10−3 < |m223 | < 3.6 × 10−3 eV2 at 90% C.L. [16]. The 13 mixing angle represents the link between the solar and the atmospheric neutrino oscillations. The best experimental constraint: sin2 213 0.14 at 90% C.L. for |m223 | = 2.5 × 10−3 eV2 , comes from the reactor experiment Chooz [17]. Both solar and atmospheric neutrino data are compatible, within the experimental sensitivity, with 13 0 favoring a near bimaximal mixing matrix with |m223 | 30 · |m212 |. Thus the 3 × 3 mixing matrix Uj becomes a trivial product of two 2 × 2 matrices, showing that the observed solar and atmospheric neutrino oscillation regimes are largely decoupled. They can be thus described by a two neutrino formalism with only one mixing angle and one square mass difference m2 as jk
P ( → ) ∼ sin2 2 sin2
1.27m2 (eV2 ) · L(km) . E (GeV)
(2)
In this approximation, the resulting leading oscillation probabilities for s, setting m212 to zero, depend only on m223 , 13 and 23 and are given by: P (e → ) = sin2 23 sin2 213 sin2 (m223 · L/4E ),
(3)
P (e → ) = cos2 23 sin2 213 sin2 (m223 · L/4E ),
(4)
P ( → ) = cos4 13 sin2 223 sin2 (m223 · L/4E ).
(5)
The three neutrino oscillation scheme will become more complicated, requiring non-standard explanations, if the → e signal with a |m2 | of 0.3 − 20 eV2 observed by LSND [18] will be confirmed by the MiniBooNE experiment at FNAL looking to → e transitions [19]. However, a large part of the allowed region of the oscillation parameters was already excluded by the KARMEN [20] and NOMAD experiments [21]. The precise measurement of the neutrino oscillation parameters can be better addressed by accelerator long-baseline oscillation experiments (LBL), since a more stringent control over the neutrino flux can be obtained as compared to the atmospheric and cosmic rays sources. Moreover experiments searching for → transitions at accelerators can explore different regions of the sin2 2 − m2 plane by a suitable choice of the L/E ratio. Of particular interest will
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Table 1 Main parameters of beams for the current generation of oscillation experiments at accelerators as compared to the previous NOMAD and CHORUS experiments at the CERN SPS WANF facility Experiment
Facility
pp (GeV/c)
L (km)
E (GeV)
p.o.t./yr (1019 )
MiniBooNE K2K MINOS OPERA, ICARUS NOMAD, CHORUS
FNAL Booster KEK PS FNAL NuMI CERN CNGS CERN WANF
8.9 12.9 120 400 450
0.5 250 730 732 0.8
0.8 1.5 3.5 17.7 24.2
100 2 20 → 34 4.5 1.5
be the detection and measurement of the sub-leading → e oscillations in the atmospheric neutrino oscillations, which can offer the possibility to discover the CP violation in the lepton sector. Therefore, neutrino oscillation physics at accelerators will probably include several phases: • 2001–2010: the present generation of LBL experiments (K2K, MINOS, OPERA, ICARUS, see next paragraph) to confirm the Super-Kamiokande evidence of oscillations of atmospheric neutrinos. • 2009–2015: next generation LBL experiments (T2K, NOvA) with improved neutrino beams, the SuperBeams (see Section 3.5) and the reactor experiment DoubleChooz, optimized to measure 13 and give a precise measure of the atmospheric parameters; • 2015–later: novel concept BetaBeam or Neutrino Factory facilities, coupled to large mass detectors, with a much improved sensitivity to 13 and a good sensitivity for leptonic CP violation and the mass hierarchy (see Section 3.4). 2.1. The present generation of long-baseline neutrino oscillation experiments Over the next 5 years the present generation of oscillation experiments at accelerators with long-baseline beams (see Table 1): K2K at KEK [16], MINOS [22] at the NUMI beam from FNAL [23] and ICARUS [24] and OPERA [25] at the CNGS beam from CERN [26], are expected to confirm the atmospheric neutrino oscillations and measure sin2 223 and |m223 | with a 10–15% accuracy if |m223 | > 10−3 eV2 . K2K and MINOS are looking for neutrino disappearance by measuring the survival probability as a function of neutrino energy while ICARUS and OPERA will search for interactions in a beam, as final evidence for → oscillations. K2K has already completed its data taking, while MINOS has started data taking in 2005. The CNGS neutrino beam is expected to start operations in the second half of 2006. Current long-baseline experiments with conventional neutrino beams can look for → e oscillations even if they are not optimized for 13 studies (see Fig. 1). As an example, MINOS at NuMI is expected to reach a sensitivity of sin2 213 = 0.08 for |m223 | = 2.5 × 10−3 eV2 , convoluted to CP and matter effects, integrating 14 × 1020 protons on target (p.o.t) in 5 years according to the FNAL proton evolution plan [27]. The sensitivity to 13 of the current experiments is limited by the power of the proton driver which determines the neutrino flux and the event statistics, by the not optimized L/E value and by the presence of the e intrinsic beam contamination and its related systematics. As an example, the CNGS neutrino energy is ∼ 10 times larger than the optimal value for 13 searches, due to the constraint of the search for appearance. 2.2. Sub-leading → e oscillations: the future challenge The unknown parameters of the mixing matrix Uj , as the angle 13 , the sign of m223 and which generates the CP violation in the neutrino oscillations, can be extracted by measuring sub-leading → e oscillations at accelerators. Reactor experiments on e disappearance are only sensitive to the 13 mixing angle. Taking into account all the contributions and not knowing a priori the size of 13 , all the six parameters of the mixing matrix are involved in the appearance probability for electron neutrinos in a muon neutrino beam, that can be
M. Bonesini, A. Guglielmi / Physics Reports 433 (2006) 65 – 126
69
10-1 CHOOZ EXCLUDED 90% C,L,
∆m223 (eV2)
10-2
MI
NO
SUPER ALLOWED 90% C,L
2.5
S
10-3
CN
GS
T2K
10-4 10-3
10-2
Co m
bin
10-1
ed
1
sin22θ
13
Fig. 1. The expected 90% C.L. sensitivity on the 13 mixing angle (matter effects and CP violation effects not included) for MINOS, ICARUS (assuming a 2.35 kt fiducial mass) and OPERA combined at nominal CNGS intensities and for the next T2K experiment, compared to the Chooz exclusion limit.
parameterized as [28] 2 2 2 P ( → e ) = 4c13 s13 s23 sin2
m213 · L 4E
2 + 8c13 s12 s13 s23 (c12 c23 · cos − s12 s13 s23 ) · cos
2 − 8c13 c12 c23 s12 s13 s23 · sin · sin
m223 L m213 L m212 L · sin · sin 4E 4E 4E
m223 L m213 L m212 L · sin · sin 4E 4E 4E
2 2 2 2 2 2 2 + 4s12 c13 (c13 c23 + s12 s23 s13 − 2c12 c23 s12 s23 s13 · cos ) · sin2
2 2 2 − 8c13 s13 s23 · cos
m223 L m213 L 2 aL · sin (1 − 2s13 ) , 4E 4E 4E
m212 L 4E (6)
where sij = sin ij , cij = cos ij , a[eV2 ] 7.6 × 10−5 (g/cm3 )E (GeV). The first term, which has the largest contribution, is 13 driven, while the fourth is driven by the solar neutrino regime. The second term is CP-even and the third as well the last-one, which account for the matter effects on the neutrino propagation as developed at the first order, result CP-odd. The CP odd term and matter effects change sign by changing neutrinos with antineutrinos. The → e transition probability is dominated by the solar term, anyway, at the distance defined by the |m223 | parameter, it is driven by the 13 term which is proportional to sin2 213 . Below sin2 213 10−3 solar neutrino oscillations will be the dominant transition mechanism, limiting the experimental sensitivity to 13 . Moreover, P ( → e ) could be strongly influenced by the unknown value of and the sign of m223 . The 13 measurement represents the first needed ingredient for the investigation of the CP leptonic violation in the → e transitions and for the mass hierarchy determination. The detection of the phase will require a major experimental effort because of the intrinsic difficulty of disentangling the several contributions to → e
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oscillation probability. A leptonic direct CP violation can be detected by comparing the electron neutrino and antineutrino appearance probabilities in a and beam, respectively, through: ACP () =
P ( → e , ) − P ( → e , ) . P ( → e , ) + P ( → e , )
(7)
The richness of the → e transition is also its weakness because it will be very difficult to extract all the parameters unambiguously in presence of correlations between 13 and [29] where additional clone solutions arise. In general, the measurement of P ( → e ) and P (¯ → ¯ e ) will result in eight allowed regions of the parameter space, the so-called eightfold-degeneracy [30]. The measure of the subleading → e transitions searches for a e excess as respect to what expected from the solar terms. It will be experimentally difficult because the Chooz limit on the e disappearance: 13 < 11◦ for |m223 | 2.5 × 10−3 eV2 , translates into a → e appearance probability less than 10% at the appearance maximum in a high energy muon neutrino beam. As already pointed out, the → e experimental sensitivity with conventional beams is limited by an unavoidable e beam contamination of about 1%. The to oscillations, with E above the mass production threshold, generate background due to a significant number of charged current interactions where a large fraction of ’s decay into electrons. In addition neutral pions in both neutral current or charged current interactions can fake an electron providing also a possible background for the e ’s. Therefore the measurement of 13 mixing angle and the investigation of the leptonic CP violation will require: • neutrino beams of high intensity and purity and low associated systematics; • the use of detectors of unprecedented mass, granularity and resolution, to collect high event statistics and keep the event backgrounds rate as low as possible, as water Cherenkov and liquid Argon detectors or magnetized iron calorimeters. The sensitivity in the oscillation experiments will depend mainly on the neutrino beam characteristics and relies on its knowledge. To improve control over the systematic errors, ancillary experiments to measure the physical processes involved in the neutrino beam production are needed. Studies on parent meson production and low energy neutrino interaction cross-sections (E 1 Gev) will be essential for the present long baseline neutrino experiments, as well as in atmospheric neutrino measurements. They will be also crucial in the design for the next generation of neutrino oscillation experiments at future accelerators. 3. Neutrino beams at accelerators Conventional accelerator neutrino beams are produced by the decay of , K’s generated at beam dumps (decay at rest) or by high energy protons hitting suitable targets (decay in flight). In such beams, different mesons are involved as sources, according to the different scale of decay lengths (see Table 2). As discussed in the following, these conventional beams have a low intensity and are not pure, admitting different neutrino flavors as minority components ( , e , e or , e , e ) in addition to the majority ones ( or ). These intrinsic features limit the experimental sensitivity in the oscillation searches. They are overcome if the neutrino parents can be fully selected, collimated and accelerated to a given energy. This can be realized with muons or selected beta decaying ions. The neutrino beam composition, as obtained from their decays, would then be perfectly predictable. The first approach brings to the Neutrino Factory, the second to the BetaBeam, as discussed in Section 3.4. However, the technical difficulties associated with developing and building these novel conception neutrino beams suggest for the middle term to improve the conventional beams by using new high intensity proton machines (proton drivers) and optimizing the beam characteristics for the → e oscillation searches, giving the SuperBeam option, see Section 3.5. 3.1. Conventional high energy muon neutrino beams High energy accelerators provide ( ) beams through the decay of , K mesons produced by protons hitting needle-shaped light targets. In order to increase the angular acceptance of the beamline and correspondingly the neutrino flux, positive (negative) mesons are charge-selected and focused by magnetic lenses, “horns” and “reflectors”,
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Table 2 Main neutrino sources at accelerators c Long lived sources ( mc 2 (7.5 − 6200) m/GeV; Br ∼ 50.100%) + → + K + → + , 0 + , 0 e+ e KL0 → − + , − e+ e , + − , + e− e + → e+ e c −2 Medium lived sources ( mc m/GeV; Br ∼ 0.1%) 2 (4.7) × 10
→ pe− ¯ e KS0 → − + , − e+ e , + − ¯ , + e− ¯ e − → ne− ¯ e c −4 Short lived sources ( mc m/GeV; Br ∼ 2 − 20%) 2 (0.5 − 1.7) × 10
D + → K 0 + , K 0 e+ e DS+ → + + → + ¯ , e+ e ¯ B 0 → D − + , D − e+ e
BCT1
SEMs
Reflector
Al Collimator
BCT2
Horn
Muon Pits Tunnel Decay
CHORUS Earth
Be Target 450 Ge V/c protons
TDX collimator
Iron Shield
NOMAD
Fig. 2. The WANF beamline at the CERN SPS; the distance of the NOMAD detector from the Be target is ∼ 840 m.
Fig. 3. Schematic layout of the CNGS neutrino beamline.
into an approximately parallel beam in a long evacuated decay tunnel where ’s ( )’s are generated. The residual hadrons and muons are stopped by an heavy absorber. When and K are collected in a wide range of momenta and solid angle, wide band neutrino beams (WBB) with a high flux and a broad energy spectrum, are produced. In case of positive charge selection of the secondary particles by the magnetic horns, a beam has typically a contamination of at a few percent level (from − , K − decays) and around 1% of e and e coming from three-body K ± , K 0 and decays, which affect the experimental sensitivity in the oscillation searches. Narrow band neutrino beams (NBB) can be obtained by momentum selecting the mesons before entering the decay region. The neutrino energy spectrum is thus much tighter ( E /E ∼ 20%), at the expense of a significantly lower flux. As examples of recent WBB neutrino beams, a schematic layout of the West Area Neutrino Facility (WANF) beamline [31] at the CERN SPS as used by the NOMAD [32] and CHORUS [33] experiments and of the CERN to Gran Sasso long baseline neutrino beam (CNGS) [26] are shown in Figs. 2 and 3. The CNGS design was accomplished on the basis
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Table 3 Main parameters of the WANF and CNGS neutrino beamlines at the CERN SPS Beam line
WANF
CNGS
Proton energy Proton beam focal point Proton intensity pot/year (shared operations)
450 GeV 50 cm from start of target 2 × 1019
400 GeV 4.5 × 1019
Target material Number of rods Target rod diameter Target rod length-separation Additional end-rod length
Beryllium 11 3 mm 10–9 cm –
Graphite 8 4 mm 10–9 cm 50 cm
Horn and reflector focusing momenta Horn and reflector length Horn and reflector current Horn and reflector distance from focal point Horn acceptance
70–70 GeV 6.56–6.54 m 100–120 kA 19.4–90.9 m 10 mrad
35–50 GeV 6.65 m 150–180 kA 2.7–43.4 m 20 mrad
Decay tunnel length–radius Tunnel vertical slope Pressure in decay tunnel
285–0.6 m +42 mrad 1.3 × 102 Pa
992–1.2 m −50 mrad 1.3 × 102 Pa
of the previous WANF experience where the neutrino beam interactions in the NOMAD detector allowed to study with high accuracy the beam features. Their main technical characteristics are listed in Table 3. The resulting spectra of the four neutrino components , , e and e of the WANF beam at CERN SPS (the component is absolutely negligible, at a 10−6 level) as well as their related main neutrino sources ( ± , K ± , K 0 and ± ) are reported in Fig. 4. In the CNGS project a substantial increase of the beamline acceptance and of the flux is obtained by moving the horn and reflector near the target and increasing their characteristic currents. The beam-optics was optimized in order to maximize the possibility to detect the → oscillation by the appearance of events in a beam initially free of . A lower , e and e contamination is also expected due to the 732 km long base-line (see Fig. 5). This conventional scheme for wide-band neutrino beams is also used in the K2K [16] at KEK and MINOS at the FNAL NuMI [23] long base-line disappearance experiments and in the MiniBooNE [19] experiment where the → e transition will be searched for as an excess of e interactions with respect to the expected natural contamination of the beam (see Table 1 and Figs. 6–8). To predict beam energy spectra, intensity and composition a sound knowledge of and K production in the primary proton beam target interactions is required. The accurate description of the K + and K 0 fluxes relative to the + flux is crucial to calculate the initial e content in the beam. Neutrino production at high energy proton accelerators involves a quite complicated cascade of meson decay and reinteraction processes in the beamline materials. The latter reduce the neutrino fluxes and increases the uncertainty in the calculations (mainly with wrong sign and wrong flavor contaminations). They are generally minimized using a target made of thin rods of low Z material interleaved with empty spaces (to let the secondary mesons exit the target without traversing too much material). The amount of material downstream of the target (i.e. horn and reflector inner conductor thickness) must be kept to the minimum. Primary protons missing the target will interact in the downstream materials producing a large fraction (typically up to 15% of at the WANF) of the minority components otherwise mainly produced by the defocused − and K − and K 0 from the target. Therefore an accurate description of the primary proton beam spot, focusing system as well as of the materials inserted in the beamline from the target to the dump (hadronic reinteraction processes) is mandatory. As a conclusion these neutrino beams at accelerators are not pure (e ) beams and knowledge of their composition suffers mainly from the uncertainties on the hadronic processes involved at generation level and particle transport which limit the experimental sensitivity in oscillation searches.
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νµ
105 104
K+
103
0
KL
π+
102 µ-
10
− νµ
105 ν−µ / 3 GeV / 109 p.o.t.
νµ / 3 GeV / 109 p.o.t.
106
73
104 K-
103 102
π-
µ+ 10 KL0
1
1 0
50 100 150 200 Neutrino energy (GeV)
0
50 100 150 200 Neutrino energy (GeV)
104
− νe
103
K
+
102
10
103
µ+
0
− νe / 3 GeV / 109 p.o.t.
νe / 3 GeV / 109 p.o.t.
νe
102
10
0
KL
1
K-
µ-
KL
1 0
50 100 150 200 Neutrino energy (GeV)
0
50
100 150 200 Neutrino energy (GeV)
Fig. 4. Composition of , , e and e energy spectra at WANF CERN SPS neutrino beam (450 GeV protons on Be) within the NOMAD transverse fiducial area of 2.6 × 2.6 m2 . The last-decay parent particles are shown.
3.2. Beam dump neutrino beams Low energy neutrino beams may also be produced by the decay at rest of , ’s generated by impinging protons on a beam dump. In a beam dump experiment, the target for the primary proton beam, where the neutrino parents are produced, is also the medium for absorbing and/or stopping the hadrons. Accordingly, no drift space is provided to hadrons to decay in. High intensity low energy proton accelerators (pbeam ∼ 1 GeV/c) such as meson factories or neutron spallation sources are commonly used. The decay sequence + → + , + → e+ e at rest gives an almost equal number of , and e with a characteristic low energy spectrum, as shown in Fig. 9. A deviation from this simple decay scheme is given by pion decay in flight, which accounts for ∼ 2% of the total flux. Negative pions are strongly absorbed when they come to rest and therefore give no contribution to the spectrum. The two most recent experiments at a beam dump, LSND [18] at LAMPF and KARMEN [20] at ISIS have given controversial results on → e oscillations that are presently addressed by the MiniBooNE experiment [19]. In high energy beam dump neutrino experiments, one instead tries to eliminate or reduce neutrinos from long and medium lived sources, such as the first two categories of Table 2. The semileptonic decays of new, short-lived particles ( ∼ 10−10 − 10−13 s) would produce “prompt” neutrinos, to be distinguished from the “non-prompt” neutrinos from , K weak decays. Early experiments, such as CDHS [35], CHARM [36] and BEBC [37] have looked mainly for the presence of charm. The present interest in high-energy beam dump experiments is instead connected to the detection of ’s, such as in the DONUT (E872) experiment at FNAL [38]. In the neutrino beam used by DONUT about 4% of all the neutrinos seen in the detector are ’s.
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103
− νµ / 2 GeV / 107 p.o.t.
νµ / 2 GeV / 107 p.o.t.
102
102
10
10
1
10-1 50 100 Neutrino energy (GeV)
150
0
10
− νe/ 5 GeV / 107 p.o.t.
νe / 5 GeV / 107 p.o.t.
0
1
50 100 Neutrino energy (GeV)
150
1
10-1
10-1 0
50 100 Neutrino energy (GeV)
150
0
50 100 Neutrino energy (GeV)
150
Fig. 5. Composition of , , e and e energy spectra at Gran Sasso of the CNGS neutrino beam (400 GeV protons on C) within a 0.5 km2 transversal fiducial area. The last-decay parent particles are shown.
Neutrino Flux at Super-Kamiokande
1011
number of neutrinos/cm2/1020POT
number of neutrinos/cm2/1020POT
Neutrino Flux at Near Detectors
νµ
1010 109
νe
νµ
108
νe 107
0
1
2
3
Eν (GeV)
4
5
105 νµ
104 103
νe
νµ
102
νe
10
0
1
2
3
4
5
Eν (GeV)
Fig. 6. Predicted K2K beam at KEK (JAPAN), from 12.9 GeV protons impinging on a Al target, at the near location detector and at the SuperKamiokande site, as reported in [34].
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200
Low Energy Beam
75
High energy Event Total
Medium energy
HE : 2740 ME : 1270 LE : 470
175 2nd Horn z =10.0 m
VµCC- events/kt/GeV
Target z= -0.34 m
Medium Energy Beam
Target z= -1.30 m
2nd Horn z =22.0 m
150 125 100
Low energy
75
High Energy Beam 50 25 Target z= -3.96 m
2nd Horn z =40.0 m
0 0
5
10
15 Ev (GeV)
20
25
30
Fig. 7. spectra from the different proposed neutrino beams at the FNAL NuMI facility, as obtained from 120 GeV protons impinging on a graphite target. The disappearance experiment will use the low energy beam. The left-hand inset shows the relative positions of the target and the two used horns. Plots refer to a 1 kt/yr exposure with perfect focalization efficiency.
νµ Flux
Fraction of νµ Flux / 0.1 GeV
10-1
νe Flux
10-2
10-3
10-4
10-5 0
0.5
1
1.5
2
2.5
3
Eν (GeV) Fig. 8. The predicted energy spectrum from the beam for the MiniBooNE experiment at FNAL, with 8.9 GeV protons impinging on the Be target. The (upper) and e (lower) components of the beam are shown.
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Fig. 9. Neutrino spectra from a low energy beam dump.
Table 4 Neutrino interactions per year in a 2 kg/cm2 detector (e.g. density 2 g/cm3 , 10 m long) for LHC at L = 1034 cm2 /s (see [41]) E 100 GeV
e
E 500 GeV
10 mrad
2 mrad
10 mrad
2 mrad
2300 11300 130
1300 7100 46
860 3700 32
750 2900 24
3.3. Neutrino beams at LHC and pp colliders Neutrino √ beams at very high energy (E 500 GeV) can be produced in pp collisions (such as at the LHC collider at s = 14 TeV) from the decay of charmed and beauty particles, as outlined in Refs. [39,40]. Some advantages are: • the possibility to have ’s and e at very high energy; • comparable numbers of e ’s and ’s (unlike conventional neutrino beams from , K decays); • a sizable fraction of (up to 10% of the e beam) from beauty particles and Ds → decays. However, due to the uncertainties in heavy quark production cross-sections, neutrino flux estimates show large uncertainties. These prompt-decay neutrinos are emitted mainly at ∼ 0◦ in forward direction, e.g. tangentially to the circulating beams. A neutrino experiment, located in an LHC straight section behind a bending magnet, would benefit from the intense, strongly forward peaked, high-energy beams produced either from beam-beam or beam-gas interactions (as the angular difference from the two beams is ∼ 1 mrad only). Table 4 reports, as an example, the number of interactions per year (assumed as 107 s) in a 2 kg/cm2 target, for two energy cuts and two typical opening angles. In addition to high energy , e neutrinos, LHC will offer the unique possibility of direct studies. Neutrino beams can be produced at LHC also from cc pairs produced in collisions between the coasting proton beams and an internal jet-gas target (as in UA6 experiment at CERN SPS) or from an extracted proton beam on a dump. In the last case the technical challenge is quite formidable, as outlined in Ref. [40]. In all cases, as neutrinos come from cc decays, the composition of the flux is affected by big uncertainties, the cc production cross-sections being quite unknown.
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A possible layout of a neutrino factory
Number of charged current interactions
_ νµ Polarization= +1
P=+0.3 P=0 P=-0.3
P=-1 0.2
0.4
νe
0.6
0.8
1
P=-1 P=-0.3
P=+0.3 0.2
0.4
0.6
0.8
1
Eν/Eµ Fig. 10. Expected layout for a Neutrino Factory at CERN (top) and corresponding energy spectra of neutrino beams for the + case (bottom) for different degrees of polarization.
3.4. Beyond conventions: Neutrino Factories and BetaBeams To overcome the limitations from conventional beams, neutrino production by decays of accelerated muons has been considered [42]. The beam related background is reduced to a 10−5 level or below, because there is only one parent particle decaying to neutrinos, with no subsequent daughter decay (+ → e+ e or − → e− e ). The basic concepts for a muon collider were introduced by G.I. Budker in 1969 and A.N. Skrinsky in 1971 [43]. The first idea to use muons to produce high intensity neutrino beams was developed by Koshkarev in 1974 [44]. The lifetime at rest is 2.2 s and its decay length (c) 660 m. Using an average acceleration of 1 MeV/m, it may nevertheless be possible to produce a high energy muon beam at energies of the order of tens of GeV, the losses being most severe at the beginning of the acceleration. Detailed calculations for such Neutrino Factory were developed within the Muon Collaboration in the USA [45] and at CERN [46] as a first step of a large new physics programme based on muon colliders. In the CERN proposed layout for a Neutrino Factory (see Fig. 10) a 4 MW H − beam is accelerated up to 2.2 GeV by a new Super Conducting Proton Linac (SPL) to produce low energy ’s in a liquid mercury target, after some
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Table 5 Oscillation channels accessible at a muon factory (+ decay) Oscillation channel
Experimental signature
e → → e e → x → x e → →
Appearance mode: detection of wrong-sign muons, − Appearance mode: detection of wrong-sign electrons, e+ Disappearance mode: energy spectrum and NC/CC Disappearance mode: energy spectrum and NC/CC Appearance mode: detection of − events Appearance mode: detection of + events
accumulation and bunch compression [46]. A magnetic horn collection system is envisaged to capture as many ’s and ’s as possible. Muons from decay are then cooled1 and phase rotated, to reduce their phase space, before being accelerated through a first Linac and then through a system composed of two recirculating Linacs, up to 50 GeV/c. Finally ’s of well defined charge and momentum are injected in the accumulator where they will circulate until their decay, delivering along the two main straight sections two intense beams. Either muon sign can be selected. The optimal muon beam energy: E = 50 GeV (E ∼ 34 GeV), accounting for the difficulties and the technical challenge for the construction of such a muon accelerator complex, must be as large as possible. As the neutrino flux grows like E2 (in the conventional neutrino beams is proportional to E ), the number of charged current neutrino events from the oscillations (Nosc ), measured by a detector at a distance L, will be proportional to E [48]: L E3 sin2 E , (8) E L2 where ∝ E is the corresponding neutrino interaction cross-section and Posc is the oscillation probability. From a general point of view the Neutrino Factory approach relies on a completely different strategy than conventional facilities, where only a fraction of the focused high energy mesons, produced by high energy protons on a target, decays giving neutrinos. In a Neutrino Factory based on decay, the primary beam power is used to produce as many (and ) as possible per GeV. Hence the factory must capture the largest fraction of produced muons and manipulate them in order to reduce their phase space in view of the final acceleration stage. Here the decay tunnel typical of conventional beams is replaced by the storage ring where each circulates until it decays. Major intrinsic advantages over a conventional neutrino source are: Nosc ∝ · · Posc ∝
• the decay + → e+ e (− → e− e ) produces a pure, well collimated, neutrino beam with equal numbers of , e ( , e ) which allow to extend the baseline to distances of several thousand kilometers; • the momentum is well defined (an accurate determination is expected by spin precession measurements) and therefore the neutrino energy spectra at the detector site are precisely calculable (see Fig. 10); • due to the introduction of a new megawatt proton driver, the flux intensity is expected to be ∼100 times more than that of conventional beams, with P = 50 GeV/c and 0.5 × 1021 -decay/yr; • the neutrino intensity can be precisely determined from the measurement of the muon current circulating in the storage ring (absolute normalization at 1% level). The Neutrino Factory lends itself naturally to the exploration of neutrino oscillations between different neutrino flavors with high sensitivity to small mixing angles and small mass differences, due to the very intense, collimated, well defined and pure beam. The detector should be able to perform both appearance and disappearance experiments, providing final lepton identification and charge discrimination which is a tag of the initial flavor and of the oscillation. Among the many possibilities for studying oscillations in different channels (see Table 5), the searches for e → transitions (“golden channel”) appears to be very attractive because this transition can be studied in appearance mode looking for − (appearance of wrong-sign ) in neutrino beams where the neutrino type that is searched for is totally absent (+ beam). With a 40 kt magnetic detector exposed to both polarity beams and 1021 muon decays, it will be possible to explore the 13 angle down to 0.1◦ , measuring the phase if m212 5 × 10−4 eV2 (systematic errors not 1 A dedicated experiment, MICE [47], is under construction at RAL to realize a prototype cooling channel section.
M. Bonesini, A. Guglielmi / Physics Reports 433 (2006) 65 – 126 EURISOL
79
Existing at CERN DECAY RING
Proton driver
Isol target & Ion source
SPS
B = 5T L = 6880 m
New RFQ Linac PSB
PS
Fig. 11. A schematic layout of the BetaBeam complex proposed at CERN.
accounted for) [29,49]. More details on the physics performances of a Neutrino Factory for a precision measurement of neutrino oscillation parameters can be found in Refs. [46,50]. One of the main concerns in the development of the Neutrino Factory project study arises from the uncertainty on production at low energy in the target. Current simulations show ∼ 30% discrepancies with respect to available data. A good knowledge of the pT , pL distributions of produced secondaries is crucial to optimize the efficiency of the collection phase: hadroproduction data with full angular coverage at low energy are therefore required. The HARP experiment at the CERN PS is presently addressing this question [51]. A completely different strategy aims at neutrino beams from the decay of radioactive isotopes accelerated in a suitable machine. As for the Neutrino Factory, the neutrino spectrum of these BetaBeams (B) [52] is completely defined by the parent decay properties and by the Lorentz boost. In the CERN proposed layout (see Fig. 11 for details), 6 He and 18 Ne ions are produced by a 0.4 MW ∼ 2 GeV proton machine (SPL) and accelerated up to (6 He) = 60 and (18 Ne) = 100, respectively, by the PS and SPS machines. The ion beams are then injected in a “decay ring” where two pure low energy e and e beams per straight section can be produced. The expected neutrino fluxes at 130 km of distance for 2.9 × 1018 6 He and 1.1 × 1018 18 Ne decays/yr are displayed in Fig. 12. In principle, all the necessary machinery has been already developed at CERN for the heavy ion physics programme. However the required improvement by ∼ 3 orders of magnitude of the presently available ion fluxes will require sub-megawatt 1–2 GeV Linacs, new target developments for heavy ion production, ion collection and acceleration system including the CERN PS and SPS and a novel decay ring [53]. Accounting for the technical challenges involved in these new facilities, the expected timescale of the BetaBeams is expected to exceed the next ten years. Since the beam does not contain or ¯ , magnetized detectors are not required. The corresponding physics potential computed with a Cherenkov water detector of 440 kt fiducial mass, has shown a 90% C.L. sensitivity to sin2 213 ∼ 0.0007 and the capability to detect a CP violation signal at 3 if || 35◦ and 13 1.0◦ [54]. Running the two ions separately both at = 100 can allow to push the investigation of sin2 213 down to 0.0002, and the CP violation search down to 25◦ for 13 1.0◦ [55,56]. 3.5. Medium term options: SuperBeams Conventional neutrino beams can be improved and optimized for → e searches, giving a SuperBeam facility. This will require: • • • •
a new proton driver, with power exceeding one megawatt, to deliver more protons on target; a narrow band beam with E ∼ 1.2 GeV; a lower intrinsic e beam contamination, by suppressing the K + and K 0 production in the target; a tunable L/E in order to explore the |m223 | parameter region as indicated by the previous experiments with neutrino beams and atmospheric neutrinos.
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x 107
x 107 SPL νµ − SPL νµ Beta νe (Ne18) − Beta νe (He6)
ν/m2/20 MeV/yr
2000
1500
1000
8000
SPL νµ
7000
SPL −νµ Beta νe (Ne18) Beta −ν (He6)
6000 ν/m2/20 MeV/yr
2500
e
5000 4000 3000 2000
500 1000 0
0 0
0.2
0.4
0.6 Eν (GeV)
0.8
1
0
0.2
0.4
0.6 Eν (GeV)
0.8
1
Fig. 12. Left: neutrino flux of B (6 He = 60, 18 Ne = 100, shared mode) and CERN-SPL SuperBeam, at 2.2 GeV, at 130 km of distance. Right: the same for 6 He = 100, 18 Ne = 100, (non shared mode, e.g. just one ion circulating in the decay ring) and a 3.5 GeV SPL SuperBeam.
The realization of neutrino SuperBeams will require the development of high power proton Linacs or Rapid Cycling Synchrotrons, expected to happen in the next decade, and the development of targets able to survive to megawatt power proton beams, whose R&D studies have already started [57]. An interesting option for the SuperBeams is the possibility to tilt the beam axis of a few degrees with respect to the position of the far detector (Off-Axis beams) [58,59]. According to the two body -decay kinematics, the neutrino flux at = 0◦ is the result of the contributions of all the pions above a given momentum giving neutrinos of similar energy, contrary to the = 0◦ case where the neutrino energy is proportional to the pion momentum (see Fig. 13): E =
m2 − m2 2(E − p cos )
,
where E , p and m are the energy, momentum and mass of the parent pion and m is the muon mass. It can be demonstrated that the spectrum at = 0◦ is peaked at an energy E,max given by E,max ()
30 MeV ,
(9)
an effect of the well-known “Jacobian peak” in the two-body decay kinematics. Off-Axis neutrino beams have several advantages with respect to the On-Axis beams. They have a narrower energy spectrum, with a smaller e contamination (since they mainly come from three body decays), although the neutrino flux is significantly smaller. In the JHF project Phase I (T2K experiment [58]) a 50 GeV proton beam from a 0.75 MW PS will produce an intense ∼ 700 MeV beam (see Fig. 14) with 0.4% e contamination. In five years a 90% C.L. sensitivity sin2 213 ∼ 0.006 (=0) will be reached: a factor 20 better than the current limit set by Chooz, as shown in Fig. 15. T2K will also measure m223 and |sin2 223 | with a ∼ 2% precision via disappearance. A possible machine upgrade to 4 MW (JHF-II), in conjunction the new Hyper-Kamiokande detector (0.54 Mt fiducial mass) will allow to investigate sin2 213 below 10−3 and the leptonic CP violation if || > 20◦ and sin2 213 ∼ 0.01 (2 years of and 6 years of operations [60]). The NOA experiment using an upgraded NuMI Off-Axis neutrino beam (E ∼ 2 GeV with a e contamination less than 0.5%) at a baseline of 810 km (12 km Off-Axis), was recently proposed at FNAL. The aim is to explore the → e oscillations with a sensitivity more than 10 times better than the MINOS experiment using a 30 kt liquid scintillator far
M. Bonesini, A. Guglielmi / Physics Reports 433 (2006) 65 – 126
Eν (GeV)
15
81
θ=0 mrad θ=7 mrad θ=14 mrad θ=27 mrad
10
5
0 10
0
30
20
40
Eπ (GeV) Fig. 13. Neutrino energy versus the pion parent energy for different Off-Axis angle .
400 350
νµ NCC (/100MeV/22.5kt/yr)
ON AXIS 300
OA20
250 200 OA30 150 100 50 0 0
1
2
3
4
5
Eν (GeV) Fig. 14. T2K neutrino beam energy spectrum for different Off-Axis angles at J-PARC.
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10-1
2 (eV2) ∆m23
10-2 Chooz excluded 2.5
T2K
10-3
ICA
RU
PS
++
10-4 10-3
10-2
SC
NG
SL
.E.
10-1
1
sin22θ13 Fig. 15. Expected sensitivity on 13 mixing angle (CP violation and matter effects not included) for a 20 GeV high intensity PS proton beam from CERN to Gran Sasso (PS++) and for the CNGS-L.E. neutrino beam compared to T2K experiment.
detector [61]. The NuMI target will receive a 120 GeV proton flux with an expected intensity of 6.5 × 1020 pot/yr. As a second phase, a new proton driver of 8 GeV and 2 MW, could increase the NuMI beam intensity to 17.2–25.2 × 1020 pot/yr, improving the experimental sensitivity by a factor two. At BNL an upgrade to 1 MW has been proposed for the existing AGS 28 GeV PS to produce a neutrino SuperBeam with E 1.5 GeV [62]. A megaton water Cherenkov detector at a baseline of 2540 km would allow the observation of the second oscillation maximum. By comparing disappearance and e appearance at the first and second oscillation maximum a better control of degeneracies could be obtained, measuring sin2 213 down to 0.003 ( = 0) in a 5 years period. Different approaches have been considered for new neutrino long-baseline experiments in Europe after the end of the present CNGS appearance programme, by improving existing infrastructures and detectors or considering new neutrino beams and detectors. A systematic study of the experimental sensitivity on sin2 213 as a function of the proton driver energy Ep and its power was performed in [63]. In this calculation the optimal base-line distance L∗ was selected in the 130.800 km range according to E /L∗ ∝ m223 ∼ 2.5 × 10−3 eV2 . In terms of proton economics, the optimum beam energy Ep 20 GeV was obtained, by minimizing the required driver power factor W = Ep × p.o.t, to reach a selected 13 sensitivity beyond the Chooz limit. This gives a beam with E 1.6 GeV well matched to a 732 km of baseline (i.e. CERN—Gran Sasso). A slightly better sensitivity than the one foreseen in T2K, sin2 213 0.005 at 90 % C.L., can be reached in a 5 years exposure of a 3.8 kt fiducial mass ICARUS-like liquid Argon detector ( = 0 and no matter effects) with a 4 MW proton driver and a useful beam time operation of 107 s/yr (see PS ++ line in Fig. 15). The possibility to improve the CERN to Gran Sasso neutrino beam performances for 13 searches even with the present SPS proton beam (Ep = 400 GeV and 4.5 × 1019 p.o.t/yr) was investigated (CNGS-L.E.) [64] (Fig. 16). The low energy neutrino flux can be increased by a factor 5 with respect to the current CNGS beam by an appropriate optimization of the target and of the focusing system. Results are shown in Fig. 15 for a 2.35 kt ICARUS-like detector. In addition, the use of a 1.5 GeV low energy Off-Axis neutrino beam from CERN to the Gulf of Taranto at 1200 km of distance has been considered [152]. As an alternative, the CERN-SPL SuperBeam (SPL-SB) [46,65,66] based on a 4MW SPL was investigated. The intense + ( − ) beam focused by a magnetic horn in a short decay tunnel will produce an intense beam mainly via
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400 GeV proton beam
83
400 GeV proton beam 10-15 v flux
v flux full CNGS L.E. dashed CNGS τ
10-16 v/cm2 / GeV/p.o.t
v/cm2 / GeV/p.o.t
10-14
full CNGS L.E. dashed CNGS τ
10-15
10-17
10-18 10-16
10-19 0
10
20
30
40 50 60 Ev (GeV)
70
80
90 100
0
10
20
30
40 50 60 Ev (GeV)
70
80
90 100
Fig. 16. The CERN low energy neutrino beams (CNGS L.E.), as compared to the current CNGS option (CNGS ).
Table 6 Some future LBL options with L/E matching m223 = 2.5 × 10−3 eV2
p-driver (MW) Ep (GeV) E() (GeV) L (km) Off-Axis beam CC no osc. (1/kt/yr) contamination (%) Detector sin2 213 × 104 (90% C.L.)
T2K
J-Parc II
NOA
PS ++
SPL-SB
B
0.75 50 0.7 295 2◦ 100 0.4 22.5 kt CH 60
4 50 0.7 295 2◦ 500 0.4 540 kt CH 6
0.8 (2) 120 2 810 0.8◦ 80 (200) 0.5 30 kt LS 38 (24)
4 20 1.6 732 – 450 1.2 3.8 kt LAr 50
4 2.2 0.27 130 – 37 0.4 440 kt CH 18
0.4 1−2.2 0.3 130 – 38 0 440 kt CH 7
All the experiments are normalized to 5 years data taking, 107 s/yr beam time operations. The J-Parc II sin2 213 sensitivity is extrapolated from T2K. Numbers quoted for NOA refer to the standard and the proton driver options (see text). The B column is computed for the = 60, 100 CC option; the CC of B indicates the CC e + e rate. Detectors are water Cherenkov (CH), LAr (liquid argon), LS (liquid scintillator) with their fiducial mass.
the -decay, providing a flux ∼ 3.6 × 1011 /yr/m2 at 130 km of distance with an average energy of 0.27 GeV (see Fig. 12). The e / ∼ 0.4% contamination, exclusively from the + → + → e+ decay chain being the K contribution suppressed by threshold effects, will be known with an error less than 2%. The use of two detectors (the far detector at L = 130 km of distance in the Frejus area) will allow for both -disappearance and → e appearance studies. The physics potential with a 440 kt fiducial mass water Cherenkov (having fixed m223 = 2.5 × 10−3 eV2 ) was extensively studied [66]. The 90% C.L. sensitivity on sin2 213 is 0.002 ( = 0, 5 years beam, see Table 6), with a 3 CP violation discovery potential (2 years with beam and 8 years with the reversed polarity beam) for > 40◦ and sin2 213 > 0.02. The performance could be improved by rising the proton energy to 3.5 GeV [67], to produce more copious secondary mesons and to focus them more efficiently into a 40 m long and 4 m diameter decay tunnel, using new status of the art RF cavities [68]. Neutrino fluxes are increased up to a factor 3, at the expense of doubling the e contamination.
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The SPL can be used as injector for a BetaBeam, requiring at most 10% of its protons, allowing a simultaneous B and SPL-SB exploitation, the two neutrino beams having similar neutrino energies (see also Fig. 12). The same detector at 130 km of distance could then be exposed to 2 × 2 beams ( and × e and e ) searching for CP, T and CPT violation in the same run. A 90% C.L. sensitivity to sin2 213 35 times better than T2K and a 3 sensitivity to CP violation if ||18◦ and 13 0.55◦ can be reached [55]. In Table 6 the features of some options for the next generation of SuperBeams and of BetaBeams are reported, rescaling the maximum source power at 4 MW and the useful time machine to 107 s/yr (see also Refs. [69]). For an appropriate choice of the L/E well matched to the m223 value, the figure of merit of the neutrino beam is determined by the -CC/kt/yr event rate and also by the e / natural beam contamination. 4. A review of hadroproduction data Existing hadroproduction data, useful for neutrino beams simulations, come mainly from old, non-dedicated experiments realized with single-arm magnetic spectrometer in the sixties. Open geometry experiments, with full angular coverage, were an exception. Single arm experiments (SAS) have inherently more systematic uncertainties than open geometry experiments (OG), as they must change the geometry of the single arm spectrometer frequently to scan the phase space and thus introduce acceptance uncertainties, even if they can benefit from reduced material along the particle path compared to the OG massive detectors. While open geometry experiments sample the phase space continuously, single arm data are sparse and cover discrete pT bins. These old experiments suffer from limited statistics and high systematics, often amounting to a 30% error on the quoted cross-section. Following the dedicated NA56/SPY experiment at CERN, new hadroproduction experiments have now been proposed or realized both at CERN and FERMILAB (HARP/PS214, P322, MIPP/E907). 4.1. Main characteristics of hadron production reactions At high energies, in fixed target experiments, 80–90% of the total cross-section consists of a great variety of manybody or multiparticle inelastic channels, with a lot of particles produced in the final state. A comparatively small fraction of the available incident energy goes into making new particles. Approximately the charged multiplicity is given by Nch = a log(s) + b, (10) √ where a =2, b =4 and s is the total energy in the center-of-momentum frame (if all available energy went into particle production a power law Nch = s 1/2 would be obtained). Most of the incident energy emerges as kinetic energy of the outgoing particles. While their longitudinal momentum component, pL , covers a wide range, the transverse momentum is quite small: on average pT 0.3 − 0.4 GeV/c, with an exponential decreasing cross-section d /dpT ∼ e−6×pT , where pT is in GeV/c. Of course, the quantity Nch is just one of the parameters describing multiparticle production. What types of particles are produced is the next consideration of interest. In general, summing over all inelastic channels, most of the produced particles are pions (of order 80–90%) followed, in order, by nucleons, K + , K − , p, . . . . The relative production rates can vary substantially in different kinematic regions. Inclusive processes of the type a + b → c + X, where c is the observed particle, can be described by three independent variables such as s, pL , pT (where pL , pT refer to particle c), giving an invariant cross-section: E
d2 d 3 p Ec = . dpL dpT2 dpc3
(11)
Feynman suggested for inclusive processes [70] an approximate scaling behavior of the single-particle inclusive invariant cross-section when expressed in terms of the transverse momentum (pT ) and of the longitudinal variable √ √ xF = 2pL∗ / s, where pL∗ and s are the particle longitudinal momentum and total energy in the center-of-momentum frame. A factorization in xF and pT of the invariant cross-section is only approximately supported by more recent data. ∗ , defined as the ratio of the particle energy in the center-of-momentum The alternative scaling variable xR = E ∗ /Emax frame to the maximum possible particle energy, was suggested by Yen [71] and Taylor et al. [72] and shown to greatly extend the range of validity of scaling at sub-asymptotic energies.
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4.2. Requirements on hadroproduction data for the study of conventional beams The study and simulation of beams can be approximately divided into two steps: the generation of primary mesons (decaying to ’s) in proton–target interactions and the subsequent transport and re-interaction of produced secondaries along the beamline (horns, reflectors, collimators, decay tunnel) giving additional neutrinos. The two steps can be decoupled and different techniques used for the two stages. A good knowledge of hadroproduction cross-sections is needed especially for the first step. We will try to illustrate what kind of data are useful taking into account , K kinematics for conventional beam production. Conventional neutrino beams are mainly produced via their parent decays: ± → ± + ( ),
(12)
K ± → ± + ( ).
(13)
Pion (kaon) decay is a two-body decay of a spinless particle and is therefore isotropic in the parent rest frame. Simple kinematical considerations give for the decay neutrinos: 1 dN = , d cos 2((1 − cos ))2 E =
m2 (K) − m2 E (K) , m2 (K) 1 + 2 2
(14)
(15)
where is the Lorentz boost of the parent meson, E (K) its parent energy and the neutrino angle with respect to the meson flight direction. Moreover in the laboratory frame: Emax 0.41p (for → ),
(16)
Emax pK (for K → ).
(17)
Neglecting focussing, the angular divergence of the neutrino beam is due to the intrinsic neutrino transverse momentum (pT = E · sin 30 MeV/c for → decay and 236 MeV/c for K + → + decay) and the additional pT of the parent meson in the production process (∼ 300 MeV/c). The neutrino flux to the detector per decay parent hadron is given by =
2 (1 + 2 2 )2
,
(18)
1 of the flux in the pion direction. As the boost factor in Eq. (18) gives a strongly where, without focusing, is only ∼ 25 peaked forward flux, that shrinks as 1/2 , the most relevant hadroproduction data are the yields or cross-sections for both ± and K ± in the forward direction in a momentum region up to 2.4 · Emax for pions and Emax for kaons. In addition, some angular scans around = 0◦ are highly desirable due to the finite beamline angular acceptance ( 10.20 mrad). As can be seen from Table 2 data on strange particle production (KS0 , ) in the same kinematical range are also needed. As an example, about 15% of the e background in a beam, such as the WANF at CERN, is due to KL0 decays. In the framework of a simple quark parton model, K ± and KS0 (KL0 ) production can be related. Assuming isospin symmetry and neglecting the momentum dependence N (KS0 ) = N (KL0 ) = 41 (NK + + 3NK − ), but clearly direct measurements are highly desirable. In the following only hadroproduction experiments relevant to neutrino beam studies will be considered.
4.2.1. A side remark about low energy beam dump and Neutrino Factory beams From the previous considerations, the most relevant data for the simulation of both low energy beam dump beams and neutrino factory beams are pion production cross-sections at low or very low energy. For low energy beam dump beamlines, where incoming proton beams have pinc ∼ 800 MeV/c, some useful data are shown in Table 7. Both experiments were performed with single arm spectrometer, where particle identification (discrimination of pions
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Table 7 Experiments studying particle production at very low energy, useful for beam simulation in beam dump experiments Experiment
pinc (MeV/c)
Target
Crawford et al. [73]
585
1 H2 ,
Cochran et al. [74]
730
H, Be, C, O, Al, Ni, Cu, Mo, Pb H, D, Be, Al, Ti, Cu, Ag, Ta, Pb, Th
Polar angle coverage
= 22.5◦ , 45◦ , 60◦ , 90◦ , 135◦ = 15◦ , 20◦ , 30◦ , 45◦ , 60◦ , 75◦ , 90◦ , 105◦ , 120◦ , 135◦ , 150◦
Table 8 Experiments studying particle production at low energy, useful for beam parameterization Experiment
pinc (GeV/c)
Target
Polar angle coverage
Lundy et al. [75] Dekkers et al. [76] Baker et al. [77] Fitch et al. [78] Allaby et al. [79] Eichten et al. [80] Cho et al. [81] Asbury et al. [82] Marmer et al. [83] Vorontzsov et al. [84] Abbott et al. [85] E910 Coll. [86] HARP Coll. [51]
13.4 8.65, 11.8, 18.8, 23.1 10.9, 20.9, 30.9 30, 33 19.2 24 12.4 12.5 12.3 10.1 14.6 6.4, 12.3, 17.5 1.5–15
Be Be, Pb, H2 Be, Al Be, Al p, B4 C, Be, Al, Cu, Pb Be, B4 C, Al, Cu, Pb Be Be Be, Cu Be, Al, Cu, Ta Be, Al, Cu, Au Be, Cu, Au, Pb, U Be, C, Al, Sn, Ta, Pb, N, O, H, H2 O
2.16◦ 0◦ , 5.7◦ ∼ 5◦ , 9◦ , 13◦ , 20◦ ∼ 14◦ , 45◦ , 90◦ ∼ 13◦ , 45◦ , 90◦ ∼ 1◦ , ∼ 3.3◦ , 5◦ , 7.3◦ 0.12◦ 12◦ , 15◦ 0◦ , 5◦ , 10◦ 3.5◦ 5.58◦ OG OG
against protons or muons and electrons) was achieved mainly with time-of-flight (TOF) techniques. The differential cross-sections d3 /d dE were measured with a total error around 10%. Data needed for neutrino factory simulations are discussed in the next section. 4.3. Low energy hadroproduction experiments Experiments at low energy (see Table 8) were performed mainly with single arm magnetic spectrometers, with some kind of particle identification as Cherenkov counters or TOF detectors. The uncertainty on particle yield is dominated by the systematic error on the calculation of the beamline acceptance. These experiments suffer from large systematic errors and low statistics. As an example the relative normalization of the Lundy et al. [75] experiment and the Dekkers et al. [76] experiment differ by more than 50%. In addition two other experiments have been performed with a large set of nuclear targets. In the experiment of Allaby et al. [79] a 19.2 GeV/c proton beam impinged on p, B4 C, Be, Al, Cu, Pb targets, while in the experiment of Eichten et al. [80] a 24 GeV/c proton beam was hitting Be, B4 C, Al, Cu, Pb targets. Additional data have also been obtained by heavy-ions experiments, such as the E802 [85] and the E910 [86] experiments at BNL. These experiments studied p-nucleus reactions in addition to nucleus–nucleus reactions to understand the systematics related to the underlying processes. The E802 experiment at BNL studied 14.6 GeV/c protons on thin Be, Al, Cu and Au targets, obtaining an overall normalization error as good as 10–15% on cross-section measurements. The E910 experiment at BNL has recently published data from 12.3 and 17.5 GeV/c protons on Be, Cu and Au targets, using an open geometry apparatus at the MPS facility at BNL. About 2.6 × 106 , 0.6 × 106 , 104 events have been recorded at 17.6, 12.3 and 6.4 GeV/c, with a low bias trigger. The experiment used a spectrometer with a good acceptance and particle identification over the region of interest for low energy neutrino beams, such as MiniBooNE. However, the small data statistics collected, especially at 6.4 GeV/c (a feature common to most heavy-ions experiments), and the lack of thick targets sensibly reduced its prospective impact. The HARP experiment has concluded its data-taking on a variety of targets, with an open geometry apparatus and redundant particle identification capabilities. It is providing hadroproduction data at low energy, with the lowest systematic errors. Some available results are reported in Section 8.
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Table 9 Experiments studying charged particle production, at medium and high energy, useful for beam parameterization Experiment
pinc (GeV/c)
Target
Geometry
Bozhko et al. [87] Barton et al. [88] MIPP/E907 [89] NA20 [90] NA56/SPY [91]
67 100 5–120 400 450
Be, Al, Cu C, Al, Cu, Ag, Pb Be, C, Cu, N, O, Pb Be Be
SAS SAS OG SAS SAS
1.2
NA56/SPY (450 GeV/c) NA20 (400 GeV/c) Barton et al. (100 GeV/c) Bozhko et al. (67 GeV/c)
1
pT (GeV/c)
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
xF Fig. 17. Coverage in the pT vs. xF plane for published single arm experiments at medium or high energy, studying charged particle production.
4.4. High energy hadroproduction experiments The relevant experiments on nuclear targets are listed in Table 9. Fig. 17 shows the coverage in the pT vs. xF plane of the experiments already performed at higher energies. In this energy range the experiment of Barton et al. [88] has studied inclusive ± , K ± , p, p production in 100 GeV/c + , K + , p collisions with C, Al, Cu, Ag, Pb targets using the M6E single-arm spectrometer at Fermilab. The experiment was a continuation of an extensive study of particle production in hadron–nucleus interactions [92]. The production of secondaries was measured over the kinematical range 0.3 xF 0.88 and 0.18 pT 0.5 GeV/c. Good charged , K and p separation in the full kinematics range was achieved using Cherenkov counters. Data were mainly taken with thick targets, while thin targets were used primarily for finite thickness corrections. The main aim of the experiment was the study of the target dependence of the secondary spectra.
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TOF1
B0
B1
TOF2 V
V
C0
C1
TOF3
B2
TOF4
TOF5
V
CEDAR
C2
p
Calorimeter Target
W1T
144m
W2T
W2S
82m
W3S
141m
W3T
78m
W4T
W5T
79m
524m Fig. 18. The NA56/SPY experimental setup. The main detectors for particle identification are the time of flight detectors (TOF1, . . ., TOF5), the Cherenkov detectors (C0–C1, CEDAR) and the calorimeter.
At higher energies, the two main experiments of interest are the NA20 experiment [90] and the recent NA56/SPY [91] experiment. In addition, the experiment of Skubic et al. [93] has studied strange particle production with Be, Cu, Pb targets at 300 GeV/c and the experiment of Edwards et al. [94] KS0 production in the forward direction from 200 GeV/c p–Be interactions. Both these experiments, however, covered a region xF > 0.25, which overlaps only partially the momentum region relevant for neutrino beams. The NA20 experiment used the H2 beamline at the CERN SPS and took data with 400 GeV/c protons on Be targets, with secondary momenta down to 60 GeV/c covering the pT range between 0 and 500 MeV/c and the xF range 0.15–0.75. Absolute fluxes were counted with four scintillator counters and the beam composition with N-type CEDAR differential Cherenkov counters [95], giving a good particle identification in the region 60–300 GeV/c. Data with 100, 300, 500 mm long Beryllium targets were taken. The NA56/SPY with 450 GeV/c incoming protons on Be has instead covered the complementary range down to 7 GeV/c. The critical points for such kind of experiments are: • the accurate simulation of the beamline, to obtain systematic errors at the 5–10% level on cross-sections evaluation; • a good determination of the incoming proton flux, to limit the systematics to the 1–2% level; • a good particle identification (PID) to separate the different outgoing particle (mainly , K). 4.4.1. A case study: the NA56/SPY experiment The NA56/SPY (secondary particle yield) experiment [91] measured the production rates of charged secondary particles ( ± , K ± , p, p) in the range 7–135 GeV/c (0.02 xF 0.30) and up to transverse momenta of 600 MeV/c in p–Be interactions at 450 GeV/c. The experiment was performed with the NA52 spectrometer [96] in the H6 SPS beamline in the North Area at CERN (see Fig. 18). The beamline was operated to transport secondary charged particles in the range 5p 200 GeV/c, within a maximum acceptance of (p/p) × = ±1.5% × 2.1 sr, defined by a set of three collimators. The beam was derived from the T4 target station served by a primary proton beam of 450 GeV/c, with typical intensities of several 1012 protons per burst. Data were collected in the secondary momentum range of 7–135, GeV/c with angular scans at fixed momenta (15 and 40 GeV/c). ˘ C2 ˘ Redundant particle identification was provided by a set of time of flight detectors (TOF1–TOF5), threshold C0. and differential (CEDAR) Cherenkov counters along the beamline and a hadron calorimeter at its end. TOF1–TOF5 scintillator hodoscopes provided the measurement of particle speed and, with an intrinsic time resolution of 100 ps or better, allowed K/p separation up to 20 GeV/c. Two Cherenkov counters (C0 and C1) were filled with N2 gas and provided /K separation up to 20 GeV/c and K/p separation above 20 GeV/c. A third Cherenkov counter (C2), filled with He gas, allowed e, rejection at 15 and 20 GeV/c and provided /K separation above 20 GeV/c. The hadron calorimeter, consisting of five uranium/scintillator modules at the end of the spectrometer, allowed an effective separation of hadrons from electrons and muons. A set of proportional chambers (WnT (n = 1, 5), WmS (m = 2, 3)) was used for particle tracking along the spectrometer.
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The trigger was based on two independent signals formed at 268 m (trigger A = TOF2 · B1) and 505 m (trigger B = TOF4 · B2) downstream of the target. At low secondary momenta (7 and 10 GeV/c), trigger A alone had been required in order to increase the detection efficiency of kaons which decay before reaching the end of the spectrometer. At higher momenta both trigger A and B were required. A veto on the Cherenkov counter signals from ’s had been included in the trigger on every other event readout in order to get a sample of triggers from particles heavier than pions, that was enriched in K content. The flux (p flux for momenta 10 GeV/c) and the p/ and K/p production ratios were separately extracted from the unbiased sample or the heavy particle enriched sample, while the ratio K/ and the other fluxes were derived quantities. This approach minimized possible bias related to different experimental configurations between light and heavy particles. Data were collected with targets made of beryllium plates of different length (100, 200, 300 mm), 2 mm high and 160 mm wide. Additional data were also taken with a target (T9-like) of three Be rods of 100 mm length and 3 mm diameter interleaved by 90 mm of air, similar in structure to the one used in the WANF at CERN [31]. The absolute intensity of the primary beam on the target was measured by Secondary Emission Monitors [97], with an accuracy of better than 2%. To derive particle yields, data were corrected for trigger and data acquisition efficiencies, particle decays in flight, strange particle decays outside the target and contributions from interactions of the primary beam with material around the target area. The uncertainty on the particle yield evaluation was dominated by the systematic error on the calculation of the H6 beamline acceptance. This is given by the product of a phase-space acceptance ( · (p/p)), defined by the apertures of three collimators, and a transmission coefficient T, which accounts for particle losses along the beamline. The transmission coefficient T was computed in the first part of the beamline (up to B1) with an improved version of the TURTLE Monte Carlo simulation [98], which includes multiple scattering and secondary interactions. Dedicated proton runs had been used to cross-check the Monte Carlo calculation and to measure the beamline transmission downstream of B1. The global systematic error on the acceptance is 5–10% depending on beam momentum and is dominated by beamline transmission at low momenta and by the accuracy of collimators settings at high momenta. Results in the forward direction for the 100 mm plate beryllium target are shown in Fig. 19. The results of Atherton et al. [90] for the same xF as NA56/SPY data are reported. In the measurement of same sign particle production ratios the uncertainties related to the acceptance definition (magnet strengths, collimators openings, etc.) cancel, and only the particle dependence of the transmission along the beamline has to be accounted for. The systematic contribution coming from this correction on the measurement of particle production ratios is of the order of 1%, due to uncertainties on the amount of material along the beamline and on the nuclear cross-sections. As an example, the measured production ratios for the 100 mm plate beryllium target in the forward direction are reported in Fig. 20. Error bars account for systematic and statistical errors added in quadrature (the total uncertainty is ∼ 3%). In addition, results for particle yields and particle ratios as a function of pT (up to 600 MeV/c) were also obtained. The target thickness dependence, to correct the measured yields of the 100 mm target for its finite length and to extract the invariant cross-section, was obtained directly from experimental data at various target lengths. In this way, the invariant cross-sections for p–Be interactions at 450 GeV/c have been derived in the forward direction in a model independent way. Results are shown in Fig. 21 and extend to higher energies the studies on p–A interactions at 24 GeV/c by Eichten et al. [80] and at 100 GeV/c by Barton et al. [88]. Systematic errors include the ones on the measured particle yields and the method to correct for the target thickness.
5. Existing parameterizations of hadroproduction data Parameterizations of the available hadroproduction data have been presented in the literature at low-energy (pinc 30 GeV/c), e.g. the Sanford–Wang [99] parametrization, and at high energy, e.g. the Atherton et al. [90], the Malensek [100] and the BMPT [101] parameterizations. One of the goals of these parameterization is to adopt a simple functional form for inclusive particle production which will be suitable for extrapolation to different centre of mass energies and/or secondary particle momenta. In addition the possibility to extend the scope to different targets (e.g from Be to C) can be useful. The main aspects of them will be reviewed in the following, including the range of their applicability.
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10
particles/ (incident protons sr (∆p/p%))
particles/ (incident protons sr (∆p/p%))
10
1
10-1 π+ π-
K+ K-
π+ π-
K+ K-
10-2
1
10-1
10-2 p
p
p
p
10-3 0
50
100 p (GeV/c)
150
0
50
100
150
p (GeV/c)
Fig. 19. Particle yields in the forward direction for the 100 mm Be target, as a function of momentum.
5.1. Low energy parameterizations Several empirical formulae for particle production at low energy have been proposed, e.g. by Cocconi, Koester and Perkins (CKP) [102], Trilling [103] and Ranft [104]. All formulae give a fairly qualitative description of experimental data between 10 and 30 GeV/c and often are not suitable for general purposes (parameter values depend on the incident particle energy). The CKP formula consists in a semi-phenomenological parameterization of the production spectrum, fitted on available data. A simple modification of the CKP formula, used for the study of high energy beams at the Serpukhov accelerator, is given in Ref. [105]: √ d2 N 2 2 2 = AE2 e−E/T e−( m +E /B) , d dE
(19)
where E, are the energy and production angle of secondaries and A, B, T are parameters determined by a fit to the experimental data. A more general parameterization for ± , K ± , p production in p–Be collisions, based on an empirical description of the data rather than a physical approach, has been proposed by Sanford and Wang [99] (S–W). The pion production cross-sections are parametrized as C5 C8 d2 N C4 = f ( = 0) × g() = [C1 p C2 (1 − p/pinc )e−(C3 p /pinc ) ][e−C6 (p−C7 pinc (cos ) ], d dp
(20)
combining a forward production term f (=0), with a term g() giving the angular dependence, where p is the secondary momentum, pinc the incident proton momentum and the production angle. The parameters Ci (i =1, . . . , 8) have been determined by a least square fit to the first four data entries of Table 8 and are shown in Table 10. All the experiments
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K/π
0.1 0.075 0.05 0.025
p/π
0.6
0.4
0.2
4
K/p
NA56/SPY Atherton et al.
3 2 1
0
20
40
60
80 p (GeV/c)
100
120
140
Fig. 20. Particle production ratios for the 100 mm Be target, in the forward direction, as function of momentum. Open (full) dots refer to negative (positive) particles.
considered there were performed with a single arm spectrometer. The experiment of Baker et al. and of Fitch et al. used an internal target, for which relatively large errors (∼ 20%) had to be assigned to the experimental data to account for effects such the AGS fringe field, etc. A comparison of the S–W parametrization with some available low energy − data is shown in Fig. 22. The main problems in the derivation of the Sanford–Wang formula are connected with the relatively small amount of experimental data available (in particular to cover the angular dependence) and the fact that it was necessary to combine different experiments with uncertainties in their relative normalizations. For example, the data of Lundy et al. [75] (used to obtain the angular dependence shape) were renormalized to the data of Dekkers et al. [76] with a normalization factor 1.5. Table 11 (from Ref. [104]) provides a direct check of the S–W formula by comparing the measured and predicted pion multiplicity N , defined as N =
pinc
2
0
0
d2 N sin d dp. d dp
(21)
The S–W parameterization has been initially applied to model the low energy K2K neutrino beam with some modifications to the original Ci parameter values to take into account the Cho et al. [81] data (see Table 17 for details). The HARP experiment data taken with a thin Al target at 12.9 GeV/c and a thin Be target at 8.9 GeV/c are currently being parametrized in terms of a Sanford–Wang fit, see Section 8 for more details. These results will be of relevance for the understanding of the K2K and MiniBooNE beams.
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102
p p-
102
E d3 σ/dp3 (mb/GeV2)
E d3 σ/dp3 (mb/GeV2)
π+ πK+ K-
10
10
1 0
50
100
150
0
50
p (GeV/c)
100
150
p (GeV/c)
Fig. 21. Inclusive invariant cross-section as a function of secondary momentum for p–Be interactions at 450 GeV/c in the forward direction.
Table 10 Original values of the parameters corresponding to the empirical parameterization of ± , K ± and p inclusive production in p–Be interactions, in the Sanford–Wang formula
+ −
K+ K− p
C1
C2
C3
C4
C5
C6
C7
C8
1.092 0.821 0.05897 0.02210 0.001426
0.6458 0.5271 0.6916 1.323 1.994
4.066 3.956 3.744 9.671 9.320
1.625 1.731 4.520 1.712 1.672
1.656 1.617 4.190 1.643 1.480
5.029 4.735 4.928 4.673 4.461
0.1722 0.1984 0.1922 0.1686 0.2026
82.65 88.75 50.28 77.27 78.00
Proton data, which are of less direct interest for neutrino beams, have been parametrized also by Wang [106] with a formula similar to the previous one for p–Be interactions: E E C G d2 N = f ( = 0) × g() = [Ap inc eB(p/pinc ) ][e−D (p −F (cos ) ](1 − p/pinc )H p/pinc , d dp
(22)
where pinc and p are incident and secondary momentum in GeV/c and is the production angle. While the longitudinal momentum distribution is consistent with the linear scaling of pions (Eq. (20)), the angular dependence has a more complicated form. With a least square fit to the experimental data of Table 8 and additional data from Allaby et al. [79], Baker et al. [107], Aubert et al. [108], Anderson et al. [109] and Bellettini et al. [110], the parameters of the formula have been determined as A = 1.30, B = 5.354, C = 0.6324, D = 3.508, E = 1.15, F = 4.129, G = 37.34, H = 20.27. The formula is claimed by the author to give a good representation of p–Be data up to 300 GeV/c.
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Fig. 22. − production as a function of psec at 10.9 GeV/c. The Sanford–Wang parameterization, described in the text, is superimposed (from Ref. [99]). Table 11 Comparison of measured and predicted pion multiplicities, N + + N − pinc (GeV/c)
Data
S–W formula
Trilling formula
10 15 20 25 30
1.9–2.3 2.5
1.84 2.19 2.56 3.01 3.55
0.72 0.85 0.95 1.04 1.12
2.9–3.7
5.2. High energy parameterizations Original parameterizations of high energy data from Atherton et al. [90] and Malensek [100] were based only on NA20 data and thus are unable to describe the behavior of the low x data of the NA56/SPY experiment. An improvement at low x with respect to these models has been obtained in the BMPT parameterization, which is fully described in the following. 5.2.1. Atherton and Malensek parameterizations Atherton et al. [90] parametrized ± , K ± and p production, in the thin target approximation, as B 2Cp 2 −C(p)2 d2 N = A e−Bp/p0 e , dp d p0 2
(23)
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Table 12 Values of the parameters corresponding to the empirical parameterization of ± , K ± and p inclusive production in p–Be interactions, for thin targets from Atherton et al. [90]
+ −
K+ K− p p
A
B
C
1.2 0.8 0.16 0.10 0.8 0.06
9.5 11.5 8.5 13.0 −0.6 16.0
5.0 5.0 3.0 3.5 3.5 3.0
Table 13 Values of the parameters corresponding to the empirical parameterization of ± , K ± and p inclusive production in p–Be interactions, for 500 mm targets, in the Malensek formula [100]
+ −
K+ K− p p
A
B
M2
D
3.598 4.122 2.924 6.107 1.708 7.990
177.2 70.60 14.15 12.33 3.510 5.810
0.7077 0.8932 1.164 1.098 1.043 1.116
27.00 11.29 19.89 17.78 −4.314 14.25
while proton production was described as 2Cp 2 −C(p)2 B +1 d2 N (p/p0 )B . =A e dp d p0 2
(24)
The values of the parameters A, B, C are given in Table 12. The Malensek formula [100] is a fit to NA20 data, taken with a 500 mm long Be target (Table 13): (1 − x)A (1 + 5e−Dx ) d2 N , = Bx dp d (1 + pT2 /M 2 )4 where x = p/pinc with p (pT ) momentum (transverse momentum) of the secondary hadron. The cross-section assumes Feynman scaling in x. The power law dependence pT−8 that holds at large pT is modified to (1 + pT2 /M 2 )−4 to account for the observed variation at low pT . The additional term (1 + 5e−Dx ) accounts empirically for the nuclear cascade process which gives more particles at low x in a thick (500 mm) target. Excluding protons, this correction term is small for most of the x range. The parameters A, B, M 2 , D depend on the type of secondary particle produced and are given in Table 13. The parameterization holds for 400 GeV/c p–Be interactions. For other energies it is sufficient to replace the parameter B in the formula with B × pinc /400. For other target lengths (L), the yield production formula can be adapted by taking into account the target production efficiency f (L). In a naive reabsorption model, where the secondaries are reabsorbed in the target without production of tertiaries, f (L) is given by f (L) =
e−L/s − e−L/p 1 − p /s
with p , s absorption lengths for protons and secondary particles.
(25)
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Table 14 Values of the parameters corresponding to the best-fit of the BMPT empirical parameterization of ± and K ± inclusive production in p–Be interactions
K p p
A (mb/GeV2 )
B
a (GeV−1 )
b (GeV−2 )
r0
r1
62.3 7.74 8.69 5.20
1.57 – 12.3 –
3.45 2.45 – 7.56
0.517 0.444 – 0.362
6.10 5.04 5.77 5.77
– – 1.47 –
0.153 0.121 – –
0.478 2 – –
1.05 1.15 – –
2.65 −3.17 – –
Best-fit results on proton and anti-proton production data are also given (see text for details).
5.2.2. The BMPT parametrization The BMPT [101] empirical parameterization of the inclusive invariant cross-sections for + , K + production in p–Be interactions is given by 3 d − E 3 = A(1 − xR ) (1 + Bx R )xR (1 + a (xR )pT + b (xR )pT2 )e−a (xR )pT . (26) dp
∗ ratio of the particle energy to the maximum energy where a (xR ) = a/xR and b (xR ) = a 2 /2xR , with xR = E ∗ /Emax kinematically available in the cms frame. This formula gives a good description of the data from NA20 and NA56/SPY, assuming an approximate factorized form in x and pT and scaling in x. The (1 − x) behavior at large x is theoretically motivated on the basis of quark counting rules derived from Triple-Regge analysis of single-particle inclusive reactions [111,112], while the (1 + Bx) empirically accounts for sub-leading contributions to the Triple-Regge trajectory. The x − behavior empirically accounts for non-direct hadron formation mechanisms at small x. The pT behavior is modeled with the known exponential fall of soft interactions and a polynomial behavior to interpolate the low pT part of the spectrum. The x dependence of a (x) and b (x) is introduced to parameterize the violation of pT invariance observed in the data. The ratio r of positive to negative data ( + / − or K + /K − ) has been empirically parameterized as
r( ) = r0 · (1 + xR )r1 ,
(27)
r(K) = r0 · (1 − xR )r1 .
(28)
The shape of these ratios is supported by the phenomenological analysis of the pp data from Ref. [113], showing that r( ) 1 for x 0, rising to about 5 for x → 1, closely following the u/d ratio of valence quarks in the projectile proton, while r(K) has a (1 − x)−3 behavior for x → 1. NA56/SPY and NA20 data only cover the fragmentation region of the proton at large x and the central region. At large x a functional behavior similar to the one exhibited by pp data is expected. In order to keep the number of free parameters limited, positive and negative mesons are assumed to have the same pT distributions. This has long been known to be only approximate in pp data [114]. The results of the best fit to the data are summarized in Table 14. Some of the parameters appeared to be redundant and have been fixed in the fitting procedure. As an example, the comparison between the empirical parameterization and the experimental data is shown in Fig. 23 for ± and K ± . The proposed empirical formulae are adequate to describe the NA20 and NA56/SPY data with 10% global accuracy. Proton and anti-proton production data, which are of less direct interest for neutrino beams, have been parameterized as 3 d a2 2 bp2T E 3 1 + ap T + pT e−apT , = A(1 + Bx R )(1 − xR ) (29) 2 dp pBe → pX E
d3 dp 3
pBe → pX
−
= A(1 − xR ) xR
1 + ap T +
a2 2 p 2 T
e−apT .
(30)
For anti-protons a functional similar to the one given in (26) has been adopted, except that an exact factorization in xR and pT has been assumed, since this was sufficient to give a reasonable fit to data. For protons the “leading particle
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Fig. 23. Invariant cross-section as a function of pT : (top-left) positive pions; (top-right) negative pions; (bottom-left) positive kaons; (bottom-right) negative kaons. Data collected at the same xL = p/pinc , where p and pinc are the momenta of the detected particle and of the incident proton in the laboratory reference frame, are displayed with the same symbol. The BMPT parameterization [101] described in the text is superimposed.
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Fig. 24. Comparison between the BMPT parameterization [101] and the one-pion inclusive invariant cross-sections in pC interactions at 100 GeV as measured by [88]. Positive (negative) pions are shown in the left (right) panel.
effect” had to be taken into account. A reasonable fit to data has been obtained by following the empirical observation that the longitudinal momentum distributions of the leading nucleon in pp collisions is flat [115], which translates into a linear rise of the inclusive invariant cross-section as a function of xR . The transverse momentum distribution is also affected by the leading particle effect, resulting in an enhanced leading particle production in the forward direction 2 (see for example [72,114]). In the proton fit, this is empirically accounted for by the term (1 − xR )bpT . The parameter a, that controls the shape of the pT distribution for non-leading particle production, has been assumed to be the same for protons and anti-protons. Results of these fits are also given in Table 14. The BMPT parameterization gives a satisfactory description of proton and anti-proton inclusive production, with a reduced 2 of about 1, in the range covered by NA56/SPY and NA20 data. At larger values of x, diffractive proton production should occur. This is not described by the BMPT parameterization. 5.3. Extrapolation to other energies and target materials The NuMI neutrino beam at FNAL is derived from a primary proton beam of 120 GeV/c momentum, equivalent to a center-of-mass energy about two times smaller than that available at NA56/SPY and NA20. In Fig. 24 the BMT parameterizations (from [101]) are compared to data collected with 100 GeV/c protons on carbon target [88], where the extrapolation from Be to C has been made using formulae (31) and (32) (see later). As discussed ∗ above xR = E ∗ /Emax has been used as scaling variable. The agreement between pion data shown in the figure and the BMPT empirical parameterization is excellent up to about x ∼ 0.8. Good agreement is also found when kaon data are considered, although the precision of kaon data from Ref. [88] is poorer.
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Fig. 25. Dependence of from xF and pT , using the Barton et al. and Skubic et al. experimental data.
At lower energies, the comparison with data measured using 24 GeV/c protons on beryllium [80], shows still a reasonable agreement in the shape of the distributions for + and K + , although the predicted + production is 35 ± 15% lower than that measured. This is also true for negative pions, while the agreement is somewhat worse for the other particles. While beryllium targets have been used in most neutrino beams, graphite targets are employed in both the CNGS and the NuMI beams. Prescriptions to rescale the inclusive invariant cross-sections to different target materials may be obtained. Invariant cross-sections Ed3 hA /dp 3 for hadron–nucleus interactions (hA → h X) depend on the mass number A of the target nucleus, via parameterizations of the type: A1 d3 hA2 d3 hA1 = · E , (31) E A2 dp 3 dp 3 where a value for = 23 would correspond to the case where particle production of a nucleus is identical to the production of a single nucleon per inelastic collision. In accordance with the scaling hypothesis, has been found to depend weakly on the incident beam momentum. It depends on the incident hadron type h and it is a smooth function of pT and xF of the produced hadron. Moreover, it has been experimentally observed that, it is almost independent of the detected particle type, with perhaps the exception of anti-protons [88]. A parameterization of as a function of xF has been proposed by Barton et al. on the basis of their own and previous data at pT = 0.3 GeV/c [88]. A pT dependence of has been clearly observed in KS0 and production by Skubic et al. [93]. A suitable representation of the whole set of data can be obtained with the parameterization: (xF ) = (0.74 − 0.55 · xF + 0.26 · xF2 ) · (0.98 + 0.21 · pT2 ),
(32)
where the xF dependence is taken from the fit of Barton et al. at pT = 0.3 GeV/c and the pT dependence is fitted to the Skubic et al. data and normalized in such a way that it reduces to the parameterization of Barton et al. at pT =0.3 GeV/c, as shown in Fig. 25.
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Table 15 Values of the parameters used in the MARS model for pion production
+ −
a
B
C
D
E
F
60.1 51.2
1.9 2.6
0.18 0.17
0.3 0.3
12 12
2.7 2.7
As a conclusion, a conservative estimate of the uncertainty in the extrapolation from beryllium to carbon data in the pT range of interest for neutrino beams: up to ∼ 600 MeV/c is around 5%, to be added to a measurement error of 5–10% for the cross-sections on beryllium, depending on the secondary momentum. The estimate of this systematic uncertainty is based both on data collected by Barton et al. [88] and on the extensive compilation of J. Kuhn on the nuclear dependence of pA → − X interactions [116]. 5.4. The MARS pion production model Another model used to parameterize pion production in proton–nucleus interactions is the MARS model [117], used in the MARS Monte Carlo code. The proton–nucleus cross-section is parameterized as E
d3 pA → dp 3
±X
= R ± (A, E0 , p, pT ) · E
d3 pp → dp 3
±X
(33)
with E0 primary proton beam energy, p, pT total and transverse pion momentum, A the atomic mass of the target nucleus. R ± is parameterized with the Barton et al. [88] and Eichten et al. [80] data to describe atomic mass dependence and scale pp data to pA data via the formula: d A d (pd → ) (pp → ) R = 2 dp dp ±
(34)
while the pp → ± X cross-section is parametrized as d3 pp → E dp 3
±X
p∗ =a 1− ∗ pmax
B
e−p
∗ /C √s
V1 (pT )V2 (pT ),
(35)
∗ are the pion momentum and maximum momentum transferred in the cms. The pT dependence is where p∗ and pmax described by
V1 (pT ) =
(1 − D)e−EpT + De−FpT
for pT 0.933 GeV/c,
0.2625/(pT2 + 0.87)4
for pT 0.933 GeV/c,
2
2
and V2 (pT ) =
0.7363e0.875pT
for pT 0.35 GeV/c,
1
for pT 0.35 GeV/c.
The values of the parameters a, B, C, D, E, F are listed in Table 15. In two detectors neutrino oscillation experiments, a potential source of systematic errors in the shape of the far detector neutrino spectrum is related to the pT spectrum of the produced particles. As an example, Fig. 26 shows the comparison of + production data from the NA20 and NA56/SPY experiments with the BMPT and MARS parameterization [118]. Fig. 27 (from [119]) shows instead the comparison of the BMPT and the MARS parameterizations with the Eichten et al. + data, at 24 GeV/c.
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102
E d3 σ/dp3 (mb/GeV2)
E d3 σ/dp3 (mb/GeV2)
100
10
102
10
1
1 0
0.1
0.2
0.3 0.4 pT (GeV/c)
0.5
0.6
0.7
0
0.1
0.2
0.3 0.4 pT (GeV/c)
0.5
0.6
Fig. 26. Comparison with available high-energy NA20 and NA56/SPY + data of the BMPT (left) and MARS (right) parameterizations.
Fig. 27. Comparison with the + data of Eichten et al. at 24 GeV/c of the MARS and BMPT parameterizations.
0.7
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101
6. Simulations of neutrino beamlines The calculation of a conventional beam with a Monte Carlo simulation is a delicate task due to complicated cascade processes involved in the neutrino production, from the meson production at the main target, the focusing system and the secondary particle reinteractions along the beam-line materials. Moreover the paucity of the present data on hadroproduction in the relevant region of the phase space can limit systematically the precision in the calculations. For LBL experiments an additional problem is the small solid angle (d 10−10 sr) at the detector location, that forces the simulation of billions of p.o.t’s to achieve a percent statistical accuracy in the results. Two main approaches are used: • fast simulation programs that parameterize production in terms of hadronic cross-sections in the target, make a simplified description of the beamline elements and produce weighted events; • full simulation programs based on the available codes for hadronic showers simulation, such as GEANT, MARS, FLUKA to produce a precise neutrino beam description. 6.1. Fast simulation programs The underlying idea in fast simulation programs is to force all the mesons to decay into a neutrino and to force all neutrinos to cross the detector volume. A weight is then assigned to each neutrino, proportional to the process probability. The fast simulation program, quoted in Ref. [101], to be referred for more details, can be considered as an example. The program is a stand-alone code developed as a tool that allows to optimize all elements and the geometry (in 3-D) of the beamline providing the results in terms of neutrino spectra and distributions at large distance with high statistics and in short time. The statistical accuracy of this way of simulating neutrino beams does not depend much on the distance between the detector position and the neutrino source as is the case for classical unweighted methods. Since all mesons—within the acceptance of the focusing optics—are exploited to produce neutrinos in the detector, the statistical accuracy is proportional to the inverse of the square root of the number of generated positive pions (for beams), namely about the number of generated proton interactions on target. A statistical accuracy of better than a percent is thus obtained with less than 105 p.o.t., for any size of the detector surface. In order to give a more quantitative appreciation of the accuracy that one can obtain in fast simulation of neutrino beams, the comparison with the published neutrino spectra measured by the CHARM II detector [36] exposed at the CERN–WANF beam is presented. The WANF neutrino beamline at CERN, to which the CHARM II detector was exposed, is described elsewhere [31]. The facility was run during several years of operation either by selecting positively charged particles ( beam) or negative ones ( beam). Neutrino/anti-neutrino interactions were collected in the CHARM II detector and fully reconstructed [36]. Fig. 28 shows the agreement between the CHARM II prediction and the fast simulation from Ref. [101]. The high energy tails of the distributions are dominated by the production of high energy secondary mesons peaked in the forward direction, and are practically insensitive to the magnetic focusing. The good agreement between the two simulations indicates that high xF production on target is well simulated and that reinteractions on the material along the beam-line are correctly taken into account. The agreement in the focusing/defocussing energy range is an indication that low xF production is correctly generated at least up to 10 mrad (the WANF angular optics acceptance). The fact that also the wrong sign contamination in the simulation behaves as the data, means that tertiary production in target and downstream material (mainly the horn neck) is described to a sufficient level of approximation. As a conclusion, due to the approximations involved in the modeling of particle re-interactions and transport along the beamline a fast simulation has its main use in the optimization of the neutrino beamline optics and may be of limited use for a full appreciation of beam systematics. 6.2. Full Monte Carlo neutrino beam calculation The precise calculation of a conventional neutrino beam requires the use of full Monte Carlo simulations in order to properly account for all the physical processes involved in the neutrino generation starting from the meson production
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109 v
ν/GeV/1013 p.o.t
ν/GeV/1013 p.o.t
109
108
v
v-
107
50
100 Eν (GeV)
v-
108
107
150
200
50
100
150
200
Eν (GeV)
Fig. 28. The WANF neutrino (left) and anti-neutrino (right) fluxes at the CHARM II detector: the dotted lines are experimental data from Ref. [36], the continuous line is the beam simulation from Ref. [101]. A logarithmic scale is used to highlight the spectral behavior at high energy as well the wrong sign contamination.
at the main target. In long-baseline simulations, different calculation methods are used to recover the effect of the small solid angle seen by the detectors at large distance which dramatically affects the neutrino yield per p.o.t. As an example, in the CNGS beam calculation the mesons are forced to decay in the direction of the detector and the neutrino flux is then properly rescaled. Different programs are used to simulate hadronic and electromagnetic interactions, particle decay and particle transport in complex geometries, providing a detailed evaluation of the neutrino beam characteristics. Of particular interest are the generators of hadronic interactions that are used in K2K, MiniBooNE, CNGS, NuMI and also in testing the performance of new facilities, such as the Neutrino Factory and SuperBeams. An accuracy of ∼ 30% is generally expected in these calculations. In particular, an agreement at the 15% level with the existing data on meson production was found with the FLUKA package [120]. A precision of few percent in the neutrino beam prediction can be obtained by a fine tuning of hadronic generators to the existing data. 6.2.1. The Geant 3.21 and MARS simulation packages The most common simulation package in use is Geant 3.21 [121], which is nearly 30 years old. Its limits are mainly in the simulation of hadronic showers, based on the 1992 release of the FLUKA model (GFLUKA) [122] or of the GHEISHA model [123]. Its main advantage is the use of a simple geometrical modeling of detector shapes and materials. Its development was discontinued about 10 years ago to allow its re-design and re-engineering through modern object oriented techniques, in the form of the GEANT4 package. The comparison of the meson yields in the forward direction as a function of the meson momentum P, as measured with a 450 GeV proton beam on a 100 mm Be target by the NA56/SPY and NA20 (P > 67.5 GeV/c) experiments with the GFLUKA predictions shows large discrepancies, in particular for negative mesons which are largely overestimated (see Fig. 29). In this comparison, the NA20 measurements were corrected for the different primary proton beam momentum (400 GeV/c). The MARS Monte Carlo code [124] has been in continuous development from about 25 years to allow threedimensional simulation of electromagnetic and hadronic cascades in the energy range from a fraction of eV to about 100 TeV. MARS makes use of a quite complicated mixture of parameterization of hadronic cross-sections, phenomenological models and data-driven production models (see for example, the MARS model for pion production described in Section 5.4). Extensive benchmarks for MARS have been reported in several studies [125], spanning a wide energy range from dosimetry applications to muon collider studies. Some examples of its application for neutrino beamline studies will be shown later, in connection with the NuMI beamline (see Figs. 42, 43).
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103
π+/ (p.o.t. *Sr*%)
10
1
10-1
K+/ (p.o.t.*Sr*%)
1
10-1
10-2 50
100
150
200 250 300 p (GeV/c)
350
400
450
50
100
150
200 250 p (GeV/c)
350
400
450
π-/ (p.o.t.*Sr*%)
10
1
10-1
K-/ (p.o.t.*Sr*%)
1
10-1
10-2
300
Fig. 29. Meson yields in the forward direction for 450 protons on a 100 mm Be target. NA56/SPY or NA20 data (•) compared with the FLUKA (◦) and GFLUKA ( ) predictions.
6.2.2. The FLUKA Monte Carlo Hadron–nucleus interactions are described in all FLUKA-based models by a Monte Carlo implementation of the Dual Parton Model code (DPM) [126] which provides a theoretical framework for describing hadron diffractive scattering
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0.2 0.175
K+/π+
0.15 0.125 0.1 0.075 0.05 0.025 0 0.2 0.175
K-/π-
0.15 0.125 0.1 0.075 0.05 0.025 0 0
0.002 0.004 0.006 0.008
0.01
0.012 0.014
θ (rad) Fig. 30. The measured K/ ratios of particle yields at 40 GeV/c as a function of the production angle with respect to he incoming proton beam direction: FLUKA (◦) and GFLUKA ( ) predictions compared to NA56/SPY data (•).
both in hadron–hadron and hadron–nucleus collisions. The DPM model can be extended to hadron–nucleus collisions by making use of the Glauber–Gribov approach [127]. The FLUKA code has undergone a continuous development and its latest version includes an hadronic generator model that has been greatly improved with respect to the 1992 version embedded in GEANT 3.21 (GFLUKA). A comparison of these hadronic generators can be found in Ref. [128]. Modifications were made to the FLUKA implementation of the DPM model along the years in order to achieve a better description of secondary particle yields. Several sets of data ranging from 16 to 450 GeV hadron–nucleon and hadron–nucleus collisions have been used to determine the behavior of the fragmentation functions, using precise experimental data on hadron multiplicity at 200 GeV as the initial constraint. The reinteractions of secondary hadrons as well as the description of nucleon and pion interactions at medium/low energies are also significantly improved in the present version of FLUKA [120]. The FLUKA predictions for proton interactions in 100 mm Be target at 450 GeV/c compared with experimental measurements performed by the NA56/SPY and NA20 Collaborations show a substantial improvement with respect to GFLUKA (see Figs. 29 and 30). The and K absolute yields are reproduced at the ∼ 15% level over the whole secondary momentum range except for a few points mostly for K − (see Figs. 31, 32). The agreement for the corresponding K + / + ratio is at the level of 10% in the momentum region 30.100 GeV/c which is expected to contribute mostly to the high energy neutrino flux (see Fig. 30). Neutrino production by p and p can occur only by successive reinteractions along the beamline. These contributions are expected to be marginal except for the neutrino flavors generated by the defocused sign mesons, i.e. the muon and electron antineutrinos in a muon neutrino beam. A comparison between FLUKA predictions and experimental data for p/p production in a Be target is shown in Fig. 33. 6.2.3. The GEANT4 simulation package The GEANT4 simulation package [129] represents a major effort to re-design and re-engineer the GEANT 3.21 Monte Carlo, using modern object oriented software techniques. Some effort has been put also in upgrading and extending existing hadronic generators. GEANT4 uses mainly parameterized models based on experimental data, such
104
104
103
103
102
102 π-/ (p.o.t.*Sr*%)
π+/ (p.o.t.*Sr*%)
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1
10
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10-2
10-3
105
10-3 0
0.005
0.01 θ (rad)
0.015
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0
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0.01 θ (rad)
0.015
0.02
103
103
102
102
10
10 K-/ (p.o.t.*Sr*%)
K+/ (p.o.t.*Sr*%)
Fig. 31. Pion yields from 100 mm Be target at different momenta P and production angle with respect to the incoming proton beam direction: FLUKA predictions compared with the NA56/SPY (P 40 GeV/c, •) and the NA20 data (P 67.5 GeV/c, •, the difference on the primary proton momentum 400 GeV/c have been accounted for). Both data and Monte Carlo in the 7.337 GeV/c range are rescaled by a common factor different for each momentum value as quoted in the labels, i.e. 67.5 × 15 means that at P = 67.5 GeV/c, the data are rescaled by a factor 15.
1
10-1
1
10-1
10-2
10-2
10-3
10-3
10-4
10-4 0
0.005
0.01 θ (rad)
0.015
0.02
0
0.005
0.01 θ (rad)
0.015
0.02
Fig. 32. Kaon yields from 100 mm Be target at different momenta P and production angle : FLUKA predictions compared with the NA56/SPY, P 40 GeV/c, and the NA20 data, P 67.5 GeV/c, (see Fig. 31 caption for more details).
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104
103
103
102
102
10
pbar/ (p.o.t.*Sr*%)
p/ (p.o.t.*Sr*%)
106
10
1
1
10-1
10-1
10-2
10-2
10-3
10-3
10-4 0
0.005
0.01 θ (rad)
0.015
0.02
0
0.005
0.01 θ (rad)
0.015
0.02
Fig. 33. Proton yields from 100 mm Be target at different momenta P and production angle calculated by FLUKA and compared with the NA56/SPY, P 40 GeV/c, and the NA20 data, P 67.5 GeV/c, (see Fig. 31 caption for more details).
as GHEISHA (also available in Geant 3.21), models based on parton string models for ECMS 5 GeV/c and cascade models (HETC [130], INUCL [131]) for ECMS 5 GeV/c. A major input at low energy (pinc 15 GeV/c) is expected from the HARP experiment. An interesting option is the availability of beam simulation tools that extend the scope of GEANT4 to the accelerator domain and may be useful to optimize the design of Neutrino Factories [132]. 7. Examples of flux computations for present and future neutrino beamlines Some examples of simulation of neutrino beamlines, using either the full simulation approach or the fast simulation approach will be presented. The examples will cover the subject at different level of depth, reflecting also the matureness of the field: from full, detailed simulations for existing experiments (e.g. the WANF for NOMAD) to feasibility studies, as is the case for neutrino factories. The use of different simulations for a neutrino beamline can help in assessing the level of the systematic errors. This is the case of some experiments (e.g. MiniBooNE, K2K) that use both fast simulations based on hadron production data parameterizations and full simulations based on packages, such as FLUKA, Geant4, MARS. Systematic errors influence both the evaluation of the neutrino flux normalization and its shape and composition. 7.1. The CERN WANF neutrino beam: a case study The NOMAD experiment [21] has searched for → and → e oscillations at the CERN SPS [31], using a conventional beam (E 24 GeV) produced by 450 GeV/c protons on a Be target. The → e oscillations were searched for as an excess of e events with respect to what expected from the natural beam contamination: e / ∼ 1% at a distance of 840 m from the Be target. The high resolution and granularity of the NOMAD detector allowed a study of a conventional neutrino beam with unprecedented accuracy and statistics (1 million of -CC events), resulting in a stringent benchmark for conventional neutrino beam studies. A complete analysis of the beam was performed with a full simulation of the beamline from the target up to the NOMAD detector using the FLUKA standalone generator. In comparison, the use of G-FLUKA instead of FLUKA for proton interactions in the beryllium target introduced an enhancement ∼ 15% in the neutrino flux with a relevant increase of the and e contaminations.
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107
To obtain more precise meson production predictions, correction functions to the secondary particle production were introduced for ± , K ± , p and p, based on the residual differences between the predicted (FLUKA) and measured (NA56/SPY and NA20) particle yields in a 100 mm thick target. For a given momentum, both the experimental and Monte Carlo (FLUKA) yields of secondaries were convoluted with the corresponding WANF angular acceptance and then integrated over all production angles (max 10 mrad). The ratio of these two integrals, r(p), was defined as the weight at a given momentum P:
( i Yi · 2 i · · i )DATA
r(p) = , (36) ( j Yj · 2 j · · j )FLUKA where Yi is the particle yield for a selected angle i , = 0.2 mrad is the angular acceptance of the NA56/SPY and NA20 data and i is the efficiency of the transport for the secondaries which contribute to the neutrino flux at NOMAD, as was determined by Monte Carlo from the initial angular distribution dN/di : i =
dN 1 · . di Yi i
(37)
For the momentum values where only the yields in the forward direction ( 0.1 mrad) were measured the weights were simply the ratios of the measured to predicted particle yields. The next step was to fit the obtained set of weights to polynomial functions of the particle momentum for each charged particle, in order to obtain reweighting functions f (p) usable at all momenta (see Fig. 34). Systematic and statistical errors of the experimental measurements were combined in quadrature and included in this reweighting procedure and in the fits. The KL0 yields were obtained from the NA56/SPY and NA20 measurements of K + and K − yields using a “quarkcounting” method KL0 =
K + + (2n − 1)K − , 2n
(38)
where n is the ratio of u to d structure functions of the proton evaluated at xR , the ratio of the kaon energy in the center of mass to its maximum possible energy at its pT . This KL0 parameterization is well described by FLUKA, except for an offset value rp , as a function of the momentum p. It follows that the fK 0 reweighting function is given by (see Fig. 34): fK 0 (p) = [+ (p)fK + (p) + − (p)fK − (p)] · rp ,
(39)
where fK ± (p) are the K ± reweighting functions and the coefficients ± (p) are determined by n and the (K − /K + ) yield ratio: + (p) =
1 , 1 + (2n − 1) · (K − /K + )
(40)
− (p) =
(2n − 1) · (K − /K + ) . 1 + (2n − 1) · (K − /K + )
(41)
To each generated particle emerging from the target the reweighting functions were then applied. The impact of these corrections on the neutrino flux is a reduction of the /pot by 5% but with larger bin-to-bin energy spectrum variation especially for the e / ratio (see Figs. 35 and 36). The comparison of the measured and the predicted neutrino energy spectra with positive focusing shows that the results of the simulations are in good agreement with the data (see Fig. 37). The shape of the CC energy spectrum is predicted to better than 2% up to 150 GeV/c. The only statistically significant difference, of up to 8% but smaller than the estimated systematic uncertainty, is observed in the CC sample. Both the shape and the total number of e CC events are well reproduced, confirming the validity of the adopted KL0 description. Similar agreement was found for neutrino beams with/without focusing, confirming the validity of the beamline simulation and allowing for the possibility to perform a sensitive search for → e oscillations at the WANF. The e energy distributions for data and Monte Carlo from this search are shown in Fig. 38.
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π+
1.4
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
K+
0 0
100
200
300
0
100
200
p (GeV/c) 1.4
300
p (GeV/c) 1.4
π−
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
K−
0 0
100
200
300
0
100
p (GeV/c)
200
300
p (GeV/c)
1.2
Κ0
1 0.8 0.6 0.4 0.2 0 0
50
100
150
200
250
300
350
p (GeV/c) Fig. 34. The reweighting functions f for ± , K ± and K 0 as a function of the meson momentum p. The points are the values of r(p), the curves are the result of fitting them with a polynomial function. Similar curves were obtained for proton production.
The fluxes of the four neutrino flavors at NOMAD were predicted with an overall uncertainty of about 8% for and e , 10% for , and 12% for e (energy-dependent and normalization errors combined), see Table 16 and Figs. 39 and 40 for more details [31], [133]. Major contributions to these uncertainties were from secondary particle production at the beryllium target, proton beam positioning on the target and particle reinteractions along the beamline. Most of these uncertainties canceled in the e / ratio resulting in an energy-dependent uncertainty from 4% to 7% and a normalization uncertainty of 4.2%. These uncertainties are essentially due to the limited amount of hadroproduction data available from the NA56/SPY and NA20 experiments and to the angular integration procedure adopted in the calculation of the meson production reweighting functions.
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106
104 νµ (a.u.)
νµ (a.u.)
105 103
104 102 103 50
100 E (GeV)
150
200
50
100 E (GeV)
150
200
50
100 E (GeV)
150
200
103 103
νe (a.u.)
νe (a.u.)
102 102
10
10
1
1 50
100 E (GeV)
150
200
Fig. 35. MC comparison of fluxes at WANF with (full line) and without (dashed line) correction functions f to the meson production in Be target.
7.2. Simulation of the K2K beamline The K2K neutrino beam (E 1.3 GeV) is produced by pion decay in flight ( + → + ) using 12.9 GeV protons from the KEK PS impinging on a Al target. A full simulation of the neutrino beamline was based on the GCALOR/FLUKA model of the GEANT3 package, while a fast simulation was based on the Sanford–Wang parameterization for hadron production at the primary target and GEANT 3.15 for secondary interactions and propagation along the beamline. Another model for + production was based instead on a modified Sanford–Wang formula, that uses experimental results from Cho et al. [81]. In this experiment yields were measured, instead of cross-sections. The parameters for + production of this modified production model are shown in Table 17. Secondary particles were then traced along the neutrino beamline by a GEANT3 based Monte Carlo simulation. The dominant neutrino source is pions, with a small fraction coming from and K decays. The expected neutrino beam at the near location and at the Super-kamiokande location are shown in Fig. 6. Prediction of the far detector spectrum in absence of oscillations is of utmost importance in any neutrino oscillation experiment. In K2K this was done by an extrapolation from a near detector by using a nominal FAR/NEAR ratio estimated by a beamline MC simulation.
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1.3 1.25 1.2 1.15 Rνe/νµ
1.1 1.05 1 0.95 0.9 0.85 0.8 20
40
60
80 E (GeV)
100
120
140
Fig. 36. The ratio of the MC calculated e / ratio with to without correction functions f to the meson production in Be target.
1.2 νµCC
1500
Data / MC
Events / 8 GeV
x 102
1000 500
νµCC
1.1 1 0.9 0.8
0 0
50
100
150
200
0
100
150
200
Visible energy (GeV)
− νµCC
− νµCC
1.4
4000
Data / MC
Events / 8 GeV
Visible energy (GeV)
50
2000
1.2 1 0.8 0.6
0 50 100 150 Visible energy (GeV)
200
0
2
− νeCC
400
50 100 150 Visible energy (GeV)
200
ν−eCC
1.5 Data / MC
Events / 16 GeV
0
200
0
1 0.5 0
0
50
100
150
Visible energy (GeV)
0
50
100
150
Visible energy (GeV)
Fig. 37. Neutrino energy spectra (left) for the data (points with error bars) and the Monte Carlo (histogram) for CC, ¯ CC and ¯ e CC interactions and their corresponding ratios (right) in the NOMAD detector. Only statistical errors are shown.
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0.025 800
0.0225 νeCC
0.02
600
0.0175
500
0.015 Reµ
Events / 8 GeV
700
400
NOMAD data Expected ratio (1σ uncertainty)
0.0125 0.01
300
0.0075 200
0.005
100
0.0025
0
0 0 20 40 60 80 100 120 140 160 180 200
102
10
Visible energy (GeV)
Visible energy (GeV)
Fig. 38. Left: neutrino energy spectra for the data (points with error bars) and the Monte Carlo (histogram) for e CC, in the NOMAD detector. The Monte Carlo distribution is normalized using the predicted relative e / ratio. Only the statistical errors are shown. The background contribution is shown in the hatched histogram. Right: predicted and measured ratio Re of e to CC events as recorded in the NOMAD detector, from [21]. Quoted errors include also systematics.
Table 16 Different contributions to normalization errors for neutrino fluxes in the WANF neutrino beam Source of uncertainty
e
e
e /
Yields of secondary particles Proton int. downstr. of the target Reinteractions of secondaries Beam position and divergence Collimators, horn and reflector Amount of material
0.034 0.002 0.014 0.056 0.007 0.012
0.029 0.024 0.070 0.021 0.034 0.022
0.039 0.003 0.017 0.058 0.015 0.007
0.064 0.013 0.067 0.035 0.024 0.012
0.036 0.003 0.018 0.002 0.011 0.005
Total
0.068
0.091
0.074
0.103
0.042
The beamline MC simulation of K2K is confirmed by a pion monitor (PIMON), which is occasionally put in the beam to measure the kinematics of the pions after their production and subsequent focussing, down to ∼ 2 GeV/c. Below this value, calculations rely on MC extrapolations. The error on the observed number of events in the K2K far detector (SK) is dominated by contributions from uncertainties of normalization (±5%) and far/near ratio (±5%). The data taken by the Harp experiment with a K2K target replica of different thickness (∼ 15 Mevts) will be of great importance for a reduction on the systematic errors on the beam knowledge (actually ∼ 7%) in the region p 2 GeV/c and their implementation inside the K2K beamline MC is under way. The recently published HARP results, see Ref. [134], show similar neutrino energy spectra arising from previous K2K and new HARP + production assumptions in the K2K beamline MC. 7.3. Simulation of the CNGS beamline The CNGS beamline (NGS reference beam [26]) was carefully studied with full simulation packages such as FLUKA, as shown in Fig. 5 and at the beginning for a rapid optimization with the neutrino beamline fast simulation quoted in paper [101]. The reliability of the second method was checked with an extensive comparison using a full beam simulation based on the FLUKA package [120] for secondary particle production and on GEANT for tracking along the beamline (FLUKA/GEANT in Fig. 41). The method followed in the WANF neutrino beam calculation based on a fine tuning of meson produced in the graphite target by FLUKA stand-alone allows to predict the CNGS beam with an expected normalization uncertainty
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0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0
v Uncertainty
Uncertainty
112
50
100 p (GeV/c)
0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0
150
ve
0
50
100 p (GeV/c)
v
0
Uncertainty
Uncertainty
0
0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 50
100 p (GeV/c)
0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0
150
150
ve
0
50
100 p (GeV/c)
150
Fig. 39. Total energy dependent error on the neutrino fluxes in the WANF neutrino beam.
0.14
ve /v
Uncertainty
0.12 0.1 0.08 0.06 0.04 0.02 0 0
20
40
60
80 p (GeV/c)
100
120
140
160
Fig. 40. Total energy dependent error on the e / ratio in the WANF neutrino beam.
as small as ∼ 3.8% for and ∼ 3.1% for the e / ratio due to the longer base-line, where the contribution of KL0 and of particle reinteractions are strongly reduced, and to the reduced amount of material between the meson production target and the end of the decay tunnel [133,135]. Before concluding, it is worth mentioning that early simulations of the CNGS beamline based on a full GEANT3 simulation disagreed with those presented here, being too optimistic by more than 20% in hadron production in the graphite target.
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Table 17 Fitted parameters for + production for the Sanford–Wang formula, from Sanford–Wang [99] and Cho et al. [81]
Sanford–Wang Cho et al.
C1
C2
C3
C4
C5
C6
C7
C8
1.092 0.94
0.6458 1.08
4.066 2.15
1.625 2.31
1.656 1.98
5.029 5.73
0.1722 0.137
82.65 24.1
10-10
ν/GeV/p.o.t/m2
v
v
10-11
10-12 ve
10-13 0
50
100 Eν (GeV)
150
200
Fig. 41. The CNGS neutrino fluxes at Gran Sasso (732 km from target). Comparison between FLUKA/GEANT simulation (the dotted lines) as described in the text and the parametrized simulation (continuous line) A logarithmic scale is used to make evident the spectral behavior at high energy as well the wrong sign contamination.
7.4. Simulation of the NuMI beamline One of the largest uncertainties in the extrapolation of the MINOS near detector spectrum to the far detector site is due to the modeling of hadron production from the NuMI target. Fig. 42 shows the expected event rates at the near detector, while Fig. 43 shows the ratio of the far detector flux to the near detector neutrino flux for four different hadron production models, as computed in [136]. The different predictions differ by up to 30% in the absolute value and up to 10% in the relative far/near ratio, depending on the hadron production model used. As a further example, Table 18 reports the number of CC events in the MINOS Far detector as computed in [137] with the same models. The lack of good quality hadroproduction data is quite evident, also in this case. As an example, Fig. 44 shows the distribution in the p − pT plane for secondary pions produced on the NuMI target at FNAL, weighted by their contribution to the neutrino event rate at the far (top) and near (bottom) detector locations. Superimposed are the present available data from experiments [90,88,91]. Holes are to be covered by the proposed MIPP experiment at Fermilab.
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106 CC Events/kt/year
100 GFLUKA BMPT MARS MALENSEK
80 60 40 20 0 0
5
10
15
20
25
30
20
25
30
Eν (GeV) GFLUKA BMPT MARS MALENSEK
Difference from Ave. %
40 20 0 -20 -40 0
5
10
15 Eν (GeV)
Fig. 42. Prediction of the absolute neutrino rates at the MINOS near detector using four hadronic models [121,101,124,100], as computed in [136].
7.5. Simulation of the Neutrino Factory beam In this case the task is much easier, as the essential point is the pion production in heavy target at low energy. A full simulation, based on programs such as FLUKA or MARS, or a fast parameterization can be used. New results with a high Z target from the HARP experiment at the CERN PS will probably help to settle this point. At low momenta, existing data on -production are mainly on Be targets with a ∼ 15% precision mostly due to acceptance uncertainties. They cover only a small fraction of the phase space (see Fig. 45 for details) requiring extrapolations by production models which are known with large uncertainty. Current simulations show 30–100% discrepancies with respect to the available data. 7.6. Simulation of low energy beam dump experiments Both LSND at LAMPF [138] and KARMEN at ISIS [139] use the same Monte Carlo code to simulate the neutrino flux by low energy protons on the complex geometries of a spallation target or beam stop. The flux is calculated for both , decay at rest (DAR) and in flight (DIF). The geometrical configuration of the target is handled by the geometry package MCNP [140]. The parameterization of pion production cross-sections is based on the data of Crawford et al. [73] and Cochren et al. [74] at Tp =585 and 730 MeV/c, that cover a wide variety of nuclear targets. The produced pions are then traced through the target geometry, where they are allowed to interact or decay. As the E866 experiment [141] measured the distribution of stopped pions inside an instrumented beam stop, it was possible to compare the Monte Carlo predictions with data, obtaining for the ratio (Monte Carlo/E866 data) the value 1.001 ± 0.024. Uncertainties of the calculated neutrino fluxes range from 6.7% for e to 12% for e and . The uncertainty on the e and fluxes is dominated by the uncertainties affecting the pion production measurements. The same Monte Carlo code was applied for studies of new facilities, such as the SNS at Oak Ridge [142], with proton beams in the 1–3 GeV energy range and intensities in excess of 1 mA. As a benchmark, Table 19 reports some measured and calculated cross-sections for
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106× Far/Near
2 1.5 1 GFLUKA BMPT MARS MALENSEK
0.5 0 0
5
10
15
20
25
30
20
25
30
Difference from Ave. (%)
Eν (GeV)
20
0 GFLUKA BMPT MARS MALENSEK
-20 0
5
10
15 Eν (GeV)
Fig. 43. Prediction of the ratio of the far neutrino flux to the near neutrino flux using four hadronic models [121,101,124,100].
Table 18 Number of CC events at the MINOS far detector, in two energy regions, as computed with different hadronic models. Model
E 6 GeV/c
E 40 GeV/c
GFLUKA FLUKA MARS BMPT
267.8 255.6 275.1 248.1
487.7 367.2 443.1 402.8
interactions at beam dumps, where the agreement suggests that Monte Carlo simulations of fluxes at beam dumps are in good shape. 8. New hadroproduction experiments Some new experiments have just been concluded, while others are foreseen for a better study of neutrino beamlines. These include the completed HARP experiment at the CERN PS for the target study of a neutrino factory and for a better knowledge of the K2K and MiniBooNE neutrino beams and the MIPP experiment at FERMILAB for a better understanding of the NuMi beam. A proposal to use the NA49 detector at CERN (P322 [144]) to study hadroproduction for use in long-baseline experiments (mainly MINOS) and atmospheric neutrino calculations was also studied. Its aims were similar to the ones of the E907/MIPP experiments at FNAL. A small test run (1 week long) took place with the NA49 setup in June 2002, collecting 5 × 105 triggers at 158 GeV/c and 1.6 × 105 triggers at 100 GeV/c with a 1% I carbon target [145]. These data will be mainly useful for atmospheric neutrinos simulations.
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Low Energy Beam Far Detector
1 Np>100
Np>30
0.8
Np>8 0.6 νµ CC Events
0.4 0.2
PT (GeV/c)
0 0
20
40
60
80
100
120 Atherton 400 GeV/c p-Be
Near Detector 1 0.8
Barton et al. 100 GeV/c p-C
0.6 SPY 450 GeV/c p-Be
0.4 0.2 0 0
20
40
60
80
100
120
P (GeV/c) Fig. 44. The distributions in p, pT for secondary pions on the NuMI target.
measured fraction of cross section
1
Eichten et al., π+ Allaby et al., π+ Abbott et al., π+
0.8 0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
1
xlab Fig. 45. Fraction of pion production cross-section measured by experiments in p–Be interactions at low energy.
8.1. The HARP experiment The design of the sophisticated set-up of the neutrino factory requires a large R&D programme which includes studies on hadron production, muon cooling and storage facilities. In this context, the HARP experiment [51] at the CERN PS was proposed to measure the secondary hadron production cross-section d2 /dpT2 dpL on various nuclear
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Table 19 Comparison data/ Monte Carlo for some typical reactions at beam dumps Reaction 12 C( , e− )12 N e gs 12 C( , e− )12 N ∗ e 56 F e( , e− )X e e− (e , e− )12 Ngs 12 C( , e− )12 N e gs 12 C( , )X 2 H (, e)pp
Exp.
Exp result (×10−42 cm2 )
Theory (×10−42 cm2 )
KARMEN
9.3 ± 0.4 ± 0.9 5.1 ± 0.6 ± 0.5 256 ± 108 ± 43 0.32 ± 0.04 ± 0.03 8.9 ± 0.3 ± 0.9 1060 ± 30 ± 180 52 ± 18
9.3 5.4 273 0.30 9.3 1380 54.3
LSND
E31 [143]
TOF
CHERENKOV SPECTROMETER B = 1.5T
TPC
DRIFT-CH DRIFT-CH DRIFT-CH DRIFT-CH
Fig. 46. The HARP apparatus. The proton beam is coming from the left.
targets by proton and pion beams (p/p 0.24%) in the 1.5–15 GeV/c momentum range with different purposes: • to obtain adequate knowledge of yields, for an optimal design of a neutrino factory: yield per incident proton per GeV, transverse (pT ) and longitudinal (pL ) momentum distribution which affect the efficiency of the transverse capture and the first phase rotation respectively; • to improve substantially the calculation of the atmospheric flux, needed for a refined study of atmospheric oscillation parameters; • to measure the low-momentum backward-going yield for a high-intensity stopped-muon source; • to increase the reliability of hadron generators in M.C. simulations. The HARP detector (see Fig. 46) consists of forward ( < 20◦ ) and large-angle ( < 160◦ ) detection systems. At the large-angle tracking and particle identification (PID) are performed by a 90% Ar and 10% methane time projection chamber (TPC) in a solenoid which contains the target, surrounded by a barrel of resistive plate chambers (RPC). The forward spectrometer is built around a 0.4 T dipole magnet for momentum measurement with large planar drift chambers (NDC, 340 m of resolution) for particle tracking and three detectors used for PID: a time-of-flight scintillation counter wall (TOFW), a threshold Cherenkov detector (CHE) and an electromagnetic calorimeter (ECAL). The incoming beam particles are tagged by two Cherenkov counters and three timing scintillation counters BTOF which provide also their interaction time at the target. The beam particle direction and their impact points on the target are measured by multi-wire proportional chambers. Data were taken with different thin and thick targets: Be, C, Al, Cu, Sn, Ta, Pb and H2 , D2 , N2 , O2 cryogenic targets. Dedicated measurements with the target used by the K2K (∼ 60 cm Al) and MiniBooNE (∼ 65 cm Be) experiments
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Table 20 Main data sets taken by HARP at CERN PS in the 2001–2002 runs Target
Energy (GeV)
Length ()
Events (106 )
Be C Al Cu Sn Ta Pb N7 O8 H1 D1 H2 MiniBooNE repl. K2K repl. H2 O
±3, ±5, ±8 ± 12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±8, ±14.5 +8.9 +12.9 +1.5
2%, 5%, 100% 2%, 5%, 100% 2%, 5%, 100% 2%, 5%, 100% 2%, 5% 2%, 5%, 100% 2%, 5%, 100% 6 cm 6 cm 6 cm 6cm 18 cm 5%, 50%, 100%, replica 5%, 50%, 100%, replica 10%, 100%
233.2
58.4
13.8 22.6 15.3 9.6
were also performed at 12.9 and 8.9 GeV/c incident proton momenta, respectively (see Table 20 for details). High statistics, about 106 events per setting, and low systematics are required to obtain a good precision on the inclusive crosssections to be measured for the optimization of the Neutrino Factory front stage and the knowledge of the atmospheric flux. Globally about 420 millions of events were collected. The experiment requires momentum measurements in the 100 MeV/c–10 GeV/c range, have a large acceptance (also in the backward direction) and have a good e, , , K, p identification. Particle trajectory and charge are reconstructed by fitting, extrapolating and matching the three-dimensional track segments in the NDC modules using the Kalman Filter technique. The reconstruction efficiency was track ∼ 85% with the momentum p and polar angle dependence well described by Monte Carlo. The resulting momentum and angular resolution were measured directly with the beam particles in runs without target, i.e. p ∼ 150 MeV/c and ∼ 1.5 mrad at 5 GeV/c [134]. Different techniques for particle identification were used in HARP (see Fig. 47), with a high redundancy covering almost the full acceptance region. At low momenta the particle identification (PID) is performed by dE/dx measurement in the TPC complemented by the measurement of particle time-of-flight with the beam BTOF and TOFW [146] counters with a precision tof = 180 ps on a distance of ∼ 10 m, which allows the separation at 90% C.L. of pions from protons and from kaons produced in the target up to 5.5 and 3 GeV/c momentum, respectively. This is complemented by the Cherenkov threshold detector, Ethr = 2.6 GeV for pion, which is used for hadron–electron and pion–proton/kaon separation below and above 2.5 GeV/c, respectively. The electromagnetic calorimeter is used only to separate hadrons from electrons below 2.5 GeV/c to study the Cherenkov performance. In addition, e/ separation by t.o.f measurements is provided by the RPC barrel surrounding the TPC. The secondary 0 measurement and beam muon identification were performed with an electromagnetic and a hadron calorimeter. First results from HARP have been obtained for a better understanding of the K2K beamline. The + production from 12.9 GeV/c protons impinging on a 5% interaction length Al target was measured in the 0.75 GeV/c < p < 6.5 GeV/c momentum range within 30 mrad < < 210 mrad polar angle well matched to the K2K experiment covering ∼ 80% and ∼ 65% of the space phase of interest for the neutrino flux at the near and far detector, respectively. Fig. 48 shows the projections of the double-differential + production cross-section d2 /dp d as a function of p in selected bins of , for p–Al data at 12.9 GeV/c. The overall error on the total cross-section is 5.8%. The average statistical error is 1.6% per point, while the average point-to-point full error is 8.2%. Data were fitted to the Sanford–Wang parameterization, the results of the fit are reported in Table 21. Globally, these data resulted compatible with but more precise than, older pion production Al data, allowing to improve the neutrino beam knowledge in the K2K experiment (see Fig. 49). The uncertainty of the neutrino flux prediction in K2K [16] was dominated by the precision in the forward + production arising from the interactions of the 12.9 GeV/c protons in the Al target. The HARP-based neutrino prediction
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102
Time of Flight Difference (ns)
dE/dx (KeV/cm)
10
10
1
10-1
1 10-1
0
1
1
2
3
Momentum (GeV/c)
4
5
6
7
8
9
10
Momentum (GeV)
1 0.999 0.998
Velocity (c units)
0.997 0.996 0.995 0.994 0.993 0.992 0.991 0.99 0
1
2
3
4
5
6
7
8
9
10
Momentum (GeV) Fig. 47. Particle identification methods in HARP: dE/dx (TPC), time of flight difference (TOF wall) and particle velocities in C4 F10 Cherenkov for , K and p as a function of the particle momentum.
was obtained by substituting the original + production cross-section assumed in the K2K beam Monte Carlo with the Sanford–Wang parameterization of the HARP data, while keeping unchanged all other ingredients of the K2K beam simulation. The resulting neutrino flux at the near and far detector sites (normalized to a unit area) and its ratio, resulted in good agreement to those from the original K2K Monte Carlo especially below 1.5 GeV neutrino energy (see Fig. 49). The current total systematic error attached to the far-to-near ratio in the K2K analysis is of the order of 7%. The error associated with the HARP measurement is below of 1% since most errors in the cross-section cancel in the ratio, giving the real possibility to achieve a considerable reduction of the total uncertainty with these HARP measurements.
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600
600 30-60 mrad
60-90 mrad
400
400
200
200
0
0 0
2
4
6
0
2
6
600
600 90-120 mrad d2σπ / (dp dΩ) (mb / (GeV/c sr))
4
120-150 mrad
400
400
200
200
0
0 0
2
4
6
0
2
4
6
600
600 150-180 mrad
180-210 mrad
400
400
200
200
0
0 0
2
4
6
0
2
4
6
p (GeV/c) Fig. 48. Projections of the double-differential + production cross-section as function of pion momentum in different bins of the pion polar angle for p–Al data at 12.9 GeV/c, as measured in HARP.
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Table 21 Sanford–Wang fit to HARP p–Al data at 12.9 GeV/c. The errors refer to the 68.27% C.L. for seven parameters C1
C2
C3
C4 = C5
C6
C7
C8
440 ± 130
0.85 ± 0.34
5.1 ± 1.3
1.78 ± 0.75
4.43 ± 0.31
0.135 ± 0.029
35.7 ± 9.6
p–Al
Φnear (a.u.)
0.25
2.5
0.2 0.15 2
0.1
0 0
0.5
1
1.5
2
2.5
3
Eν (GeV) 0.25
Φfar/Φnear (10-6)
0.05 1.5
1
Φfar (a.u.)
0.2 0.15 0.5
0.1 0.05 0 0
0.5
1
1.5 Eν (GeV)
2
2.5
3
0 0
0.5
1
1.5
2
2.5
3
Eν (GeV)
Fig. 49. Muon neutrino fluxes in the K2K near (top-left) and far (down-left) detector, unit-area normalized, and their far-to-near ratio (right) as a function of the neutrino energy as predicted by the default K2K Monte Carlo simulation (dotted histogram and empty squares with error boxes) and by including the HARP + production measurements (filled circles with error bars).
8.2. E907 (MIPP) The MIPP (FNAL-E907) experiment [89], approved in November 2001, started the data taking in 2005 after an engineering test-run. It make use of 5–80 GeV secondary beams of protons, anti-protons, ± , K ± from the 120 GeV main injector at Fermilab, to measure particle production cross-section on various nuclei. Its goals include: • a model independent understanding of neutrino production for MINOS at Numi, i.e. the study of meson production from a MINOS-like target at 120 GeV; • tuning of Monte Carlo simulation codes (GEANT, MARS, . . .) for atmospheric neutrino experiments, extensive air shower experiments; • low energy pion production for the design of Neutrino Factory/Muon Collider beams; • search for glueballs, non-perturbative QCD studies, nuclear scaling. The planned data taking is shown in Table 22 and has recently started. The hadroproduction spectrum on a MINOS target can be measured with the Main Injector Beam that closely matches the beam emittance used in NUMI. As MINOS will not build a hadronic hose [147], that would have improved the far/near flux ratio uncertainties, hadroproduction measurements such as the ones MIPP can provide are crucial. In addition, for the Neutrino Factory project and the atmospheric neutrinos, while HARP covers the low energy part of the spectrum, MIPP will cover the remaining energy range up to 100 GeV. To reduce costs, the MIPP experiment plans to re-use components from decommissioned experiments at FERMILAB and elsewhere, to reduce expenditures. A secondary beamline from the Main Injector will be tagged with two threshold Cherenkov counters in the experimental hall MC7, where the MIPP detector (shown in
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Table 22 Data taking foreseen for MIPP at Fermilab Beam
Target
Energy (GeV)
Events (106 )
, k, p , k, p , k, p
NO Be C Cu Pb H NuMI
5–110 5–110 5–110 120
18.0 30.0 18.0 9.9
p
Fig. 50. The MIPP apparatus.
Fig. 50) will be installed. Large angle target fragmentation particles will be measured by a TPC inside a large aperture magnet (the Jolly Green Giant 262 × 124 × 221 cm3 with a 7 KG field), while forward high momentum tracks will be measured by a system of chambers from the E690 experiment. The EOS-TPC, built at LBL for heavy ion studies, has been used in the E-910 particle production experiment at BNL and has good PID capabilities, through dE/dx measurements: a 3 /k separation up to 0.7 GeV/c and K/p separation up to 1.1 GeV/c. In the forward region PID will be obtained through a TOF system (between 1 and 2.5 GeV), a threshold Cherenkov from E-910 filled with Freon ( /K/p thresholds are at 2.5/7.5/17.5 GeV/c) and above 7.5 GeV from a SELEX-type Rich counter [148] filled with Neon ( /K/p thresholds are at 12/42/80 GeV/c). The main limits of the MIPP experiment are connected to a low data taking rate, mainly due to the use of old re-used devices. As an example, the EOS TPC electronics is limited to 30 Hz readout speed, to be compared to the 3 kHz of the HARP TPC. An upgrade of the TPC related electronics is being considered to cope with the need for high statistics. 8.3. Future measurements Some interest has been raised about the possibility to do a hadroproduction experiment at CERN SPS for a precise understanding of the neutrino beam in construction at JPARC for the T2K experiment [149]. Contrary to what happened in K2K, a pion monitor to measure the hadron spectrum may be impossible at least at higher momenta. This will imply an even higher dependence on MC hadron production models for the beamline simulation, increasing the systematic
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error on the far/near ratio R. The minimum needs will be some good quality data taken with the same material of the T2K target with a 5%, 50% and 100%I target. A conceptual design of such an experiment would require a detector with good tracking and PID capabilities. Two options for an experiment at CERN SPS have been considered. The first uses the NA49 detector [150] that is mainly limited by the low speed of the DAQ ( 50 triggers/spill), while the second aims at the use of the COMPASS detector [151]. This more recent setup can be used for hadroproduction measurements with an angular acceptance ± 180 mrad, good momentum measurement for p 2.5 GeV/c, good PID for pions above ∼ 3 GeV/c and kaons above ∼ 9 GeV/c and a high speed DAQ capable of recording 5 × 104 triggers/spill. The low momentum PID capabilities can be supplemented by adding a dedicated TOF detector similar to the Harp TOFW detector [146]. 9. Conclusions Hadroproduction for neutrino experiments is a well established field since the 1970s. From the former neutrino experiments, measurements were required to calculate the neutrino beam fluxes. In the future, the search for small-sized effects like the subleading → e oscillations for the 13 mixing angle measurement and the claimed high precision era for the next generation of long-baseline neutrino oscillation experiments requires data with low systematic uncertainties for a full understanding of the beam systematics. New interesting data are expected from the recent open geometry HARP experiment at the CERN PS and from the MIPP experimental FNAL. These ancillary experiments will be of utmost importance in this context, also for the design of the foreseen long-term new neutrino facilities, such as the neutrino factory. Acknowledgments We would like to thank all our colleagues of the NA56/SPY and HARP experiments for many enlightening discussions on the subject: in particular K. Elsener, that by inviting us to NBI02 and NBI03, triggered the first draft of this work. We acknowledge also the generous help in advice, careful reading of the manuscript and discussions from L. DiLella and Jeff Wyss. We are indebted to M. Baldo-Ceolin and A. Pullia who raised our interest in neutrino physics. The support of the European Community-Research Infrastructure Activity under the FP6 “Structuring the European Research Area” program (CARE, Contract no. RII3-CT-2003-506395) is acknowledged. References [1] L. Wolfenstein, Phys. Rev. D 17 (1978) 2369; S.P. Mikheev, A.Y. Smirnov, Nuovo Cim. C 9 (1986) 17. [2] K. Kimura, A. Takamura, H. Yokomakura, Phys. Rev. D 66 (2002) 073005 [arXiv:hep-ph/0205295]; E.K. Akhmedov, R. Johansson, M. Lindner, T. Ohlsson, T. Schwetz, JHEP 0404 (2004) 078 [arXiv:hep-ph/0402175]; M. Freund, Phys. Rev. D 64 (2001) 053003 [arXiv:hep-ph/0103300] [3] B.T. Cleveland, et al., [Homestake Collaboration], Astrophys. J. 496 (1998) 505. [4] W. Hampel, et al., [Gallex Collaboration], Phys. Lett. B 447 (1999) 127; M. Altmann, et al., [GNO Collaboration], Phys. Lett. B 490 (2000) 16 [arXiv:hep-ex/0006034] [5] J.N. Abdurashitov, et al., [SAGE Collaboration], J. Exp. Theor. Phys. 95 (2002) 181 [Zh. Eksp. Teor. Fiz. 122 (2002) 211] [arXiv:astroph/0204245]. [6] S. Fukuda, et al., [Super-Kamiokande Collaboration], Phys. Lett. B 539 (2002) 179 [arXiv:hep-ex/0205075]. [7] S.N. Ahmed, et al., [SNO Collaboration], Phys. Rev. Lett. 92 (2004) 181301 [arXiv:nucl-ex/0309004]. [8] K. Eguchi, et al., [KamLAND Collaboration], Phys. Rev. Lett. 90 (2003) 021802 [arXiv:hep-ex/0212021]. [9] T. Araki, et al., [KamLAND Collaboration], Phys. Rev. Lett. 94 (2005) 081801 [arXiv:hep-ex/0406035]. [10] Y. Fukuda, et al., [Super-Kamiokande Collaboration], Phys. Rev. Lett. 81 (1998) 1562 [arXiv:hep-ex/9807003]. [11] M.C. Sanchez, et al., [Soudan 2 Collaboration], Phys. Rev. D 68 (2003) 113004 [arXiv:hep-ex/0307069]. [12] M. Ambrosio, et al., [MACRO Collaboration], Phys. Lett. B 566 (2003) 35 [arXiv:hep-ex/0304037]. [13] Y. Ashie, et al., [Super-Kamiokande Collaboration], Phys. Rev. Lett. 93 (2004) 101801 [arXiv:hep-ex/0404034]. [14] S. Fukuda, et al., [Super-Kamiokande Collaboration], Phys. Rev. Lett. 85 (2000) 3999 [arXiv:hep-ex/0009001]. [15] Y. Ashie, et al., [Super-Kamiokande Collaboration], Phys. Rev. D 71 (2005) 112005 [arXiv:hep-ex/0501064]. [16] E. Aliu, et al., [K2K Collaboration], Phys. Rev. Lett. 94 (2005) 081802 [arXiv:hep-ex/0411038]. [17] M. Apollonio, et al., [CHOOZ Collaboration], Eur. Phys. J. C 27 (2003) 331 [arXiv:hep-ex/0301017]. [18] A. Aguilar, et al., [LSND Collaboration], Phys. Rev. D 64 (2001) 112007 [arXiv:hep-ex/0104049]. [19] E. Church, et al., [BooNe Collaboration], Preprint arXiv:nucl-ex/9706011.
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Hadroproduction experiments for precise neutrino beam calculations M. Bonesinia,∗ , A. Guglielmib a Sezione INFN Milano-Bicocca, Dipartimento di Fisica G. Occhialini, Piazza Scienza 3, Milano, Italy b Sezione INFN Padova, Dipartimento di Fisica G. Galilei, via Marzolo 8, Padova, Italy
Accepted 11 July 2006 editor: J.V. Allaby
Abstract The discovery of the neutrino oscillation pattern with solar and atmospheric neutrinos has stimulated systematic studies with long-baseline accelerator experiments. Precise neutrino beamline calculations have demonstrated the importance and paucity of existing hadroproduction data needed to shape the primary meson production in targets and tune available Monte Carlo codes for hadronic shower simulation. After a brief introduction to the physics of neutrino beams, available hadron production data will be reviewed with regards to their parametrization. Fast simulations based on such parameterizations and full Monte Carlo simulations of neutrino beamlines will then be illustrated. The prospective impact of new hadroproduction experiments, such as HARP at CERN and MIPP at Fermilab, will be shown together with some neutrino beamline simulations. © 2006 Elsevier B.V. All rights reserved. PACS: 13.15.+g; 13.60.Hb; 13.75.−n; 13.85.−t
Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Neutrino oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. The present generation of long-baseline neutrino oscillation experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Sub-leading → e oscillations: the future challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Neutrino beams at accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Conventional high energy muon neutrino beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Beam dump neutrino beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Neutrino beams at LHC and pp colliders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Beyond conventions: Neutrino Factories and BetaBeams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Medium term options: SuperBeams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. A review of hadroproduction data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Main characteristics of hadron production reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Requirements on hadroproduction data for the study of conventional beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1. A side remark about low energy beam dump and Neutrino Factory beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ∗ Corresponding author.
E-mail address: [email protected] (M. Bonesini). 0370-1573/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physrep.2006.07.004
66 66 68 68 70 70 73 76 77 79 84 84 85 85
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4.3. Low energy hadroproduction experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.4. High energy hadroproduction experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.4.1. A case study: the NA56/SPY experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5. Existing parameterizations of hadroproduction data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.1. Low energy parameterizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.2. High energy parameterizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.2.1. Atherton and Malensek parameterizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.2.2. The BMPT parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.3. Extrapolation to other energies and target materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.4. The MARS pion production model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6. Simulations of neutrino beamlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.1. Fast simulation programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.2. Full Monte Carlo neutrino beam calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.2.1. The Geant 3.21 and MARS simulation packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.2.2. The FLUKA Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.2.3. The GEANT4 simulation package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 7. Examples of flux computations for present and future neutrino beamlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 7.1. The CERN WANF neutrino beam: a case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 7.2. Simulation of the K2K beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 7.3. Simulation of the CNGS beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.4. Simulation of the NuMI beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7.5. Simulation of the Neutrino Factory beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 7.6. Simulation of low energy beam dump experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 8. New hadroproduction experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 8.1. The HARP experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 8.2. E907 (MIPP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 8.3. Future measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 9. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
1. Introduction A renewed interest in precise determination of crucial parameters of neutrino beams as absolute fluxes, energy shape distributions and flavor composition, has been triggered by the recent discovery of neutrino oscillations with solar and atmospheric neutrinos. This discovery has stimulated systematic studies with accelerator based experiments. The new long baseline oscillation experiments, such as ICARUS and OPERA at the CNGS at CERN, MINOS at NuMI at FNAL, K2K at KEK and T2K at JHF impose severe requirements for precise beam calculations with small systematic uncertainty. In addition new projects, such as the Neutrino Factory or the SuperBeams, are stimulating similar considerations. An essential point is the paucity of available hadroproduction data to be used to shape the primary meson production in targets or to tune the available Monte Carlo codes for hadronic showers simulation. After a brief introduction on the status of neutrino oscillations, the physics of neutrino beams will be briefly outlined, with emphasis on the hadroproduction data needed for their optimization and understanding. The prospective impact of new hadroproduction experiments, such as HARP at CERN PS and MIPP at Fermilab, for the understanding of K2K and MiniBooNE results will be shown. Some examples of neutrino beam simulation, with both a fast parameterized approach and a full Monte Carlo simulation, will then be illustrated. 2. Neutrino oscillations Oscillations between neutrinos of different flavor require the existence of a m = 0 term for the neutrino mass and flavor lepton number violation interaction which cannot be simply accommodated within the Standard Model (SM). In the standard scenario of three neutrino generations, the observed flavor oscillations in solar and atmospheric neutrinos can be described by a mixing matrix U which translates between mass (1 , 2 , 3 ) and flavor eigenstates (e , , ). Six independent parameters have to be experimentally measured: three mixing angles 12 , 13 and 23 , two mass-squared differences m212 and m223 , where m2ij = m2i − m2j , and a CP violating phase .
M. Bonesini, A. Guglielmi / Physics Reports 433 (2006) 65 – 126
67
In vacuum the oscillation probability between two neutrino flavors , is given by P ( → ) = −4
jk
Re[W ] sin2
k>j
m2j k L 4E
±2
k>j
jk
Im[W ] sin2
m2j k L 2E
,
(1)
jk
where = e, , , j = 1, 2, 3 and the coefficients W are expressed in function of the mixing matrix elements Uj as
W = Uj U∗j U∗k Uk . The neutrino energy E and the baseline L (distance of the neutrino source from the detector), combined in the oscillation formula into the L/E ratio, are the relevant experimental parameters. Oscillations are perturbed if neutrinos propagate in matter [1], depending on the sign of m223 [2]. The measurement of this quantity can fix the ordering with which mass eigenstates are coupled to flavor eigenstates (neutrino mass hierarchy). Solar neutrino oscillations were observed in the Homestake [3], Gallex-GNO [4], SAGE [5], Super-Kamiokande [6] and SNO [7] experiments giving a convincing evidence of , appearance and a first precise determination of the solar oscillation parameters. A combined data analysis of solar neutrino experiments and of the KamLAND [8] long-baseline reactor experiment running at the solar m2 scale constrains the solar mixing angle and mass splitting −5 to |m212 | = 7.9+0.6 eV2 , tan 12 = 0.40+0.10 −0.07 [9]. −0.5 × 10 A clear signal of disappearance of atmospheric neutrinos and an anomalous value of the ratio of electron to muon neutrino events were reported by the Super-Kamiokande experiment [10], then confirmed by the Soudan2 [11] and Macro [12] experiments. Super-Kamiokande provided an indirect evidence of appearance excluding pure oscillations into sterile neutrinos at 99% C.L. [13,14]. As a result an almost pure → transition, connected with the m2 and m3 mass eigenstates, with parameters 1.5 × 10−3 eV2 < |m223 | < 3.4 × 10−3 eV2 , sin2 223 > 0.92 [15] at 90% C.L was found. A first confirmation has been obtained in the long-baseline experiment K2K which observed a disappearance in a 1.5 GeV neutrino beam sent to the Super-Kamiokande detector (L = 250 km), measuring 1.9 × 10−3 < |m223 | < 3.6 × 10−3 eV2 at 90% C.L. [16]. The 13 mixing angle represents the link between the solar and the atmospheric neutrino oscillations. The best experimental constraint: sin2 213 0.14 at 90% C.L. for |m223 | = 2.5 × 10−3 eV2 , comes from the reactor experiment Chooz [17]. Both solar and atmospheric neutrino data are compatible, within the experimental sensitivity, with 13 0 favoring a near bimaximal mixing matrix with |m223 | 30 · |m212 |. Thus the 3 × 3 mixing matrix Uj becomes a trivial product of two 2 × 2 matrices, showing that the observed solar and atmospheric neutrino oscillation regimes are largely decoupled. They can be thus described by a two neutrino formalism with only one mixing angle and one square mass difference m2 as jk
P ( → ) ∼ sin2 2 sin2
1.27m2 (eV2 ) · L(km) . E (GeV)
(2)
In this approximation, the resulting leading oscillation probabilities for s, setting m212 to zero, depend only on m223 , 13 and 23 and are given by: P (e → ) = sin2 23 sin2 213 sin2 (m223 · L/4E ),
(3)
P (e → ) = cos2 23 sin2 213 sin2 (m223 · L/4E ),
(4)
P ( → ) = cos4 13 sin2 223 sin2 (m223 · L/4E ).
(5)
The three neutrino oscillation scheme will become more complicated, requiring non-standard explanations, if the → e signal with a |m2 | of 0.3 − 20 eV2 observed by LSND [18] will be confirmed by the MiniBooNE experiment at FNAL looking to → e transitions [19]. However, a large part of the allowed region of the oscillation parameters was already excluded by the KARMEN [20] and NOMAD experiments [21]. The precise measurement of the neutrino oscillation parameters can be better addressed by accelerator long-baseline oscillation experiments (LBL), since a more stringent control over the neutrino flux can be obtained as compared to the atmospheric and cosmic rays sources. Moreover experiments searching for → transitions at accelerators can explore different regions of the sin2 2 − m2 plane by a suitable choice of the L/E ratio. Of particular interest will
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Table 1 Main parameters of beams for the current generation of oscillation experiments at accelerators as compared to the previous NOMAD and CHORUS experiments at the CERN SPS WANF facility Experiment
Facility
pp (GeV/c)
L (km)
E (GeV)
p.o.t./yr (1019 )
MiniBooNE K2K MINOS OPERA, ICARUS NOMAD, CHORUS
FNAL Booster KEK PS FNAL NuMI CERN CNGS CERN WANF
8.9 12.9 120 400 450
0.5 250 730 732 0.8
0.8 1.5 3.5 17.7 24.2
100 2 20 → 34 4.5 1.5
be the detection and measurement of the sub-leading → e oscillations in the atmospheric neutrino oscillations, which can offer the possibility to discover the CP violation in the lepton sector. Therefore, neutrino oscillation physics at accelerators will probably include several phases: • 2001–2010: the present generation of LBL experiments (K2K, MINOS, OPERA, ICARUS, see next paragraph) to confirm the Super-Kamiokande evidence of oscillations of atmospheric neutrinos. • 2009–2015: next generation LBL experiments (T2K, NOvA) with improved neutrino beams, the SuperBeams (see Section 3.5) and the reactor experiment DoubleChooz, optimized to measure 13 and give a precise measure of the atmospheric parameters; • 2015–later: novel concept BetaBeam or Neutrino Factory facilities, coupled to large mass detectors, with a much improved sensitivity to 13 and a good sensitivity for leptonic CP violation and the mass hierarchy (see Section 3.4). 2.1. The present generation of long-baseline neutrino oscillation experiments Over the next 5 years the present generation of oscillation experiments at accelerators with long-baseline beams (see Table 1): K2K at KEK [16], MINOS [22] at the NUMI beam from FNAL [23] and ICARUS [24] and OPERA [25] at the CNGS beam from CERN [26], are expected to confirm the atmospheric neutrino oscillations and measure sin2 223 and |m223 | with a 10–15% accuracy if |m223 | > 10−3 eV2 . K2K and MINOS are looking for neutrino disappearance by measuring the survival probability as a function of neutrino energy while ICARUS and OPERA will search for interactions in a beam, as final evidence for → oscillations. K2K has already completed its data taking, while MINOS has started data taking in 2005. The CNGS neutrino beam is expected to start operations in the second half of 2006. Current long-baseline experiments with conventional neutrino beams can look for → e oscillations even if they are not optimized for 13 studies (see Fig. 1). As an example, MINOS at NuMI is expected to reach a sensitivity of sin2 213 = 0.08 for |m223 | = 2.5 × 10−3 eV2 , convoluted to CP and matter effects, integrating 14 × 1020 protons on target (p.o.t) in 5 years according to the FNAL proton evolution plan [27]. The sensitivity to 13 of the current experiments is limited by the power of the proton driver which determines the neutrino flux and the event statistics, by the not optimized L/E value and by the presence of the e intrinsic beam contamination and its related systematics. As an example, the CNGS neutrino energy is ∼ 10 times larger than the optimal value for 13 searches, due to the constraint of the search for appearance. 2.2. Sub-leading → e oscillations: the future challenge The unknown parameters of the mixing matrix Uj , as the angle 13 , the sign of m223 and which generates the CP violation in the neutrino oscillations, can be extracted by measuring sub-leading → e oscillations at accelerators. Reactor experiments on e disappearance are only sensitive to the 13 mixing angle. Taking into account all the contributions and not knowing a priori the size of 13 , all the six parameters of the mixing matrix are involved in the appearance probability for electron neutrinos in a muon neutrino beam, that can be
M. Bonesini, A. Guglielmi / Physics Reports 433 (2006) 65 – 126
69
10-1 CHOOZ EXCLUDED 90% C,L,
∆m223 (eV2)
10-2
MI
NO
SUPER ALLOWED 90% C,L
2.5
S
10-3
CN
GS
T2K
10-4 10-3
10-2
Co m
bin
10-1
ed
1
sin22θ
13
Fig. 1. The expected 90% C.L. sensitivity on the 13 mixing angle (matter effects and CP violation effects not included) for MINOS, ICARUS (assuming a 2.35 kt fiducial mass) and OPERA combined at nominal CNGS intensities and for the next T2K experiment, compared to the Chooz exclusion limit.
parameterized as [28] 2 2 2 P ( → e ) = 4c13 s13 s23 sin2
m213 · L 4E
2 + 8c13 s12 s13 s23 (c12 c23 · cos − s12 s13 s23 ) · cos
2 − 8c13 c12 c23 s12 s13 s23 · sin · sin
m223 L m213 L m212 L · sin · sin 4E 4E 4E
m223 L m213 L m212 L · sin · sin 4E 4E 4E
2 2 2 2 2 2 2 + 4s12 c13 (c13 c23 + s12 s23 s13 − 2c12 c23 s12 s23 s13 · cos ) · sin2
2 2 2 − 8c13 s13 s23 · cos
m223 L m213 L 2 aL · sin (1 − 2s13 ) , 4E 4E 4E
m212 L 4E (6)
where sij = sin ij , cij = cos ij , a[eV2 ] 7.6 × 10−5 (g/cm3 )E (GeV). The first term, which has the largest contribution, is 13 driven, while the fourth is driven by the solar neutrino regime. The second term is CP-even and the third as well the last-one, which account for the matter effects on the neutrino propagation as developed at the first order, result CP-odd. The CP odd term and matter effects change sign by changing neutrinos with antineutrinos. The → e transition probability is dominated by the solar term, anyway, at the distance defined by the |m223 | parameter, it is driven by the 13 term which is proportional to sin2 213 . Below sin2 213 10−3 solar neutrino oscillations will be the dominant transition mechanism, limiting the experimental sensitivity to 13 . Moreover, P ( → e ) could be strongly influenced by the unknown value of and the sign of m223 . The 13 measurement represents the first needed ingredient for the investigation of the CP leptonic violation in the → e transitions and for the mass hierarchy determination. The detection of the phase will require a major experimental effort because of the intrinsic difficulty of disentangling the several contributions to → e
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oscillation probability. A leptonic direct CP violation can be detected by comparing the electron neutrino and antineutrino appearance probabilities in a and beam, respectively, through: ACP () =
P ( → e , ) − P ( → e , ) . P ( → e , ) + P ( → e , )
(7)
The richness of the → e transition is also its weakness because it will be very difficult to extract all the parameters unambiguously in presence of correlations between 13 and [29] where additional clone solutions arise. In general, the measurement of P ( → e ) and P (¯ → ¯ e ) will result in eight allowed regions of the parameter space, the so-called eightfold-degeneracy [30]. The measure of the subleading → e transitions searches for a e excess as respect to what expected from the solar terms. It will be experimentally difficult because the Chooz limit on the e disappearance: 13 < 11◦ for |m223 | 2.5 × 10−3 eV2 , translates into a → e appearance probability less than 10% at the appearance maximum in a high energy muon neutrino beam. As already pointed out, the → e experimental sensitivity with conventional beams is limited by an unavoidable e beam contamination of about 1%. The to oscillations, with E above the mass production threshold, generate background due to a significant number of charged current interactions where a large fraction of ’s decay into electrons. In addition neutral pions in both neutral current or charged current interactions can fake an electron providing also a possible background for the e ’s. Therefore the measurement of 13 mixing angle and the investigation of the leptonic CP violation will require: • neutrino beams of high intensity and purity and low associated systematics; • the use of detectors of unprecedented mass, granularity and resolution, to collect high event statistics and keep the event backgrounds rate as low as possible, as water Cherenkov and liquid Argon detectors or magnetized iron calorimeters. The sensitivity in the oscillation experiments will depend mainly on the neutrino beam characteristics and relies on its knowledge. To improve control over the systematic errors, ancillary experiments to measure the physical processes involved in the neutrino beam production are needed. Studies on parent meson production and low energy neutrino interaction cross-sections (E 1 Gev) will be essential for the present long baseline neutrino experiments, as well as in atmospheric neutrino measurements. They will be also crucial in the design for the next generation of neutrino oscillation experiments at future accelerators. 3. Neutrino beams at accelerators Conventional accelerator neutrino beams are produced by the decay of , K’s generated at beam dumps (decay at rest) or by high energy protons hitting suitable targets (decay in flight). In such beams, different mesons are involved as sources, according to the different scale of decay lengths (see Table 2). As discussed in the following, these conventional beams have a low intensity and are not pure, admitting different neutrino flavors as minority components ( , e , e or , e , e ) in addition to the majority ones ( or ). These intrinsic features limit the experimental sensitivity in the oscillation searches. They are overcome if the neutrino parents can be fully selected, collimated and accelerated to a given energy. This can be realized with muons or selected beta decaying ions. The neutrino beam composition, as obtained from their decays, would then be perfectly predictable. The first approach brings to the Neutrino Factory, the second to the BetaBeam, as discussed in Section 3.4. However, the technical difficulties associated with developing and building these novel conception neutrino beams suggest for the middle term to improve the conventional beams by using new high intensity proton machines (proton drivers) and optimizing the beam characteristics for the → e oscillation searches, giving the SuperBeam option, see Section 3.5. 3.1. Conventional high energy muon neutrino beams High energy accelerators provide ( ) beams through the decay of , K mesons produced by protons hitting needle-shaped light targets. In order to increase the angular acceptance of the beamline and correspondingly the neutrino flux, positive (negative) mesons are charge-selected and focused by magnetic lenses, “horns” and “reflectors”,
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71
Table 2 Main neutrino sources at accelerators c Long lived sources ( mc 2 (7.5 − 6200) m/GeV; Br ∼ 50.100%) + → + K + → + , 0 + , 0 e+ e KL0 → − + , − e+ e , + − , + e− e + → e+ e c −2 Medium lived sources ( mc m/GeV; Br ∼ 0.1%) 2 (4.7) × 10
→ pe− ¯ e KS0 → − + , − e+ e , + − ¯ , + e− ¯ e − → ne− ¯ e c −4 Short lived sources ( mc m/GeV; Br ∼ 2 − 20%) 2 (0.5 − 1.7) × 10
D + → K 0 + , K 0 e+ e DS+ → + + → + ¯ , e+ e ¯ B 0 → D − + , D − e+ e
BCT1
SEMs
Reflector
Al Collimator
BCT2
Horn
Muon Pits Tunnel Decay
CHORUS Earth
Be Target 450 Ge V/c protons
TDX collimator
Iron Shield
NOMAD
Fig. 2. The WANF beamline at the CERN SPS; the distance of the NOMAD detector from the Be target is ∼ 840 m.
Fig. 3. Schematic layout of the CNGS neutrino beamline.
into an approximately parallel beam in a long evacuated decay tunnel where ’s ( )’s are generated. The residual hadrons and muons are stopped by an heavy absorber. When and K are collected in a wide range of momenta and solid angle, wide band neutrino beams (WBB) with a high flux and a broad energy spectrum, are produced. In case of positive charge selection of the secondary particles by the magnetic horns, a beam has typically a contamination of at a few percent level (from − , K − decays) and around 1% of e and e coming from three-body K ± , K 0 and decays, which affect the experimental sensitivity in the oscillation searches. Narrow band neutrino beams (NBB) can be obtained by momentum selecting the mesons before entering the decay region. The neutrino energy spectrum is thus much tighter ( E /E ∼ 20%), at the expense of a significantly lower flux. As examples of recent WBB neutrino beams, a schematic layout of the West Area Neutrino Facility (WANF) beamline [31] at the CERN SPS as used by the NOMAD [32] and CHORUS [33] experiments and of the CERN to Gran Sasso long baseline neutrino beam (CNGS) [26] are shown in Figs. 2 and 3. The CNGS design was accomplished on the basis
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Table 3 Main parameters of the WANF and CNGS neutrino beamlines at the CERN SPS Beam line
WANF
CNGS
Proton energy Proton beam focal point Proton intensity pot/year (shared operations)
450 GeV 50 cm from start of target 2 × 1019
400 GeV 4.5 × 1019
Target material Number of rods Target rod diameter Target rod length-separation Additional end-rod length
Beryllium 11 3 mm 10–9 cm –
Graphite 8 4 mm 10–9 cm 50 cm
Horn and reflector focusing momenta Horn and reflector length Horn and reflector current Horn and reflector distance from focal point Horn acceptance
70–70 GeV 6.56–6.54 m 100–120 kA 19.4–90.9 m 10 mrad
35–50 GeV 6.65 m 150–180 kA 2.7–43.4 m 20 mrad
Decay tunnel length–radius Tunnel vertical slope Pressure in decay tunnel
285–0.6 m +42 mrad 1.3 × 102 Pa
992–1.2 m −50 mrad 1.3 × 102 Pa
of the previous WANF experience where the neutrino beam interactions in the NOMAD detector allowed to study with high accuracy the beam features. Their main technical characteristics are listed in Table 3. The resulting spectra of the four neutrino components , , e and e of the WANF beam at CERN SPS (the component is absolutely negligible, at a 10−6 level) as well as their related main neutrino sources ( ± , K ± , K 0 and ± ) are reported in Fig. 4. In the CNGS project a substantial increase of the beamline acceptance and of the flux is obtained by moving the horn and reflector near the target and increasing their characteristic currents. The beam-optics was optimized in order to maximize the possibility to detect the → oscillation by the appearance of events in a beam initially free of . A lower , e and e contamination is also expected due to the 732 km long base-line (see Fig. 5). This conventional scheme for wide-band neutrino beams is also used in the K2K [16] at KEK and MINOS at the FNAL NuMI [23] long base-line disappearance experiments and in the MiniBooNE [19] experiment where the → e transition will be searched for as an excess of e interactions with respect to the expected natural contamination of the beam (see Table 1 and Figs. 6–8). To predict beam energy spectra, intensity and composition a sound knowledge of and K production in the primary proton beam target interactions is required. The accurate description of the K + and K 0 fluxes relative to the + flux is crucial to calculate the initial e content in the beam. Neutrino production at high energy proton accelerators involves a quite complicated cascade of meson decay and reinteraction processes in the beamline materials. The latter reduce the neutrino fluxes and increases the uncertainty in the calculations (mainly with wrong sign and wrong flavor contaminations). They are generally minimized using a target made of thin rods of low Z material interleaved with empty spaces (to let the secondary mesons exit the target without traversing too much material). The amount of material downstream of the target (i.e. horn and reflector inner conductor thickness) must be kept to the minimum. Primary protons missing the target will interact in the downstream materials producing a large fraction (typically up to 15% of at the WANF) of the minority components otherwise mainly produced by the defocused − and K − and K 0 from the target. Therefore an accurate description of the primary proton beam spot, focusing system as well as of the materials inserted in the beamline from the target to the dump (hadronic reinteraction processes) is mandatory. As a conclusion these neutrino beams at accelerators are not pure (e ) beams and knowledge of their composition suffers mainly from the uncertainties on the hadronic processes involved at generation level and particle transport which limit the experimental sensitivity in oscillation searches.
M. Bonesini, A. Guglielmi / Physics Reports 433 (2006) 65 – 126
νµ
105 104
K+
103
0
KL
π+
102 µ-
10
− νµ
105 ν−µ / 3 GeV / 109 p.o.t.
νµ / 3 GeV / 109 p.o.t.
106
73
104 K-
103 102
π-
µ+ 10 KL0
1
1 0
50 100 150 200 Neutrino energy (GeV)
0
50 100 150 200 Neutrino energy (GeV)
104
− νe
103
K
+
102
10
103
µ+
0
− νe / 3 GeV / 109 p.o.t.
νe / 3 GeV / 109 p.o.t.
νe
102
10
0
KL
1
K-
µ-
KL
1 0
50 100 150 200 Neutrino energy (GeV)
0
50
100 150 200 Neutrino energy (GeV)
Fig. 4. Composition of , , e and e energy spectra at WANF CERN SPS neutrino beam (450 GeV protons on Be) within the NOMAD transverse fiducial area of 2.6 × 2.6 m2 . The last-decay parent particles are shown.
3.2. Beam dump neutrino beams Low energy neutrino beams may also be produced by the decay at rest of , ’s generated by impinging protons on a beam dump. In a beam dump experiment, the target for the primary proton beam, where the neutrino parents are produced, is also the medium for absorbing and/or stopping the hadrons. Accordingly, no drift space is provided to hadrons to decay in. High intensity low energy proton accelerators (pbeam ∼ 1 GeV/c) such as meson factories or neutron spallation sources are commonly used. The decay sequence + → + , + → e+ e at rest gives an almost equal number of , and e with a characteristic low energy spectrum, as shown in Fig. 9. A deviation from this simple decay scheme is given by pion decay in flight, which accounts for ∼ 2% of the total flux. Negative pions are strongly absorbed when they come to rest and therefore give no contribution to the spectrum. The two most recent experiments at a beam dump, LSND [18] at LAMPF and KARMEN [20] at ISIS have given controversial results on → e oscillations that are presently addressed by the MiniBooNE experiment [19]. In high energy beam dump neutrino experiments, one instead tries to eliminate or reduce neutrinos from long and medium lived sources, such as the first two categories of Table 2. The semileptonic decays of new, short-lived particles ( ∼ 10−10 − 10−13 s) would produce “prompt” neutrinos, to be distinguished from the “non-prompt” neutrinos from , K weak decays. Early experiments, such as CDHS [35], CHARM [36] and BEBC [37] have looked mainly for the presence of charm. The present interest in high-energy beam dump experiments is instead connected to the detection of ’s, such as in the DONUT (E872) experiment at FNAL [38]. In the neutrino beam used by DONUT about 4% of all the neutrinos seen in the detector are ’s.
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103
− νµ / 2 GeV / 107 p.o.t.
νµ / 2 GeV / 107 p.o.t.
102
102
10
10
1
10-1 50 100 Neutrino energy (GeV)
150
0
10
− νe/ 5 GeV / 107 p.o.t.
νe / 5 GeV / 107 p.o.t.
0
1
50 100 Neutrino energy (GeV)
150
1
10-1
10-1 0
50 100 Neutrino energy (GeV)
150
0
50 100 Neutrino energy (GeV)
150
Fig. 5. Composition of , , e and e energy spectra at Gran Sasso of the CNGS neutrino beam (400 GeV protons on C) within a 0.5 km2 transversal fiducial area. The last-decay parent particles are shown.
Neutrino Flux at Super-Kamiokande
1011
number of neutrinos/cm2/1020POT
number of neutrinos/cm2/1020POT
Neutrino Flux at Near Detectors
νµ
1010 109
νe
νµ
108
νe 107
0
1
2
3
Eν (GeV)
4
5
105 νµ
104 103
νe
νµ
102
νe
10
0
1
2
3
4
5
Eν (GeV)
Fig. 6. Predicted K2K beam at KEK (JAPAN), from 12.9 GeV protons impinging on a Al target, at the near location detector and at the SuperKamiokande site, as reported in [34].
M. Bonesini, A. Guglielmi / Physics Reports 433 (2006) 65 – 126
200
Low Energy Beam
75
High energy Event Total
Medium energy
HE : 2740 ME : 1270 LE : 470
175 2nd Horn z =10.0 m
VµCC- events/kt/GeV
Target z= -0.34 m
Medium Energy Beam
Target z= -1.30 m
2nd Horn z =22.0 m
150 125 100
Low energy
75
High Energy Beam 50 25 Target z= -3.96 m
2nd Horn z =40.0 m
0 0
5
10
15 Ev (GeV)
20
25
30
Fig. 7. spectra from the different proposed neutrino beams at the FNAL NuMI facility, as obtained from 120 GeV protons impinging on a graphite target. The disappearance experiment will use the low energy beam. The left-hand inset shows the relative positions of the target and the two used horns. Plots refer to a 1 kt/yr exposure with perfect focalization efficiency.
νµ Flux
Fraction of νµ Flux / 0.1 GeV
10-1
νe Flux
10-2
10-3
10-4
10-5 0
0.5
1
1.5
2
2.5
3
Eν (GeV) Fig. 8. The predicted energy spectrum from the beam for the MiniBooNE experiment at FNAL, with 8.9 GeV protons impinging on the Be target. The (upper) and e (lower) components of the beam are shown.
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Fig. 9. Neutrino spectra from a low energy beam dump.
Table 4 Neutrino interactions per year in a 2 kg/cm2 detector (e.g. density 2 g/cm3 , 10 m long) for LHC at L = 1034 cm2 /s (see [41]) E 100 GeV
e
E 500 GeV
10 mrad
2 mrad
10 mrad
2 mrad
2300 11300 130
1300 7100 46
860 3700 32
750 2900 24
3.3. Neutrino beams at LHC and pp colliders Neutrino √ beams at very high energy (E 500 GeV) can be produced in pp collisions (such as at the LHC collider at s = 14 TeV) from the decay of charmed and beauty particles, as outlined in Refs. [39,40]. Some advantages are: • the possibility to have ’s and e at very high energy; • comparable numbers of e ’s and ’s (unlike conventional neutrino beams from , K decays); • a sizable fraction of (up to 10% of the e beam) from beauty particles and Ds → decays. However, due to the uncertainties in heavy quark production cross-sections, neutrino flux estimates show large uncertainties. These prompt-decay neutrinos are emitted mainly at ∼ 0◦ in forward direction, e.g. tangentially to the circulating beams. A neutrino experiment, located in an LHC straight section behind a bending magnet, would benefit from the intense, strongly forward peaked, high-energy beams produced either from beam-beam or beam-gas interactions (as the angular difference from the two beams is ∼ 1 mrad only). Table 4 reports, as an example, the number of interactions per year (assumed as 107 s) in a 2 kg/cm2 target, for two energy cuts and two typical opening angles. In addition to high energy , e neutrinos, LHC will offer the unique possibility of direct studies. Neutrino beams can be produced at LHC also from cc pairs produced in collisions between the coasting proton beams and an internal jet-gas target (as in UA6 experiment at CERN SPS) or from an extracted proton beam on a dump. In the last case the technical challenge is quite formidable, as outlined in Ref. [40]. In all cases, as neutrinos come from cc decays, the composition of the flux is affected by big uncertainties, the cc production cross-sections being quite unknown.
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A possible layout of a neutrino factory
Number of charged current interactions
_ νµ Polarization= +1
P=+0.3 P=0 P=-0.3
P=-1 0.2
0.4
νe
0.6
0.8
1
P=-1 P=-0.3
P=+0.3 0.2
0.4
0.6
0.8
1
Eν/Eµ Fig. 10. Expected layout for a Neutrino Factory at CERN (top) and corresponding energy spectra of neutrino beams for the + case (bottom) for different degrees of polarization.
3.4. Beyond conventions: Neutrino Factories and BetaBeams To overcome the limitations from conventional beams, neutrino production by decays of accelerated muons has been considered [42]. The beam related background is reduced to a 10−5 level or below, because there is only one parent particle decaying to neutrinos, with no subsequent daughter decay (+ → e+ e or − → e− e ). The basic concepts for a muon collider were introduced by G.I. Budker in 1969 and A.N. Skrinsky in 1971 [43]. The first idea to use muons to produce high intensity neutrino beams was developed by Koshkarev in 1974 [44]. The lifetime at rest is 2.2 s and its decay length (c) 660 m. Using an average acceleration of 1 MeV/m, it may nevertheless be possible to produce a high energy muon beam at energies of the order of tens of GeV, the losses being most severe at the beginning of the acceleration. Detailed calculations for such Neutrino Factory were developed within the Muon Collaboration in the USA [45] and at CERN [46] as a first step of a large new physics programme based on muon colliders. In the CERN proposed layout for a Neutrino Factory (see Fig. 10) a 4 MW H − beam is accelerated up to 2.2 GeV by a new Super Conducting Proton Linac (SPL) to produce low energy ’s in a liquid mercury target, after some
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Table 5 Oscillation channels accessible at a muon factory (+ decay) Oscillation channel
Experimental signature
e → → e e → x → x e → →
Appearance mode: detection of wrong-sign muons, − Appearance mode: detection of wrong-sign electrons, e+ Disappearance mode: energy spectrum and NC/CC Disappearance mode: energy spectrum and NC/CC Appearance mode: detection of − events Appearance mode: detection of + events
accumulation and bunch compression [46]. A magnetic horn collection system is envisaged to capture as many ’s and ’s as possible. Muons from decay are then cooled1 and phase rotated, to reduce their phase space, before being accelerated through a first Linac and then through a system composed of two recirculating Linacs, up to 50 GeV/c. Finally ’s of well defined charge and momentum are injected in the accumulator where they will circulate until their decay, delivering along the two main straight sections two intense beams. Either muon sign can be selected. The optimal muon beam energy: E = 50 GeV (E ∼ 34 GeV), accounting for the difficulties and the technical challenge for the construction of such a muon accelerator complex, must be as large as possible. As the neutrino flux grows like E2 (in the conventional neutrino beams is proportional to E ), the number of charged current neutrino events from the oscillations (Nosc ), measured by a detector at a distance L, will be proportional to E [48]: L E3 sin2 E , (8) E L2 where ∝ E is the corresponding neutrino interaction cross-section and Posc is the oscillation probability. From a general point of view the Neutrino Factory approach relies on a completely different strategy than conventional facilities, where only a fraction of the focused high energy mesons, produced by high energy protons on a target, decays giving neutrinos. In a Neutrino Factory based on decay, the primary beam power is used to produce as many (and ) as possible per GeV. Hence the factory must capture the largest fraction of produced muons and manipulate them in order to reduce their phase space in view of the final acceleration stage. Here the decay tunnel typical of conventional beams is replaced by the storage ring where each circulates until it decays. Major intrinsic advantages over a conventional neutrino source are: Nosc ∝ · · Posc ∝
• the decay + → e+ e (− → e− e ) produces a pure, well collimated, neutrino beam with equal numbers of , e ( , e ) which allow to extend the baseline to distances of several thousand kilometers; • the momentum is well defined (an accurate determination is expected by spin precession measurements) and therefore the neutrino energy spectra at the detector site are precisely calculable (see Fig. 10); • due to the introduction of a new megawatt proton driver, the flux intensity is expected to be ∼100 times more than that of conventional beams, with P = 50 GeV/c and 0.5 × 1021 -decay/yr; • the neutrino intensity can be precisely determined from the measurement of the muon current circulating in the storage ring (absolute normalization at 1% level). The Neutrino Factory lends itself naturally to the exploration of neutrino oscillations between different neutrino flavors with high sensitivity to small mixing angles and small mass differences, due to the very intense, collimated, well defined and pure beam. The detector should be able to perform both appearance and disappearance experiments, providing final lepton identification and charge discrimination which is a tag of the initial flavor and of the oscillation. Among the many possibilities for studying oscillations in different channels (see Table 5), the searches for e → transitions (“golden channel”) appears to be very attractive because this transition can be studied in appearance mode looking for − (appearance of wrong-sign ) in neutrino beams where the neutrino type that is searched for is totally absent (+ beam). With a 40 kt magnetic detector exposed to both polarity beams and 1021 muon decays, it will be possible to explore the 13 angle down to 0.1◦ , measuring the phase if m212 5 × 10−4 eV2 (systematic errors not 1 A dedicated experiment, MICE [47], is under construction at RAL to realize a prototype cooling channel section.
M. Bonesini, A. Guglielmi / Physics Reports 433 (2006) 65 – 126 EURISOL
79
Existing at CERN DECAY RING
Proton driver
Isol target & Ion source
SPS
B = 5T L = 6880 m
New RFQ Linac PSB
PS
Fig. 11. A schematic layout of the BetaBeam complex proposed at CERN.
accounted for) [29,49]. More details on the physics performances of a Neutrino Factory for a precision measurement of neutrino oscillation parameters can be found in Refs. [46,50]. One of the main concerns in the development of the Neutrino Factory project study arises from the uncertainty on production at low energy in the target. Current simulations show ∼ 30% discrepancies with respect to available data. A good knowledge of the pT , pL distributions of produced secondaries is crucial to optimize the efficiency of the collection phase: hadroproduction data with full angular coverage at low energy are therefore required. The HARP experiment at the CERN PS is presently addressing this question [51]. A completely different strategy aims at neutrino beams from the decay of radioactive isotopes accelerated in a suitable machine. As for the Neutrino Factory, the neutrino spectrum of these BetaBeams (B) [52] is completely defined by the parent decay properties and by the Lorentz boost. In the CERN proposed layout (see Fig. 11 for details), 6 He and 18 Ne ions are produced by a 0.4 MW ∼ 2 GeV proton machine (SPL) and accelerated up to (6 He) = 60 and (18 Ne) = 100, respectively, by the PS and SPS machines. The ion beams are then injected in a “decay ring” where two pure low energy e and e beams per straight section can be produced. The expected neutrino fluxes at 130 km of distance for 2.9 × 1018 6 He and 1.1 × 1018 18 Ne decays/yr are displayed in Fig. 12. In principle, all the necessary machinery has been already developed at CERN for the heavy ion physics programme. However the required improvement by ∼ 3 orders of magnitude of the presently available ion fluxes will require sub-megawatt 1–2 GeV Linacs, new target developments for heavy ion production, ion collection and acceleration system including the CERN PS and SPS and a novel decay ring [53]. Accounting for the technical challenges involved in these new facilities, the expected timescale of the BetaBeams is expected to exceed the next ten years. Since the beam does not contain or ¯ , magnetized detectors are not required. The corresponding physics potential computed with a Cherenkov water detector of 440 kt fiducial mass, has shown a 90% C.L. sensitivity to sin2 213 ∼ 0.0007 and the capability to detect a CP violation signal at 3 if || 35◦ and 13 1.0◦ [54]. Running the two ions separately both at = 100 can allow to push the investigation of sin2 213 down to 0.0002, and the CP violation search down to 25◦ for 13 1.0◦ [55,56]. 3.5. Medium term options: SuperBeams Conventional neutrino beams can be improved and optimized for → e searches, giving a SuperBeam facility. This will require: • • • •
a new proton driver, with power exceeding one megawatt, to deliver more protons on target; a narrow band beam with E ∼ 1.2 GeV; a lower intrinsic e beam contamination, by suppressing the K + and K 0 production in the target; a tunable L/E in order to explore the |m223 | parameter region as indicated by the previous experiments with neutrino beams and atmospheric neutrinos.
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x 107
x 107 SPL νµ − SPL νµ Beta νe (Ne18) − Beta νe (He6)
ν/m2/20 MeV/yr
2000
1500
1000
8000
SPL νµ
7000
SPL −νµ Beta νe (Ne18) Beta −ν (He6)
6000 ν/m2/20 MeV/yr
2500
e
5000 4000 3000 2000
500 1000 0
0 0
0.2
0.4
0.6 Eν (GeV)
0.8
1
0
0.2
0.4
0.6 Eν (GeV)
0.8
1
Fig. 12. Left: neutrino flux of B (6 He = 60, 18 Ne = 100, shared mode) and CERN-SPL SuperBeam, at 2.2 GeV, at 130 km of distance. Right: the same for 6 He = 100, 18 Ne = 100, (non shared mode, e.g. just one ion circulating in the decay ring) and a 3.5 GeV SPL SuperBeam.
The realization of neutrino SuperBeams will require the development of high power proton Linacs or Rapid Cycling Synchrotrons, expected to happen in the next decade, and the development of targets able to survive to megawatt power proton beams, whose R&D studies have already started [57]. An interesting option for the SuperBeams is the possibility to tilt the beam axis of a few degrees with respect to the position of the far detector (Off-Axis beams) [58,59]. According to the two body -decay kinematics, the neutrino flux at = 0◦ is the result of the contributions of all the pions above a given momentum giving neutrinos of similar energy, contrary to the = 0◦ case where the neutrino energy is proportional to the pion momentum (see Fig. 13): E =
m2 − m2 2(E − p cos )
,
where E , p and m are the energy, momentum and mass of the parent pion and m is the muon mass. It can be demonstrated that the spectrum at = 0◦ is peaked at an energy E,max given by E,max ()
30 MeV ,
(9)
an effect of the well-known “Jacobian peak” in the two-body decay kinematics. Off-Axis neutrino beams have several advantages with respect to the On-Axis beams. They have a narrower energy spectrum, with a smaller e contamination (since they mainly come from three body decays), although the neutrino flux is significantly smaller. In the JHF project Phase I (T2K experiment [58]) a 50 GeV proton beam from a 0.75 MW PS will produce an intense ∼ 700 MeV beam (see Fig. 14) with 0.4% e contamination. In five years a 90% C.L. sensitivity sin2 213 ∼ 0.006 (=0) will be reached: a factor 20 better than the current limit set by Chooz, as shown in Fig. 15. T2K will also measure m223 and |sin2 223 | with a ∼ 2% precision via disappearance. A possible machine upgrade to 4 MW (JHF-II), in conjunction the new Hyper-Kamiokande detector (0.54 Mt fiducial mass) will allow to investigate sin2 213 below 10−3 and the leptonic CP violation if || > 20◦ and sin2 213 ∼ 0.01 (2 years of and 6 years of operations [60]). The NOA experiment using an upgraded NuMI Off-Axis neutrino beam (E ∼ 2 GeV with a e contamination less than 0.5%) at a baseline of 810 km (12 km Off-Axis), was recently proposed at FNAL. The aim is to explore the → e oscillations with a sensitivity more than 10 times better than the MINOS experiment using a 30 kt liquid scintillator far
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Eν (GeV)
15
81
θ=0 mrad θ=7 mrad θ=14 mrad θ=27 mrad
10
5
0 10
0
30
20
40
Eπ (GeV) Fig. 13. Neutrino energy versus the pion parent energy for different Off-Axis angle .
400 350
νµ NCC (/100MeV/22.5kt/yr)
ON AXIS 300
OA20
250 200 OA30 150 100 50 0 0
1
2
3
4
5
Eν (GeV) Fig. 14. T2K neutrino beam energy spectrum for different Off-Axis angles at J-PARC.
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10-1
2 (eV2) ∆m23
10-2 Chooz excluded 2.5
T2K
10-3
ICA
RU
PS
++
10-4 10-3
10-2
SC
NG
SL
.E.
10-1
1
sin22θ13 Fig. 15. Expected sensitivity on 13 mixing angle (CP violation and matter effects not included) for a 20 GeV high intensity PS proton beam from CERN to Gran Sasso (PS++) and for the CNGS-L.E. neutrino beam compared to T2K experiment.
detector [61]. The NuMI target will receive a 120 GeV proton flux with an expected intensity of 6.5 × 1020 pot/yr. As a second phase, a new proton driver of 8 GeV and 2 MW, could increase the NuMI beam intensity to 17.2–25.2 × 1020 pot/yr, improving the experimental sensitivity by a factor two. At BNL an upgrade to 1 MW has been proposed for the existing AGS 28 GeV PS to produce a neutrino SuperBeam with E 1.5 GeV [62]. A megaton water Cherenkov detector at a baseline of 2540 km would allow the observation of the second oscillation maximum. By comparing disappearance and e appearance at the first and second oscillation maximum a better control of degeneracies could be obtained, measuring sin2 213 down to 0.003 ( = 0) in a 5 years period. Different approaches have been considered for new neutrino long-baseline experiments in Europe after the end of the present CNGS appearance programme, by improving existing infrastructures and detectors or considering new neutrino beams and detectors. A systematic study of the experimental sensitivity on sin2 213 as a function of the proton driver energy Ep and its power was performed in [63]. In this calculation the optimal base-line distance L∗ was selected in the 130.800 km range according to E /L∗ ∝ m223 ∼ 2.5 × 10−3 eV2 . In terms of proton economics, the optimum beam energy Ep 20 GeV was obtained, by minimizing the required driver power factor W = Ep × p.o.t, to reach a selected 13 sensitivity beyond the Chooz limit. This gives a beam with E 1.6 GeV well matched to a 732 km of baseline (i.e. CERN—Gran Sasso). A slightly better sensitivity than the one foreseen in T2K, sin2 213 0.005 at 90 % C.L., can be reached in a 5 years exposure of a 3.8 kt fiducial mass ICARUS-like liquid Argon detector ( = 0 and no matter effects) with a 4 MW proton driver and a useful beam time operation of 107 s/yr (see PS ++ line in Fig. 15). The possibility to improve the CERN to Gran Sasso neutrino beam performances for 13 searches even with the present SPS proton beam (Ep = 400 GeV and 4.5 × 1019 p.o.t/yr) was investigated (CNGS-L.E.) [64] (Fig. 16). The low energy neutrino flux can be increased by a factor 5 with respect to the current CNGS beam by an appropriate optimization of the target and of the focusing system. Results are shown in Fig. 15 for a 2.35 kt ICARUS-like detector. In addition, the use of a 1.5 GeV low energy Off-Axis neutrino beam from CERN to the Gulf of Taranto at 1200 km of distance has been considered [152]. As an alternative, the CERN-SPL SuperBeam (SPL-SB) [46,65,66] based on a 4MW SPL was investigated. The intense + ( − ) beam focused by a magnetic horn in a short decay tunnel will produce an intense beam mainly via
M. Bonesini, A. Guglielmi / Physics Reports 433 (2006) 65 – 126
400 GeV proton beam
83
400 GeV proton beam 10-15 v flux
v flux full CNGS L.E. dashed CNGS τ
10-16 v/cm2 / GeV/p.o.t
v/cm2 / GeV/p.o.t
10-14
full CNGS L.E. dashed CNGS τ
10-15
10-17
10-18 10-16
10-19 0
10
20
30
40 50 60 Ev (GeV)
70
80
90 100
0
10
20
30
40 50 60 Ev (GeV)
70
80
90 100
Fig. 16. The CERN low energy neutrino beams (CNGS L.E.), as compared to the current CNGS option (CNGS ).
Table 6 Some future LBL options with L/E matching m223 = 2.5 × 10−3 eV2
p-driver (MW) Ep (GeV) E() (GeV) L (km) Off-Axis beam CC no osc. (1/kt/yr) contamination (%) Detector sin2 213 × 104 (90% C.L.)
T2K
J-Parc II
NOA
PS ++
SPL-SB
B
0.75 50 0.7 295 2◦ 100 0.4 22.5 kt CH 60
4 50 0.7 295 2◦ 500 0.4 540 kt CH 6
0.8 (2) 120 2 810 0.8◦ 80 (200) 0.5 30 kt LS 38 (24)
4 20 1.6 732 – 450 1.2 3.8 kt LAr 50
4 2.2 0.27 130 – 37 0.4 440 kt CH 18
0.4 1−2.2 0.3 130 – 38 0 440 kt CH 7
All the experiments are normalized to 5 years data taking, 107 s/yr beam time operations. The J-Parc II sin2 213 sensitivity is extrapolated from T2K. Numbers quoted for NOA refer to the standard and the proton driver options (see text). The B column is computed for the = 60, 100 CC option; the CC of B indicates the CC e + e rate. Detectors are water Cherenkov (CH), LAr (liquid argon), LS (liquid scintillator) with their fiducial mass.
the -decay, providing a flux ∼ 3.6 × 1011 /yr/m2 at 130 km of distance with an average energy of 0.27 GeV (see Fig. 12). The e / ∼ 0.4% contamination, exclusively from the + → + → e+ decay chain being the K contribution suppressed by threshold effects, will be known with an error less than 2%. The use of two detectors (the far detector at L = 130 km of distance in the Frejus area) will allow for both -disappearance and → e appearance studies. The physics potential with a 440 kt fiducial mass water Cherenkov (having fixed m223 = 2.5 × 10−3 eV2 ) was extensively studied [66]. The 90% C.L. sensitivity on sin2 213 is 0.002 ( = 0, 5 years beam, see Table 6), with a 3 CP violation discovery potential (2 years with beam and 8 years with the reversed polarity beam) for > 40◦ and sin2 213 > 0.02. The performance could be improved by rising the proton energy to 3.5 GeV [67], to produce more copious secondary mesons and to focus them more efficiently into a 40 m long and 4 m diameter decay tunnel, using new status of the art RF cavities [68]. Neutrino fluxes are increased up to a factor 3, at the expense of doubling the e contamination.
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The SPL can be used as injector for a BetaBeam, requiring at most 10% of its protons, allowing a simultaneous B and SPL-SB exploitation, the two neutrino beams having similar neutrino energies (see also Fig. 12). The same detector at 130 km of distance could then be exposed to 2 × 2 beams ( and × e and e ) searching for CP, T and CPT violation in the same run. A 90% C.L. sensitivity to sin2 213 35 times better than T2K and a 3 sensitivity to CP violation if ||18◦ and 13 0.55◦ can be reached [55]. In Table 6 the features of some options for the next generation of SuperBeams and of BetaBeams are reported, rescaling the maximum source power at 4 MW and the useful time machine to 107 s/yr (see also Refs. [69]). For an appropriate choice of the L/E well matched to the m223 value, the figure of merit of the neutrino beam is determined by the -CC/kt/yr event rate and also by the e / natural beam contamination. 4. A review of hadroproduction data Existing hadroproduction data, useful for neutrino beams simulations, come mainly from old, non-dedicated experiments realized with single-arm magnetic spectrometer in the sixties. Open geometry experiments, with full angular coverage, were an exception. Single arm experiments (SAS) have inherently more systematic uncertainties than open geometry experiments (OG), as they must change the geometry of the single arm spectrometer frequently to scan the phase space and thus introduce acceptance uncertainties, even if they can benefit from reduced material along the particle path compared to the OG massive detectors. While open geometry experiments sample the phase space continuously, single arm data are sparse and cover discrete pT bins. These old experiments suffer from limited statistics and high systematics, often amounting to a 30% error on the quoted cross-section. Following the dedicated NA56/SPY experiment at CERN, new hadroproduction experiments have now been proposed or realized both at CERN and FERMILAB (HARP/PS214, P322, MIPP/E907). 4.1. Main characteristics of hadron production reactions At high energies, in fixed target experiments, 80–90% of the total cross-section consists of a great variety of manybody or multiparticle inelastic channels, with a lot of particles produced in the final state. A comparatively small fraction of the available incident energy goes into making new particles. Approximately the charged multiplicity is given by Nch = a log(s) + b, (10) √ where a =2, b =4 and s is the total energy in the center-of-momentum frame (if all available energy went into particle production a power law Nch = s 1/2 would be obtained). Most of the incident energy emerges as kinetic energy of the outgoing particles. While their longitudinal momentum component, pL , covers a wide range, the transverse momentum is quite small: on average pT 0.3 − 0.4 GeV/c, with an exponential decreasing cross-section d /dpT ∼ e−6×pT , where pT is in GeV/c. Of course, the quantity Nch is just one of the parameters describing multiparticle production. What types of particles are produced is the next consideration of interest. In general, summing over all inelastic channels, most of the produced particles are pions (of order 80–90%) followed, in order, by nucleons, K + , K − , p, . . . . The relative production rates can vary substantially in different kinematic regions. Inclusive processes of the type a + b → c + X, where c is the observed particle, can be described by three independent variables such as s, pL , pT (where pL , pT refer to particle c), giving an invariant cross-section: E
d2 d 3 p Ec = . dpL dpT2 dpc3
(11)
Feynman suggested for inclusive processes [70] an approximate scaling behavior of the single-particle inclusive invariant cross-section when expressed in terms of the transverse momentum (pT ) and of the longitudinal variable √ √ xF = 2pL∗ / s, where pL∗ and s are the particle longitudinal momentum and total energy in the center-of-momentum frame. A factorization in xF and pT of the invariant cross-section is only approximately supported by more recent data. ∗ , defined as the ratio of the particle energy in the center-of-momentum The alternative scaling variable xR = E ∗ /Emax frame to the maximum possible particle energy, was suggested by Yen [71] and Taylor et al. [72] and shown to greatly extend the range of validity of scaling at sub-asymptotic energies.
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4.2. Requirements on hadroproduction data for the study of conventional beams The study and simulation of beams can be approximately divided into two steps: the generation of primary mesons (decaying to ’s) in proton–target interactions and the subsequent transport and re-interaction of produced secondaries along the beamline (horns, reflectors, collimators, decay tunnel) giving additional neutrinos. The two steps can be decoupled and different techniques used for the two stages. A good knowledge of hadroproduction cross-sections is needed especially for the first step. We will try to illustrate what kind of data are useful taking into account , K kinematics for conventional beam production. Conventional neutrino beams are mainly produced via their parent decays: ± → ± + ( ),
(12)
K ± → ± + ( ).
(13)
Pion (kaon) decay is a two-body decay of a spinless particle and is therefore isotropic in the parent rest frame. Simple kinematical considerations give for the decay neutrinos: 1 dN = , d cos 2((1 − cos ))2 E =
m2 (K) − m2 E (K) , m2 (K) 1 + 2 2
(14)
(15)
where is the Lorentz boost of the parent meson, E (K) its parent energy and the neutrino angle with respect to the meson flight direction. Moreover in the laboratory frame: Emax 0.41p (for → ),
(16)
Emax pK (for K → ).
(17)
Neglecting focussing, the angular divergence of the neutrino beam is due to the intrinsic neutrino transverse momentum (pT = E · sin 30 MeV/c for → decay and 236 MeV/c for K + → + decay) and the additional pT of the parent meson in the production process (∼ 300 MeV/c). The neutrino flux to the detector per decay parent hadron is given by =
2 (1 + 2 2 )2
,
(18)
1 of the flux in the pion direction. As the boost factor in Eq. (18) gives a strongly where, without focusing, is only ∼ 25 peaked forward flux, that shrinks as 1/2 , the most relevant hadroproduction data are the yields or cross-sections for both ± and K ± in the forward direction in a momentum region up to 2.4 · Emax for pions and Emax for kaons. In addition, some angular scans around = 0◦ are highly desirable due to the finite beamline angular acceptance ( 10.20 mrad). As can be seen from Table 2 data on strange particle production (KS0 , ) in the same kinematical range are also needed. As an example, about 15% of the e background in a beam, such as the WANF at CERN, is due to KL0 decays. In the framework of a simple quark parton model, K ± and KS0 (KL0 ) production can be related. Assuming isospin symmetry and neglecting the momentum dependence N (KS0 ) = N (KL0 ) = 41 (NK + + 3NK − ), but clearly direct measurements are highly desirable. In the following only hadroproduction experiments relevant to neutrino beam studies will be considered.
4.2.1. A side remark about low energy beam dump and Neutrino Factory beams From the previous considerations, the most relevant data for the simulation of both low energy beam dump beams and neutrino factory beams are pion production cross-sections at low or very low energy. For low energy beam dump beamlines, where incoming proton beams have pinc ∼ 800 MeV/c, some useful data are shown in Table 7. Both experiments were performed with single arm spectrometer, where particle identification (discrimination of pions
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Table 7 Experiments studying particle production at very low energy, useful for beam simulation in beam dump experiments Experiment
pinc (MeV/c)
Target
Crawford et al. [73]
585
1 H2 ,
Cochran et al. [74]
730
H, Be, C, O, Al, Ni, Cu, Mo, Pb H, D, Be, Al, Ti, Cu, Ag, Ta, Pb, Th
Polar angle coverage
= 22.5◦ , 45◦ , 60◦ , 90◦ , 135◦ = 15◦ , 20◦ , 30◦ , 45◦ , 60◦ , 75◦ , 90◦ , 105◦ , 120◦ , 135◦ , 150◦
Table 8 Experiments studying particle production at low energy, useful for beam parameterization Experiment
pinc (GeV/c)
Target
Polar angle coverage
Lundy et al. [75] Dekkers et al. [76] Baker et al. [77] Fitch et al. [78] Allaby et al. [79] Eichten et al. [80] Cho et al. [81] Asbury et al. [82] Marmer et al. [83] Vorontzsov et al. [84] Abbott et al. [85] E910 Coll. [86] HARP Coll. [51]
13.4 8.65, 11.8, 18.8, 23.1 10.9, 20.9, 30.9 30, 33 19.2 24 12.4 12.5 12.3 10.1 14.6 6.4, 12.3, 17.5 1.5–15
Be Be, Pb, H2 Be, Al Be, Al p, B4 C, Be, Al, Cu, Pb Be, B4 C, Al, Cu, Pb Be Be Be, Cu Be, Al, Cu, Ta Be, Al, Cu, Au Be, Cu, Au, Pb, U Be, C, Al, Sn, Ta, Pb, N, O, H, H2 O
2.16◦ 0◦ , 5.7◦ ∼ 5◦ , 9◦ , 13◦ , 20◦ ∼ 14◦ , 45◦ , 90◦ ∼ 13◦ , 45◦ , 90◦ ∼ 1◦ , ∼ 3.3◦ , 5◦ , 7.3◦ 0.12◦ 12◦ , 15◦ 0◦ , 5◦ , 10◦ 3.5◦ 5.58◦ OG OG
against protons or muons and electrons) was achieved mainly with time-of-flight (TOF) techniques. The differential cross-sections d3 /d dE were measured with a total error around 10%. Data needed for neutrino factory simulations are discussed in the next section. 4.3. Low energy hadroproduction experiments Experiments at low energy (see Table 8) were performed mainly with single arm magnetic spectrometers, with some kind of particle identification as Cherenkov counters or TOF detectors. The uncertainty on particle yield is dominated by the systematic error on the calculation of the beamline acceptance. These experiments suffer from large systematic errors and low statistics. As an example the relative normalization of the Lundy et al. [75] experiment and the Dekkers et al. [76] experiment differ by more than 50%. In addition two other experiments have been performed with a large set of nuclear targets. In the experiment of Allaby et al. [79] a 19.2 GeV/c proton beam impinged on p, B4 C, Be, Al, Cu, Pb targets, while in the experiment of Eichten et al. [80] a 24 GeV/c proton beam was hitting Be, B4 C, Al, Cu, Pb targets. Additional data have also been obtained by heavy-ions experiments, such as the E802 [85] and the E910 [86] experiments at BNL. These experiments studied p-nucleus reactions in addition to nucleus–nucleus reactions to understand the systematics related to the underlying processes. The E802 experiment at BNL studied 14.6 GeV/c protons on thin Be, Al, Cu and Au targets, obtaining an overall normalization error as good as 10–15% on cross-section measurements. The E910 experiment at BNL has recently published data from 12.3 and 17.5 GeV/c protons on Be, Cu and Au targets, using an open geometry apparatus at the MPS facility at BNL. About 2.6 × 106 , 0.6 × 106 , 104 events have been recorded at 17.6, 12.3 and 6.4 GeV/c, with a low bias trigger. The experiment used a spectrometer with a good acceptance and particle identification over the region of interest for low energy neutrino beams, such as MiniBooNE. However, the small data statistics collected, especially at 6.4 GeV/c (a feature common to most heavy-ions experiments), and the lack of thick targets sensibly reduced its prospective impact. The HARP experiment has concluded its data-taking on a variety of targets, with an open geometry apparatus and redundant particle identification capabilities. It is providing hadroproduction data at low energy, with the lowest systematic errors. Some available results are reported in Section 8.
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Table 9 Experiments studying charged particle production, at medium and high energy, useful for beam parameterization Experiment
pinc (GeV/c)
Target
Geometry
Bozhko et al. [87] Barton et al. [88] MIPP/E907 [89] NA20 [90] NA56/SPY [91]
67 100 5–120 400 450
Be, Al, Cu C, Al, Cu, Ag, Pb Be, C, Cu, N, O, Pb Be Be
SAS SAS OG SAS SAS
1.2
NA56/SPY (450 GeV/c) NA20 (400 GeV/c) Barton et al. (100 GeV/c) Bozhko et al. (67 GeV/c)
1
pT (GeV/c)
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
xF Fig. 17. Coverage in the pT vs. xF plane for published single arm experiments at medium or high energy, studying charged particle production.
4.4. High energy hadroproduction experiments The relevant experiments on nuclear targets are listed in Table 9. Fig. 17 shows the coverage in the pT vs. xF plane of the experiments already performed at higher energies. In this energy range the experiment of Barton et al. [88] has studied inclusive ± , K ± , p, p production in 100 GeV/c + , K + , p collisions with C, Al, Cu, Ag, Pb targets using the M6E single-arm spectrometer at Fermilab. The experiment was a continuation of an extensive study of particle production in hadron–nucleus interactions [92]. The production of secondaries was measured over the kinematical range 0.3 xF 0.88 and 0.18 pT 0.5 GeV/c. Good charged , K and p separation in the full kinematics range was achieved using Cherenkov counters. Data were mainly taken with thick targets, while thin targets were used primarily for finite thickness corrections. The main aim of the experiment was the study of the target dependence of the secondary spectra.
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TOF1
B0
B1
TOF2 V
V
C0
C1
TOF3
B2
TOF4
TOF5
V
CEDAR
C2
p
Calorimeter Target
W1T
144m
W2T
W2S
82m
W3S
141m
W3T
78m
W4T
W5T
79m
524m Fig. 18. The NA56/SPY experimental setup. The main detectors for particle identification are the time of flight detectors (TOF1, . . ., TOF5), the Cherenkov detectors (C0–C1, CEDAR) and the calorimeter.
At higher energies, the two main experiments of interest are the NA20 experiment [90] and the recent NA56/SPY [91] experiment. In addition, the experiment of Skubic et al. [93] has studied strange particle production with Be, Cu, Pb targets at 300 GeV/c and the experiment of Edwards et al. [94] KS0 production in the forward direction from 200 GeV/c p–Be interactions. Both these experiments, however, covered a region xF > 0.25, which overlaps only partially the momentum region relevant for neutrino beams. The NA20 experiment used the H2 beamline at the CERN SPS and took data with 400 GeV/c protons on Be targets, with secondary momenta down to 60 GeV/c covering the pT range between 0 and 500 MeV/c and the xF range 0.15–0.75. Absolute fluxes were counted with four scintillator counters and the beam composition with N-type CEDAR differential Cherenkov counters [95], giving a good particle identification in the region 60–300 GeV/c. Data with 100, 300, 500 mm long Beryllium targets were taken. The NA56/SPY with 450 GeV/c incoming protons on Be has instead covered the complementary range down to 7 GeV/c. The critical points for such kind of experiments are: • the accurate simulation of the beamline, to obtain systematic errors at the 5–10% level on cross-sections evaluation; • a good determination of the incoming proton flux, to limit the systematics to the 1–2% level; • a good particle identification (PID) to separate the different outgoing particle (mainly , K). 4.4.1. A case study: the NA56/SPY experiment The NA56/SPY (secondary particle yield) experiment [91] measured the production rates of charged secondary particles ( ± , K ± , p, p) in the range 7–135 GeV/c (0.02 xF 0.30) and up to transverse momenta of 600 MeV/c in p–Be interactions at 450 GeV/c. The experiment was performed with the NA52 spectrometer [96] in the H6 SPS beamline in the North Area at CERN (see Fig. 18). The beamline was operated to transport secondary charged particles in the range 5p 200 GeV/c, within a maximum acceptance of (p/p) × = ±1.5% × 2.1 sr, defined by a set of three collimators. The beam was derived from the T4 target station served by a primary proton beam of 450 GeV/c, with typical intensities of several 1012 protons per burst. Data were collected in the secondary momentum range of 7–135, GeV/c with angular scans at fixed momenta (15 and 40 GeV/c). ˘ C2 ˘ Redundant particle identification was provided by a set of time of flight detectors (TOF1–TOF5), threshold C0. and differential (CEDAR) Cherenkov counters along the beamline and a hadron calorimeter at its end. TOF1–TOF5 scintillator hodoscopes provided the measurement of particle speed and, with an intrinsic time resolution of 100 ps or better, allowed K/p separation up to 20 GeV/c. Two Cherenkov counters (C0 and C1) were filled with N2 gas and provided /K separation up to 20 GeV/c and K/p separation above 20 GeV/c. A third Cherenkov counter (C2), filled with He gas, allowed e, rejection at 15 and 20 GeV/c and provided /K separation above 20 GeV/c. The hadron calorimeter, consisting of five uranium/scintillator modules at the end of the spectrometer, allowed an effective separation of hadrons from electrons and muons. A set of proportional chambers (WnT (n = 1, 5), WmS (m = 2, 3)) was used for particle tracking along the spectrometer.
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The trigger was based on two independent signals formed at 268 m (trigger A = TOF2 · B1) and 505 m (trigger B = TOF4 · B2) downstream of the target. At low secondary momenta (7 and 10 GeV/c), trigger A alone had been required in order to increase the detection efficiency of kaons which decay before reaching the end of the spectrometer. At higher momenta both trigger A and B were required. A veto on the Cherenkov counter signals from ’s had been included in the trigger on every other event readout in order to get a sample of triggers from particles heavier than pions, that was enriched in K content. The flux (p flux for momenta 10 GeV/c) and the p/ and K/p production ratios were separately extracted from the unbiased sample or the heavy particle enriched sample, while the ratio K/ and the other fluxes were derived quantities. This approach minimized possible bias related to different experimental configurations between light and heavy particles. Data were collected with targets made of beryllium plates of different length (100, 200, 300 mm), 2 mm high and 160 mm wide. Additional data were also taken with a target (T9-like) of three Be rods of 100 mm length and 3 mm diameter interleaved by 90 mm of air, similar in structure to the one used in the WANF at CERN [31]. The absolute intensity of the primary beam on the target was measured by Secondary Emission Monitors [97], with an accuracy of better than 2%. To derive particle yields, data were corrected for trigger and data acquisition efficiencies, particle decays in flight, strange particle decays outside the target and contributions from interactions of the primary beam with material around the target area. The uncertainty on the particle yield evaluation was dominated by the systematic error on the calculation of the H6 beamline acceptance. This is given by the product of a phase-space acceptance ( · (p/p)), defined by the apertures of three collimators, and a transmission coefficient T, which accounts for particle losses along the beamline. The transmission coefficient T was computed in the first part of the beamline (up to B1) with an improved version of the TURTLE Monte Carlo simulation [98], which includes multiple scattering and secondary interactions. Dedicated proton runs had been used to cross-check the Monte Carlo calculation and to measure the beamline transmission downstream of B1. The global systematic error on the acceptance is 5–10% depending on beam momentum and is dominated by beamline transmission at low momenta and by the accuracy of collimators settings at high momenta. Results in the forward direction for the 100 mm plate beryllium target are shown in Fig. 19. The results of Atherton et al. [90] for the same xF as NA56/SPY data are reported. In the measurement of same sign particle production ratios the uncertainties related to the acceptance definition (magnet strengths, collimators openings, etc.) cancel, and only the particle dependence of the transmission along the beamline has to be accounted for. The systematic contribution coming from this correction on the measurement of particle production ratios is of the order of 1%, due to uncertainties on the amount of material along the beamline and on the nuclear cross-sections. As an example, the measured production ratios for the 100 mm plate beryllium target in the forward direction are reported in Fig. 20. Error bars account for systematic and statistical errors added in quadrature (the total uncertainty is ∼ 3%). In addition, results for particle yields and particle ratios as a function of pT (up to 600 MeV/c) were also obtained. The target thickness dependence, to correct the measured yields of the 100 mm target for its finite length and to extract the invariant cross-section, was obtained directly from experimental data at various target lengths. In this way, the invariant cross-sections for p–Be interactions at 450 GeV/c have been derived in the forward direction in a model independent way. Results are shown in Fig. 21 and extend to higher energies the studies on p–A interactions at 24 GeV/c by Eichten et al. [80] and at 100 GeV/c by Barton et al. [88]. Systematic errors include the ones on the measured particle yields and the method to correct for the target thickness.
5. Existing parameterizations of hadroproduction data Parameterizations of the available hadroproduction data have been presented in the literature at low-energy (pinc 30 GeV/c), e.g. the Sanford–Wang [99] parametrization, and at high energy, e.g. the Atherton et al. [90], the Malensek [100] and the BMPT [101] parameterizations. One of the goals of these parameterization is to adopt a simple functional form for inclusive particle production which will be suitable for extrapolation to different centre of mass energies and/or secondary particle momenta. In addition the possibility to extend the scope to different targets (e.g from Be to C) can be useful. The main aspects of them will be reviewed in the following, including the range of their applicability.
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10
particles/ (incident protons sr (∆p/p%))
particles/ (incident protons sr (∆p/p%))
10
1
10-1 π+ π-
K+ K-
π+ π-
K+ K-
10-2
1
10-1
10-2 p
p
p
p
10-3 0
50
100 p (GeV/c)
150
0
50
100
150
p (GeV/c)
Fig. 19. Particle yields in the forward direction for the 100 mm Be target, as a function of momentum.
5.1. Low energy parameterizations Several empirical formulae for particle production at low energy have been proposed, e.g. by Cocconi, Koester and Perkins (CKP) [102], Trilling [103] and Ranft [104]. All formulae give a fairly qualitative description of experimental data between 10 and 30 GeV/c and often are not suitable for general purposes (parameter values depend on the incident particle energy). The CKP formula consists in a semi-phenomenological parameterization of the production spectrum, fitted on available data. A simple modification of the CKP formula, used for the study of high energy beams at the Serpukhov accelerator, is given in Ref. [105]: √ d2 N 2 2 2 = AE2 e−E/T e−( m +E /B) , d dE
(19)
where E, are the energy and production angle of secondaries and A, B, T are parameters determined by a fit to the experimental data. A more general parameterization for ± , K ± , p production in p–Be collisions, based on an empirical description of the data rather than a physical approach, has been proposed by Sanford and Wang [99] (S–W). The pion production cross-sections are parametrized as C5 C8 d2 N C4 = f ( = 0) × g() = [C1 p C2 (1 − p/pinc )e−(C3 p /pinc ) ][e−C6 (p−C7 pinc (cos ) ], d dp
(20)
combining a forward production term f (=0), with a term g() giving the angular dependence, where p is the secondary momentum, pinc the incident proton momentum and the production angle. The parameters Ci (i =1, . . . , 8) have been determined by a least square fit to the first four data entries of Table 8 and are shown in Table 10. All the experiments
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K/π
0.1 0.075 0.05 0.025
p/π
0.6
0.4
0.2
4
K/p
NA56/SPY Atherton et al.
3 2 1
0
20
40
60
80 p (GeV/c)
100
120
140
Fig. 20. Particle production ratios for the 100 mm Be target, in the forward direction, as function of momentum. Open (full) dots refer to negative (positive) particles.
considered there were performed with a single arm spectrometer. The experiment of Baker et al. and of Fitch et al. used an internal target, for which relatively large errors (∼ 20%) had to be assigned to the experimental data to account for effects such the AGS fringe field, etc. A comparison of the S–W parametrization with some available low energy − data is shown in Fig. 22. The main problems in the derivation of the Sanford–Wang formula are connected with the relatively small amount of experimental data available (in particular to cover the angular dependence) and the fact that it was necessary to combine different experiments with uncertainties in their relative normalizations. For example, the data of Lundy et al. [75] (used to obtain the angular dependence shape) were renormalized to the data of Dekkers et al. [76] with a normalization factor 1.5. Table 11 (from Ref. [104]) provides a direct check of the S–W formula by comparing the measured and predicted pion multiplicity N , defined as N =
pinc
2
0
0
d2 N sin d dp. d dp
(21)
The S–W parameterization has been initially applied to model the low energy K2K neutrino beam with some modifications to the original Ci parameter values to take into account the Cho et al. [81] data (see Table 17 for details). The HARP experiment data taken with a thin Al target at 12.9 GeV/c and a thin Be target at 8.9 GeV/c are currently being parametrized in terms of a Sanford–Wang fit, see Section 8 for more details. These results will be of relevance for the understanding of the K2K and MiniBooNE beams.
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102
p p-
102
E d3 σ/dp3 (mb/GeV2)
E d3 σ/dp3 (mb/GeV2)
π+ πK+ K-
10
10
1 0
50
100
150
0
50
p (GeV/c)
100
150
p (GeV/c)
Fig. 21. Inclusive invariant cross-section as a function of secondary momentum for p–Be interactions at 450 GeV/c in the forward direction.
Table 10 Original values of the parameters corresponding to the empirical parameterization of ± , K ± and p inclusive production in p–Be interactions, in the Sanford–Wang formula
+ −
K+ K− p
C1
C2
C3
C4
C5
C6
C7
C8
1.092 0.821 0.05897 0.02210 0.001426
0.6458 0.5271 0.6916 1.323 1.994
4.066 3.956 3.744 9.671 9.320
1.625 1.731 4.520 1.712 1.672
1.656 1.617 4.190 1.643 1.480
5.029 4.735 4.928 4.673 4.461
0.1722 0.1984 0.1922 0.1686 0.2026
82.65 88.75 50.28 77.27 78.00
Proton data, which are of less direct interest for neutrino beams, have been parametrized also by Wang [106] with a formula similar to the previous one for p–Be interactions: E E C G d2 N = f ( = 0) × g() = [Ap inc eB(p/pinc ) ][e−D (p −F (cos ) ](1 − p/pinc )H p/pinc , d dp
(22)
where pinc and p are incident and secondary momentum in GeV/c and is the production angle. While the longitudinal momentum distribution is consistent with the linear scaling of pions (Eq. (20)), the angular dependence has a more complicated form. With a least square fit to the experimental data of Table 8 and additional data from Allaby et al. [79], Baker et al. [107], Aubert et al. [108], Anderson et al. [109] and Bellettini et al. [110], the parameters of the formula have been determined as A = 1.30, B = 5.354, C = 0.6324, D = 3.508, E = 1.15, F = 4.129, G = 37.34, H = 20.27. The formula is claimed by the author to give a good representation of p–Be data up to 300 GeV/c.
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Fig. 22. − production as a function of psec at 10.9 GeV/c. The Sanford–Wang parameterization, described in the text, is superimposed (from Ref. [99]). Table 11 Comparison of measured and predicted pion multiplicities, N + + N − pinc (GeV/c)
Data
S–W formula
Trilling formula
10 15 20 25 30
1.9–2.3 2.5
1.84 2.19 2.56 3.01 3.55
0.72 0.85 0.95 1.04 1.12
2.9–3.7
5.2. High energy parameterizations Original parameterizations of high energy data from Atherton et al. [90] and Malensek [100] were based only on NA20 data and thus are unable to describe the behavior of the low x data of the NA56/SPY experiment. An improvement at low x with respect to these models has been obtained in the BMPT parameterization, which is fully described in the following. 5.2.1. Atherton and Malensek parameterizations Atherton et al. [90] parametrized ± , K ± and p production, in the thin target approximation, as B 2Cp 2 −C(p)2 d2 N = A e−Bp/p0 e , dp d p0 2
(23)
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Table 12 Values of the parameters corresponding to the empirical parameterization of ± , K ± and p inclusive production in p–Be interactions, for thin targets from Atherton et al. [90]
+ −
K+ K− p p
A
B
C
1.2 0.8 0.16 0.10 0.8 0.06
9.5 11.5 8.5 13.0 −0.6 16.0
5.0 5.0 3.0 3.5 3.5 3.0
Table 13 Values of the parameters corresponding to the empirical parameterization of ± , K ± and p inclusive production in p–Be interactions, for 500 mm targets, in the Malensek formula [100]
+ −
K+ K− p p
A
B
M2
D
3.598 4.122 2.924 6.107 1.708 7.990
177.2 70.60 14.15 12.33 3.510 5.810
0.7077 0.8932 1.164 1.098 1.043 1.116
27.00 11.29 19.89 17.78 −4.314 14.25
while proton production was described as 2Cp 2 −C(p)2 B +1 d2 N (p/p0 )B . =A e dp d p0 2
(24)
The values of the parameters A, B, C are given in Table 12. The Malensek formula [100] is a fit to NA20 data, taken with a 500 mm long Be target (Table 13): (1 − x)A (1 + 5e−Dx ) d2 N , = Bx dp d (1 + pT2 /M 2 )4 where x = p/pinc with p (pT ) momentum (transverse momentum) of the secondary hadron. The cross-section assumes Feynman scaling in x. The power law dependence pT−8 that holds at large pT is modified to (1 + pT2 /M 2 )−4 to account for the observed variation at low pT . The additional term (1 + 5e−Dx ) accounts empirically for the nuclear cascade process which gives more particles at low x in a thick (500 mm) target. Excluding protons, this correction term is small for most of the x range. The parameters A, B, M 2 , D depend on the type of secondary particle produced and are given in Table 13. The parameterization holds for 400 GeV/c p–Be interactions. For other energies it is sufficient to replace the parameter B in the formula with B × pinc /400. For other target lengths (L), the yield production formula can be adapted by taking into account the target production efficiency f (L). In a naive reabsorption model, where the secondaries are reabsorbed in the target without production of tertiaries, f (L) is given by f (L) =
e−L/s − e−L/p 1 − p /s
with p , s absorption lengths for protons and secondary particles.
(25)
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Table 14 Values of the parameters corresponding to the best-fit of the BMPT empirical parameterization of ± and K ± inclusive production in p–Be interactions
K p p
A (mb/GeV2 )
B
a (GeV−1 )
b (GeV−2 )
r0
r1
62.3 7.74 8.69 5.20
1.57 – 12.3 –
3.45 2.45 – 7.56
0.517 0.444 – 0.362
6.10 5.04 5.77 5.77
– – 1.47 –
0.153 0.121 – –
0.478 2 – –
1.05 1.15 – –
2.65 −3.17 – –
Best-fit results on proton and anti-proton production data are also given (see text for details).
5.2.2. The BMPT parametrization The BMPT [101] empirical parameterization of the inclusive invariant cross-sections for + , K + production in p–Be interactions is given by 3 d − E 3 = A(1 − xR ) (1 + Bx R )xR (1 + a (xR )pT + b (xR )pT2 )e−a (xR )pT . (26) dp
∗ ratio of the particle energy to the maximum energy where a (xR ) = a/xR and b (xR ) = a 2 /2xR , with xR = E ∗ /Emax kinematically available in the cms frame. This formula gives a good description of the data from NA20 and NA56/SPY, assuming an approximate factorized form in x and pT and scaling in x. The (1 − x) behavior at large x is theoretically motivated on the basis of quark counting rules derived from Triple-Regge analysis of single-particle inclusive reactions [111,112], while the (1 + Bx) empirically accounts for sub-leading contributions to the Triple-Regge trajectory. The x − behavior empirically accounts for non-direct hadron formation mechanisms at small x. The pT behavior is modeled with the known exponential fall of soft interactions and a polynomial behavior to interpolate the low pT part of the spectrum. The x dependence of a (x) and b (x) is introduced to parameterize the violation of pT invariance observed in the data. The ratio r of positive to negative data ( + / − or K + /K − ) has been empirically parameterized as
r( ) = r0 · (1 + xR )r1 ,
(27)
r(K) = r0 · (1 − xR )r1 .
(28)
The shape of these ratios is supported by the phenomenological analysis of the pp data from Ref. [113], showing that r( ) 1 for x 0, rising to about 5 for x → 1, closely following the u/d ratio of valence quarks in the projectile proton, while r(K) has a (1 − x)−3 behavior for x → 1. NA56/SPY and NA20 data only cover the fragmentation region of the proton at large x and the central region. At large x a functional behavior similar to the one exhibited by pp data is expected. In order to keep the number of free parameters limited, positive and negative mesons are assumed to have the same pT distributions. This has long been known to be only approximate in pp data [114]. The results of the best fit to the data are summarized in Table 14. Some of the parameters appeared to be redundant and have been fixed in the fitting procedure. As an example, the comparison between the empirical parameterization and the experimental data is shown in Fig. 23 for ± and K ± . The proposed empirical formulae are adequate to describe the NA20 and NA56/SPY data with 10% global accuracy. Proton and anti-proton production data, which are of less direct interest for neutrino beams, have been parameterized as 3 d a2 2 bp2T E 3 1 + ap T + pT e−apT , = A(1 + Bx R )(1 − xR ) (29) 2 dp pBe → pX E
d3 dp 3
pBe → pX
−
= A(1 − xR ) xR
1 + ap T +
a2 2 p 2 T
e−apT .
(30)
For anti-protons a functional similar to the one given in (26) has been adopted, except that an exact factorization in xR and pT has been assumed, since this was sufficient to give a reasonable fit to data. For protons the “leading particle
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Fig. 23. Invariant cross-section as a function of pT : (top-left) positive pions; (top-right) negative pions; (bottom-left) positive kaons; (bottom-right) negative kaons. Data collected at the same xL = p/pinc , where p and pinc are the momenta of the detected particle and of the incident proton in the laboratory reference frame, are displayed with the same symbol. The BMPT parameterization [101] described in the text is superimposed.
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Fig. 24. Comparison between the BMPT parameterization [101] and the one-pion inclusive invariant cross-sections in pC interactions at 100 GeV as measured by [88]. Positive (negative) pions are shown in the left (right) panel.
effect” had to be taken into account. A reasonable fit to data has been obtained by following the empirical observation that the longitudinal momentum distributions of the leading nucleon in pp collisions is flat [115], which translates into a linear rise of the inclusive invariant cross-section as a function of xR . The transverse momentum distribution is also affected by the leading particle effect, resulting in an enhanced leading particle production in the forward direction 2 (see for example [72,114]). In the proton fit, this is empirically accounted for by the term (1 − xR )bpT . The parameter a, that controls the shape of the pT distribution for non-leading particle production, has been assumed to be the same for protons and anti-protons. Results of these fits are also given in Table 14. The BMPT parameterization gives a satisfactory description of proton and anti-proton inclusive production, with a reduced 2 of about 1, in the range covered by NA56/SPY and NA20 data. At larger values of x, diffractive proton production should occur. This is not described by the BMPT parameterization. 5.3. Extrapolation to other energies and target materials The NuMI neutrino beam at FNAL is derived from a primary proton beam of 120 GeV/c momentum, equivalent to a center-of-mass energy about two times smaller than that available at NA56/SPY and NA20. In Fig. 24 the BMT parameterizations (from [101]) are compared to data collected with 100 GeV/c protons on carbon target [88], where the extrapolation from Be to C has been made using formulae (31) and (32) (see later). As discussed ∗ above xR = E ∗ /Emax has been used as scaling variable. The agreement between pion data shown in the figure and the BMPT empirical parameterization is excellent up to about x ∼ 0.8. Good agreement is also found when kaon data are considered, although the precision of kaon data from Ref. [88] is poorer.
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Fig. 25. Dependence of from xF and pT , using the Barton et al. and Skubic et al. experimental data.
At lower energies, the comparison with data measured using 24 GeV/c protons on beryllium [80], shows still a reasonable agreement in the shape of the distributions for + and K + , although the predicted + production is 35 ± 15% lower than that measured. This is also true for negative pions, while the agreement is somewhat worse for the other particles. While beryllium targets have been used in most neutrino beams, graphite targets are employed in both the CNGS and the NuMI beams. Prescriptions to rescale the inclusive invariant cross-sections to different target materials may be obtained. Invariant cross-sections Ed3 hA /dp 3 for hadron–nucleus interactions (hA → h X) depend on the mass number A of the target nucleus, via parameterizations of the type: A1 d3 hA2 d3 hA1 = · E , (31) E A2 dp 3 dp 3 where a value for = 23 would correspond to the case where particle production of a nucleus is identical to the production of a single nucleon per inelastic collision. In accordance with the scaling hypothesis, has been found to depend weakly on the incident beam momentum. It depends on the incident hadron type h and it is a smooth function of pT and xF of the produced hadron. Moreover, it has been experimentally observed that, it is almost independent of the detected particle type, with perhaps the exception of anti-protons [88]. A parameterization of as a function of xF has been proposed by Barton et al. on the basis of their own and previous data at pT = 0.3 GeV/c [88]. A pT dependence of has been clearly observed in KS0 and production by Skubic et al. [93]. A suitable representation of the whole set of data can be obtained with the parameterization: (xF ) = (0.74 − 0.55 · xF + 0.26 · xF2 ) · (0.98 + 0.21 · pT2 ),
(32)
where the xF dependence is taken from the fit of Barton et al. at pT = 0.3 GeV/c and the pT dependence is fitted to the Skubic et al. data and normalized in such a way that it reduces to the parameterization of Barton et al. at pT =0.3 GeV/c, as shown in Fig. 25.
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Table 15 Values of the parameters used in the MARS model for pion production
+ −
a
B
C
D
E
F
60.1 51.2
1.9 2.6
0.18 0.17
0.3 0.3
12 12
2.7 2.7
As a conclusion, a conservative estimate of the uncertainty in the extrapolation from beryllium to carbon data in the pT range of interest for neutrino beams: up to ∼ 600 MeV/c is around 5%, to be added to a measurement error of 5–10% for the cross-sections on beryllium, depending on the secondary momentum. The estimate of this systematic uncertainty is based both on data collected by Barton et al. [88] and on the extensive compilation of J. Kuhn on the nuclear dependence of pA → − X interactions [116]. 5.4. The MARS pion production model Another model used to parameterize pion production in proton–nucleus interactions is the MARS model [117], used in the MARS Monte Carlo code. The proton–nucleus cross-section is parameterized as E
d3 pA → dp 3
±X
= R ± (A, E0 , p, pT ) · E
d3 pp → dp 3
±X
(33)
with E0 primary proton beam energy, p, pT total and transverse pion momentum, A the atomic mass of the target nucleus. R ± is parameterized with the Barton et al. [88] and Eichten et al. [80] data to describe atomic mass dependence and scale pp data to pA data via the formula: d A d (pd → ) (pp → ) R = 2 dp dp ±
(34)
while the pp → ± X cross-section is parametrized as d3 pp → E dp 3
±X
p∗ =a 1− ∗ pmax
B
e−p
∗ /C √s
V1 (pT )V2 (pT ),
(35)
∗ are the pion momentum and maximum momentum transferred in the cms. The pT dependence is where p∗ and pmax described by
V1 (pT ) =
(1 − D)e−EpT + De−FpT
for pT 0.933 GeV/c,
0.2625/(pT2 + 0.87)4
for pT 0.933 GeV/c,
2
2
and V2 (pT ) =
0.7363e0.875pT
for pT 0.35 GeV/c,
1
for pT 0.35 GeV/c.
The values of the parameters a, B, C, D, E, F are listed in Table 15. In two detectors neutrino oscillation experiments, a potential source of systematic errors in the shape of the far detector neutrino spectrum is related to the pT spectrum of the produced particles. As an example, Fig. 26 shows the comparison of + production data from the NA20 and NA56/SPY experiments with the BMPT and MARS parameterization [118]. Fig. 27 (from [119]) shows instead the comparison of the BMPT and the MARS parameterizations with the Eichten et al. + data, at 24 GeV/c.
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102
E d3 σ/dp3 (mb/GeV2)
E d3 σ/dp3 (mb/GeV2)
100
10
102
10
1
1 0
0.1
0.2
0.3 0.4 pT (GeV/c)
0.5
0.6
0.7
0
0.1
0.2
0.3 0.4 pT (GeV/c)
0.5
0.6
Fig. 26. Comparison with available high-energy NA20 and NA56/SPY + data of the BMPT (left) and MARS (right) parameterizations.
Fig. 27. Comparison with the + data of Eichten et al. at 24 GeV/c of the MARS and BMPT parameterizations.
0.7
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6. Simulations of neutrino beamlines The calculation of a conventional beam with a Monte Carlo simulation is a delicate task due to complicated cascade processes involved in the neutrino production, from the meson production at the main target, the focusing system and the secondary particle reinteractions along the beam-line materials. Moreover the paucity of the present data on hadroproduction in the relevant region of the phase space can limit systematically the precision in the calculations. For LBL experiments an additional problem is the small solid angle (d 10−10 sr) at the detector location, that forces the simulation of billions of p.o.t’s to achieve a percent statistical accuracy in the results. Two main approaches are used: • fast simulation programs that parameterize production in terms of hadronic cross-sections in the target, make a simplified description of the beamline elements and produce weighted events; • full simulation programs based on the available codes for hadronic showers simulation, such as GEANT, MARS, FLUKA to produce a precise neutrino beam description. 6.1. Fast simulation programs The underlying idea in fast simulation programs is to force all the mesons to decay into a neutrino and to force all neutrinos to cross the detector volume. A weight is then assigned to each neutrino, proportional to the process probability. The fast simulation program, quoted in Ref. [101], to be referred for more details, can be considered as an example. The program is a stand-alone code developed as a tool that allows to optimize all elements and the geometry (in 3-D) of the beamline providing the results in terms of neutrino spectra and distributions at large distance with high statistics and in short time. The statistical accuracy of this way of simulating neutrino beams does not depend much on the distance between the detector position and the neutrino source as is the case for classical unweighted methods. Since all mesons—within the acceptance of the focusing optics—are exploited to produce neutrinos in the detector, the statistical accuracy is proportional to the inverse of the square root of the number of generated positive pions (for beams), namely about the number of generated proton interactions on target. A statistical accuracy of better than a percent is thus obtained with less than 105 p.o.t., for any size of the detector surface. In order to give a more quantitative appreciation of the accuracy that one can obtain in fast simulation of neutrino beams, the comparison with the published neutrino spectra measured by the CHARM II detector [36] exposed at the CERN–WANF beam is presented. The WANF neutrino beamline at CERN, to which the CHARM II detector was exposed, is described elsewhere [31]. The facility was run during several years of operation either by selecting positively charged particles ( beam) or negative ones ( beam). Neutrino/anti-neutrino interactions were collected in the CHARM II detector and fully reconstructed [36]. Fig. 28 shows the agreement between the CHARM II prediction and the fast simulation from Ref. [101]. The high energy tails of the distributions are dominated by the production of high energy secondary mesons peaked in the forward direction, and are practically insensitive to the magnetic focusing. The good agreement between the two simulations indicates that high xF production on target is well simulated and that reinteractions on the material along the beam-line are correctly taken into account. The agreement in the focusing/defocussing energy range is an indication that low xF production is correctly generated at least up to 10 mrad (the WANF angular optics acceptance). The fact that also the wrong sign contamination in the simulation behaves as the data, means that tertiary production in target and downstream material (mainly the horn neck) is described to a sufficient level of approximation. As a conclusion, due to the approximations involved in the modeling of particle re-interactions and transport along the beamline a fast simulation has its main use in the optimization of the neutrino beamline optics and may be of limited use for a full appreciation of beam systematics. 6.2. Full Monte Carlo neutrino beam calculation The precise calculation of a conventional neutrino beam requires the use of full Monte Carlo simulations in order to properly account for all the physical processes involved in the neutrino generation starting from the meson production
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Fig. 28. The WANF neutrino (left) and anti-neutrino (right) fluxes at the CHARM II detector: the dotted lines are experimental data from Ref. [36], the continuous line is the beam simulation from Ref. [101]. A logarithmic scale is used to highlight the spectral behavior at high energy as well the wrong sign contamination.
at the main target. In long-baseline simulations, different calculation methods are used to recover the effect of the small solid angle seen by the detectors at large distance which dramatically affects the neutrino yield per p.o.t. As an example, in the CNGS beam calculation the mesons are forced to decay in the direction of the detector and the neutrino flux is then properly rescaled. Different programs are used to simulate hadronic and electromagnetic interactions, particle decay and particle transport in complex geometries, providing a detailed evaluation of the neutrino beam characteristics. Of particular interest are the generators of hadronic interactions that are used in K2K, MiniBooNE, CNGS, NuMI and also in testing the performance of new facilities, such as the Neutrino Factory and SuperBeams. An accuracy of ∼ 30% is generally expected in these calculations. In particular, an agreement at the 15% level with the existing data on meson production was found with the FLUKA package [120]. A precision of few percent in the neutrino beam prediction can be obtained by a fine tuning of hadronic generators to the existing data. 6.2.1. The Geant 3.21 and MARS simulation packages The most common simulation package in use is Geant 3.21 [121], which is nearly 30 years old. Its limits are mainly in the simulation of hadronic showers, based on the 1992 release of the FLUKA model (GFLUKA) [122] or of the GHEISHA model [123]. Its main advantage is the use of a simple geometrical modeling of detector shapes and materials. Its development was discontinued about 10 years ago to allow its re-design and re-engineering through modern object oriented techniques, in the form of the GEANT4 package. The comparison of the meson yields in the forward direction as a function of the meson momentum P, as measured with a 450 GeV proton beam on a 100 mm Be target by the NA56/SPY and NA20 (P > 67.5 GeV/c) experiments with the GFLUKA predictions shows large discrepancies, in particular for negative mesons which are largely overestimated (see Fig. 29). In this comparison, the NA20 measurements were corrected for the different primary proton beam momentum (400 GeV/c). The MARS Monte Carlo code [124] has been in continuous development from about 25 years to allow threedimensional simulation of electromagnetic and hadronic cascades in the energy range from a fraction of eV to about 100 TeV. MARS makes use of a quite complicated mixture of parameterization of hadronic cross-sections, phenomenological models and data-driven production models (see for example, the MARS model for pion production described in Section 5.4). Extensive benchmarks for MARS have been reported in several studies [125], spanning a wide energy range from dosimetry applications to muon collider studies. Some examples of its application for neutrino beamline studies will be shown later, in connection with the NuMI beamline (see Figs. 42, 43).
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Fig. 29. Meson yields in the forward direction for 450 protons on a 100 mm Be target. NA56/SPY or NA20 data (•) compared with the FLUKA (◦) and GFLUKA ( ) predictions.
6.2.2. The FLUKA Monte Carlo Hadron–nucleus interactions are described in all FLUKA-based models by a Monte Carlo implementation of the Dual Parton Model code (DPM) [126] which provides a theoretical framework for describing hadron diffractive scattering
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0.01
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θ (rad) Fig. 30. The measured K/ ratios of particle yields at 40 GeV/c as a function of the production angle with respect to he incoming proton beam direction: FLUKA (◦) and GFLUKA ( ) predictions compared to NA56/SPY data (•).
both in hadron–hadron and hadron–nucleus collisions. The DPM model can be extended to hadron–nucleus collisions by making use of the Glauber–Gribov approach [127]. The FLUKA code has undergone a continuous development and its latest version includes an hadronic generator model that has been greatly improved with respect to the 1992 version embedded in GEANT 3.21 (GFLUKA). A comparison of these hadronic generators can be found in Ref. [128]. Modifications were made to the FLUKA implementation of the DPM model along the years in order to achieve a better description of secondary particle yields. Several sets of data ranging from 16 to 450 GeV hadron–nucleon and hadron–nucleus collisions have been used to determine the behavior of the fragmentation functions, using precise experimental data on hadron multiplicity at 200 GeV as the initial constraint. The reinteractions of secondary hadrons as well as the description of nucleon and pion interactions at medium/low energies are also significantly improved in the present version of FLUKA [120]. The FLUKA predictions for proton interactions in 100 mm Be target at 450 GeV/c compared with experimental measurements performed by the NA56/SPY and NA20 Collaborations show a substantial improvement with respect to GFLUKA (see Figs. 29 and 30). The and K absolute yields are reproduced at the ∼ 15% level over the whole secondary momentum range except for a few points mostly for K − (see Figs. 31, 32). The agreement for the corresponding K + / + ratio is at the level of 10% in the momentum region 30.100 GeV/c which is expected to contribute mostly to the high energy neutrino flux (see Fig. 30). Neutrino production by p and p can occur only by successive reinteractions along the beamline. These contributions are expected to be marginal except for the neutrino flavors generated by the defocused sign mesons, i.e. the muon and electron antineutrinos in a muon neutrino beam. A comparison between FLUKA predictions and experimental data for p/p production in a Be target is shown in Fig. 33. 6.2.3. The GEANT4 simulation package The GEANT4 simulation package [129] represents a major effort to re-design and re-engineer the GEANT 3.21 Monte Carlo, using modern object oriented software techniques. Some effort has been put also in upgrading and extending existing hadronic generators. GEANT4 uses mainly parameterized models based on experimental data, such
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Fig. 31. Pion yields from 100 mm Be target at different momenta P and production angle with respect to the incoming proton beam direction: FLUKA predictions compared with the NA56/SPY (P 40 GeV/c, •) and the NA20 data (P 67.5 GeV/c, •, the difference on the primary proton momentum 400 GeV/c have been accounted for). Both data and Monte Carlo in the 7.337 GeV/c range are rescaled by a common factor different for each momentum value as quoted in the labels, i.e. 67.5 × 15 means that at P = 67.5 GeV/c, the data are rescaled by a factor 15.
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Fig. 32. Kaon yields from 100 mm Be target at different momenta P and production angle : FLUKA predictions compared with the NA56/SPY, P 40 GeV/c, and the NA20 data, P 67.5 GeV/c, (see Fig. 31 caption for more details).
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Fig. 33. Proton yields from 100 mm Be target at different momenta P and production angle calculated by FLUKA and compared with the NA56/SPY, P 40 GeV/c, and the NA20 data, P 67.5 GeV/c, (see Fig. 31 caption for more details).
as GHEISHA (also available in Geant 3.21), models based on parton string models for ECMS 5 GeV/c and cascade models (HETC [130], INUCL [131]) for ECMS 5 GeV/c. A major input at low energy (pinc 15 GeV/c) is expected from the HARP experiment. An interesting option is the availability of beam simulation tools that extend the scope of GEANT4 to the accelerator domain and may be useful to optimize the design of Neutrino Factories [132]. 7. Examples of flux computations for present and future neutrino beamlines Some examples of simulation of neutrino beamlines, using either the full simulation approach or the fast simulation approach will be presented. The examples will cover the subject at different level of depth, reflecting also the matureness of the field: from full, detailed simulations for existing experiments (e.g. the WANF for NOMAD) to feasibility studies, as is the case for neutrino factories. The use of different simulations for a neutrino beamline can help in assessing the level of the systematic errors. This is the case of some experiments (e.g. MiniBooNE, K2K) that use both fast simulations based on hadron production data parameterizations and full simulations based on packages, such as FLUKA, Geant4, MARS. Systematic errors influence both the evaluation of the neutrino flux normalization and its shape and composition. 7.1. The CERN WANF neutrino beam: a case study The NOMAD experiment [21] has searched for → and → e oscillations at the CERN SPS [31], using a conventional beam (E 24 GeV) produced by 450 GeV/c protons on a Be target. The → e oscillations were searched for as an excess of e events with respect to what expected from the natural beam contamination: e / ∼ 1% at a distance of 840 m from the Be target. The high resolution and granularity of the NOMAD detector allowed a study of a conventional neutrino beam with unprecedented accuracy and statistics (1 million of -CC events), resulting in a stringent benchmark for conventional neutrino beam studies. A complete analysis of the beam was performed with a full simulation of the beamline from the target up to the NOMAD detector using the FLUKA standalone generator. In comparison, the use of G-FLUKA instead of FLUKA for proton interactions in the beryllium target introduced an enhancement ∼ 15% in the neutrino flux with a relevant increase of the and e contaminations.
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To obtain more precise meson production predictions, correction functions to the secondary particle production were introduced for ± , K ± , p and p, based on the residual differences between the predicted (FLUKA) and measured (NA56/SPY and NA20) particle yields in a 100 mm thick target. For a given momentum, both the experimental and Monte Carlo (FLUKA) yields of secondaries were convoluted with the corresponding WANF angular acceptance and then integrated over all production angles (max 10 mrad). The ratio of these two integrals, r(p), was defined as the weight at a given momentum P:
( i Yi · 2 i · · i )DATA
r(p) = , (36) ( j Yj · 2 j · · j )FLUKA where Yi is the particle yield for a selected angle i , = 0.2 mrad is the angular acceptance of the NA56/SPY and NA20 data and i is the efficiency of the transport for the secondaries which contribute to the neutrino flux at NOMAD, as was determined by Monte Carlo from the initial angular distribution dN/di : i =
dN 1 · . di Yi i
(37)
For the momentum values where only the yields in the forward direction ( 0.1 mrad) were measured the weights were simply the ratios of the measured to predicted particle yields. The next step was to fit the obtained set of weights to polynomial functions of the particle momentum for each charged particle, in order to obtain reweighting functions f (p) usable at all momenta (see Fig. 34). Systematic and statistical errors of the experimental measurements were combined in quadrature and included in this reweighting procedure and in the fits. The KL0 yields were obtained from the NA56/SPY and NA20 measurements of K + and K − yields using a “quarkcounting” method KL0 =
K + + (2n − 1)K − , 2n
(38)
where n is the ratio of u to d structure functions of the proton evaluated at xR , the ratio of the kaon energy in the center of mass to its maximum possible energy at its pT . This KL0 parameterization is well described by FLUKA, except for an offset value rp , as a function of the momentum p. It follows that the fK 0 reweighting function is given by (see Fig. 34): fK 0 (p) = [+ (p)fK + (p) + − (p)fK − (p)] · rp ,
(39)
where fK ± (p) are the K ± reweighting functions and the coefficients ± (p) are determined by n and the (K − /K + ) yield ratio: + (p) =
1 , 1 + (2n − 1) · (K − /K + )
(40)
− (p) =
(2n − 1) · (K − /K + ) . 1 + (2n − 1) · (K − /K + )
(41)
To each generated particle emerging from the target the reweighting functions were then applied. The impact of these corrections on the neutrino flux is a reduction of the /pot by 5% but with larger bin-to-bin energy spectrum variation especially for the e / ratio (see Figs. 35 and 36). The comparison of the measured and the predicted neutrino energy spectra with positive focusing shows that the results of the simulations are in good agreement with the data (see Fig. 37). The shape of the CC energy spectrum is predicted to better than 2% up to 150 GeV/c. The only statistically significant difference, of up to 8% but smaller than the estimated systematic uncertainty, is observed in the CC sample. Both the shape and the total number of e CC events are well reproduced, confirming the validity of the adopted KL0 description. Similar agreement was found for neutrino beams with/without focusing, confirming the validity of the beamline simulation and allowing for the possibility to perform a sensitive search for → e oscillations at the WANF. The e energy distributions for data and Monte Carlo from this search are shown in Fig. 38.
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p (GeV/c) Fig. 34. The reweighting functions f for ± , K ± and K 0 as a function of the meson momentum p. The points are the values of r(p), the curves are the result of fitting them with a polynomial function. Similar curves were obtained for proton production.
The fluxes of the four neutrino flavors at NOMAD were predicted with an overall uncertainty of about 8% for and e , 10% for , and 12% for e (energy-dependent and normalization errors combined), see Table 16 and Figs. 39 and 40 for more details [31], [133]. Major contributions to these uncertainties were from secondary particle production at the beryllium target, proton beam positioning on the target and particle reinteractions along the beamline. Most of these uncertainties canceled in the e / ratio resulting in an energy-dependent uncertainty from 4% to 7% and a normalization uncertainty of 4.2%. These uncertainties are essentially due to the limited amount of hadroproduction data available from the NA56/SPY and NA20 experiments and to the angular integration procedure adopted in the calculation of the meson production reweighting functions.
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Fig. 35. MC comparison of fluxes at WANF with (full line) and without (dashed line) correction functions f to the meson production in Be target.
7.2. Simulation of the K2K beamline The K2K neutrino beam (E 1.3 GeV) is produced by pion decay in flight ( + → + ) using 12.9 GeV protons from the KEK PS impinging on a Al target. A full simulation of the neutrino beamline was based on the GCALOR/FLUKA model of the GEANT3 package, while a fast simulation was based on the Sanford–Wang parameterization for hadron production at the primary target and GEANT 3.15 for secondary interactions and propagation along the beamline. Another model for + production was based instead on a modified Sanford–Wang formula, that uses experimental results from Cho et al. [81]. In this experiment yields were measured, instead of cross-sections. The parameters for + production of this modified production model are shown in Table 17. Secondary particles were then traced along the neutrino beamline by a GEANT3 based Monte Carlo simulation. The dominant neutrino source is pions, with a small fraction coming from and K decays. The expected neutrino beam at the near location and at the Super-kamiokande location are shown in Fig. 6. Prediction of the far detector spectrum in absence of oscillations is of utmost importance in any neutrino oscillation experiment. In K2K this was done by an extrapolation from a near detector by using a nominal FAR/NEAR ratio estimated by a beamline MC simulation.
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Fig. 36. The ratio of the MC calculated e / ratio with to without correction functions f to the meson production in Be target.
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Fig. 37. Neutrino energy spectra (left) for the data (points with error bars) and the Monte Carlo (histogram) for CC, ¯ CC and ¯ e CC interactions and their corresponding ratios (right) in the NOMAD detector. Only statistical errors are shown.
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Visible energy (GeV)
Fig. 38. Left: neutrino energy spectra for the data (points with error bars) and the Monte Carlo (histogram) for e CC, in the NOMAD detector. The Monte Carlo distribution is normalized using the predicted relative e / ratio. Only the statistical errors are shown. The background contribution is shown in the hatched histogram. Right: predicted and measured ratio Re of e to CC events as recorded in the NOMAD detector, from [21]. Quoted errors include also systematics.
Table 16 Different contributions to normalization errors for neutrino fluxes in the WANF neutrino beam Source of uncertainty
e
e
e /
Yields of secondary particles Proton int. downstr. of the target Reinteractions of secondaries Beam position and divergence Collimators, horn and reflector Amount of material
0.034 0.002 0.014 0.056 0.007 0.012
0.029 0.024 0.070 0.021 0.034 0.022
0.039 0.003 0.017 0.058 0.015 0.007
0.064 0.013 0.067 0.035 0.024 0.012
0.036 0.003 0.018 0.002 0.011 0.005
Total
0.068
0.091
0.074
0.103
0.042
The beamline MC simulation of K2K is confirmed by a pion monitor (PIMON), which is occasionally put in the beam to measure the kinematics of the pions after their production and subsequent focussing, down to ∼ 2 GeV/c. Below this value, calculations rely on MC extrapolations. The error on the observed number of events in the K2K far detector (SK) is dominated by contributions from uncertainties of normalization (±5%) and far/near ratio (±5%). The data taken by the Harp experiment with a K2K target replica of different thickness (∼ 15 Mevts) will be of great importance for a reduction on the systematic errors on the beam knowledge (actually ∼ 7%) in the region p 2 GeV/c and their implementation inside the K2K beamline MC is under way. The recently published HARP results, see Ref. [134], show similar neutrino energy spectra arising from previous K2K and new HARP + production assumptions in the K2K beamline MC. 7.3. Simulation of the CNGS beamline The CNGS beamline (NGS reference beam [26]) was carefully studied with full simulation packages such as FLUKA, as shown in Fig. 5 and at the beginning for a rapid optimization with the neutrino beamline fast simulation quoted in paper [101]. The reliability of the second method was checked with an extensive comparison using a full beam simulation based on the FLUKA package [120] for secondary particle production and on GEANT for tracking along the beamline (FLUKA/GEANT in Fig. 41). The method followed in the WANF neutrino beam calculation based on a fine tuning of meson produced in the graphite target by FLUKA stand-alone allows to predict the CNGS beam with an expected normalization uncertainty
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v Uncertainty
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ve
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Fig. 39. Total energy dependent error on the neutrino fluxes in the WANF neutrino beam.
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ve /v
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Fig. 40. Total energy dependent error on the e / ratio in the WANF neutrino beam.
as small as ∼ 3.8% for and ∼ 3.1% for the e / ratio due to the longer base-line, where the contribution of KL0 and of particle reinteractions are strongly reduced, and to the reduced amount of material between the meson production target and the end of the decay tunnel [133,135]. Before concluding, it is worth mentioning that early simulations of the CNGS beamline based on a full GEANT3 simulation disagreed with those presented here, being too optimistic by more than 20% in hadron production in the graphite target.
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Table 17 Fitted parameters for + production for the Sanford–Wang formula, from Sanford–Wang [99] and Cho et al. [81]
Sanford–Wang Cho et al.
C1
C2
C3
C4
C5
C6
C7
C8
1.092 0.94
0.6458 1.08
4.066 2.15
1.625 2.31
1.656 1.98
5.029 5.73
0.1722 0.137
82.65 24.1
10-10
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v
v
10-11
10-12 ve
10-13 0
50
100 Eν (GeV)
150
200
Fig. 41. The CNGS neutrino fluxes at Gran Sasso (732 km from target). Comparison between FLUKA/GEANT simulation (the dotted lines) as described in the text and the parametrized simulation (continuous line) A logarithmic scale is used to make evident the spectral behavior at high energy as well the wrong sign contamination.
7.4. Simulation of the NuMI beamline One of the largest uncertainties in the extrapolation of the MINOS near detector spectrum to the far detector site is due to the modeling of hadron production from the NuMI target. Fig. 42 shows the expected event rates at the near detector, while Fig. 43 shows the ratio of the far detector flux to the near detector neutrino flux for four different hadron production models, as computed in [136]. The different predictions differ by up to 30% in the absolute value and up to 10% in the relative far/near ratio, depending on the hadron production model used. As a further example, Table 18 reports the number of CC events in the MINOS Far detector as computed in [137] with the same models. The lack of good quality hadroproduction data is quite evident, also in this case. As an example, Fig. 44 shows the distribution in the p − pT plane for secondary pions produced on the NuMI target at FNAL, weighted by their contribution to the neutrino event rate at the far (top) and near (bottom) detector locations. Superimposed are the present available data from experiments [90,88,91]. Holes are to be covered by the proposed MIPP experiment at Fermilab.
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106 CC Events/kt/year
100 GFLUKA BMPT MARS MALENSEK
80 60 40 20 0 0
5
10
15
20
25
30
20
25
30
Eν (GeV) GFLUKA BMPT MARS MALENSEK
Difference from Ave. %
40 20 0 -20 -40 0
5
10
15 Eν (GeV)
Fig. 42. Prediction of the absolute neutrino rates at the MINOS near detector using four hadronic models [121,101,124,100], as computed in [136].
7.5. Simulation of the Neutrino Factory beam In this case the task is much easier, as the essential point is the pion production in heavy target at low energy. A full simulation, based on programs such as FLUKA or MARS, or a fast parameterization can be used. New results with a high Z target from the HARP experiment at the CERN PS will probably help to settle this point. At low momenta, existing data on -production are mainly on Be targets with a ∼ 15% precision mostly due to acceptance uncertainties. They cover only a small fraction of the phase space (see Fig. 45 for details) requiring extrapolations by production models which are known with large uncertainty. Current simulations show 30–100% discrepancies with respect to the available data. 7.6. Simulation of low energy beam dump experiments Both LSND at LAMPF [138] and KARMEN at ISIS [139] use the same Monte Carlo code to simulate the neutrino flux by low energy protons on the complex geometries of a spallation target or beam stop. The flux is calculated for both , decay at rest (DAR) and in flight (DIF). The geometrical configuration of the target is handled by the geometry package MCNP [140]. The parameterization of pion production cross-sections is based on the data of Crawford et al. [73] and Cochren et al. [74] at Tp =585 and 730 MeV/c, that cover a wide variety of nuclear targets. The produced pions are then traced through the target geometry, where they are allowed to interact or decay. As the E866 experiment [141] measured the distribution of stopped pions inside an instrumented beam stop, it was possible to compare the Monte Carlo predictions with data, obtaining for the ratio (Monte Carlo/E866 data) the value 1.001 ± 0.024. Uncertainties of the calculated neutrino fluxes range from 6.7% for e to 12% for e and . The uncertainty on the e and fluxes is dominated by the uncertainties affecting the pion production measurements. The same Monte Carlo code was applied for studies of new facilities, such as the SNS at Oak Ridge [142], with proton beams in the 1–3 GeV energy range and intensities in excess of 1 mA. As a benchmark, Table 19 reports some measured and calculated cross-sections for
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106× Far/Near
2 1.5 1 GFLUKA BMPT MARS MALENSEK
0.5 0 0
5
10
15
20
25
30
20
25
30
Difference from Ave. (%)
Eν (GeV)
20
0 GFLUKA BMPT MARS MALENSEK
-20 0
5
10
15 Eν (GeV)
Fig. 43. Prediction of the ratio of the far neutrino flux to the near neutrino flux using four hadronic models [121,101,124,100].
Table 18 Number of CC events at the MINOS far detector, in two energy regions, as computed with different hadronic models. Model
E 6 GeV/c
E 40 GeV/c
GFLUKA FLUKA MARS BMPT
267.8 255.6 275.1 248.1
487.7 367.2 443.1 402.8
interactions at beam dumps, where the agreement suggests that Monte Carlo simulations of fluxes at beam dumps are in good shape. 8. New hadroproduction experiments Some new experiments have just been concluded, while others are foreseen for a better study of neutrino beamlines. These include the completed HARP experiment at the CERN PS for the target study of a neutrino factory and for a better knowledge of the K2K and MiniBooNE neutrino beams and the MIPP experiment at FERMILAB for a better understanding of the NuMi beam. A proposal to use the NA49 detector at CERN (P322 [144]) to study hadroproduction for use in long-baseline experiments (mainly MINOS) and atmospheric neutrino calculations was also studied. Its aims were similar to the ones of the E907/MIPP experiments at FNAL. A small test run (1 week long) took place with the NA49 setup in June 2002, collecting 5 × 105 triggers at 158 GeV/c and 1.6 × 105 triggers at 100 GeV/c with a 1% I carbon target [145]. These data will be mainly useful for atmospheric neutrinos simulations.
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Low Energy Beam Far Detector
1 Np>100
Np>30
0.8
Np>8 0.6 νµ CC Events
0.4 0.2
PT (GeV/c)
0 0
20
40
60
80
100
120 Atherton 400 GeV/c p-Be
Near Detector 1 0.8
Barton et al. 100 GeV/c p-C
0.6 SPY 450 GeV/c p-Be
0.4 0.2 0 0
20
40
60
80
100
120
P (GeV/c) Fig. 44. The distributions in p, pT for secondary pions on the NuMI target.
measured fraction of cross section
1
Eichten et al., π+ Allaby et al., π+ Abbott et al., π+
0.8 0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
1
xlab Fig. 45. Fraction of pion production cross-section measured by experiments in p–Be interactions at low energy.
8.1. The HARP experiment The design of the sophisticated set-up of the neutrino factory requires a large R&D programme which includes studies on hadron production, muon cooling and storage facilities. In this context, the HARP experiment [51] at the CERN PS was proposed to measure the secondary hadron production cross-section d2 /dpT2 dpL on various nuclear
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Table 19 Comparison data/ Monte Carlo for some typical reactions at beam dumps Reaction 12 C( , e− )12 N e gs 12 C( , e− )12 N ∗ e 56 F e( , e− )X e e− (e , e− )12 Ngs 12 C( , e− )12 N e gs 12 C( , )X 2 H (, e)pp
Exp.
Exp result (×10−42 cm2 )
Theory (×10−42 cm2 )
KARMEN
9.3 ± 0.4 ± 0.9 5.1 ± 0.6 ± 0.5 256 ± 108 ± 43 0.32 ± 0.04 ± 0.03 8.9 ± 0.3 ± 0.9 1060 ± 30 ± 180 52 ± 18
9.3 5.4 273 0.30 9.3 1380 54.3
LSND
E31 [143]
TOF
CHERENKOV SPECTROMETER B = 1.5T
TPC
DRIFT-CH DRIFT-CH DRIFT-CH DRIFT-CH
Fig. 46. The HARP apparatus. The proton beam is coming from the left.
targets by proton and pion beams (p/p 0.24%) in the 1.5–15 GeV/c momentum range with different purposes: • to obtain adequate knowledge of yields, for an optimal design of a neutrino factory: yield per incident proton per GeV, transverse (pT ) and longitudinal (pL ) momentum distribution which affect the efficiency of the transverse capture and the first phase rotation respectively; • to improve substantially the calculation of the atmospheric flux, needed for a refined study of atmospheric oscillation parameters; • to measure the low-momentum backward-going yield for a high-intensity stopped-muon source; • to increase the reliability of hadron generators in M.C. simulations. The HARP detector (see Fig. 46) consists of forward ( < 20◦ ) and large-angle ( < 160◦ ) detection systems. At the large-angle tracking and particle identification (PID) are performed by a 90% Ar and 10% methane time projection chamber (TPC) in a solenoid which contains the target, surrounded by a barrel of resistive plate chambers (RPC). The forward spectrometer is built around a 0.4 T dipole magnet for momentum measurement with large planar drift chambers (NDC, 340 m of resolution) for particle tracking and three detectors used for PID: a time-of-flight scintillation counter wall (TOFW), a threshold Cherenkov detector (CHE) and an electromagnetic calorimeter (ECAL). The incoming beam particles are tagged by two Cherenkov counters and three timing scintillation counters BTOF which provide also their interaction time at the target. The beam particle direction and their impact points on the target are measured by multi-wire proportional chambers. Data were taken with different thin and thick targets: Be, C, Al, Cu, Sn, Ta, Pb and H2 , D2 , N2 , O2 cryogenic targets. Dedicated measurements with the target used by the K2K (∼ 60 cm Al) and MiniBooNE (∼ 65 cm Be) experiments
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Table 20 Main data sets taken by HARP at CERN PS in the 2001–2002 runs Target
Energy (GeV)
Length ()
Events (106 )
Be C Al Cu Sn Ta Pb N7 O8 H1 D1 H2 MiniBooNE repl. K2K repl. H2 O
±3, ±5, ±8 ± 12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±5, ±8, ±12, ±15 ±3, ±8, ±14.5 +8.9 +12.9 +1.5
2%, 5%, 100% 2%, 5%, 100% 2%, 5%, 100% 2%, 5%, 100% 2%, 5% 2%, 5%, 100% 2%, 5%, 100% 6 cm 6 cm 6 cm 6cm 18 cm 5%, 50%, 100%, replica 5%, 50%, 100%, replica 10%, 100%
233.2
58.4
13.8 22.6 15.3 9.6
were also performed at 12.9 and 8.9 GeV/c incident proton momenta, respectively (see Table 20 for details). High statistics, about 106 events per setting, and low systematics are required to obtain a good precision on the inclusive crosssections to be measured for the optimization of the Neutrino Factory front stage and the knowledge of the atmospheric flux. Globally about 420 millions of events were collected. The experiment requires momentum measurements in the 100 MeV/c–10 GeV/c range, have a large acceptance (also in the backward direction) and have a good e, , , K, p identification. Particle trajectory and charge are reconstructed by fitting, extrapolating and matching the three-dimensional track segments in the NDC modules using the Kalman Filter technique. The reconstruction efficiency was track ∼ 85% with the momentum p and polar angle dependence well described by Monte Carlo. The resulting momentum and angular resolution were measured directly with the beam particles in runs without target, i.e. p ∼ 150 MeV/c and ∼ 1.5 mrad at 5 GeV/c [134]. Different techniques for particle identification were used in HARP (see Fig. 47), with a high redundancy covering almost the full acceptance region. At low momenta the particle identification (PID) is performed by dE/dx measurement in the TPC complemented by the measurement of particle time-of-flight with the beam BTOF and TOFW [146] counters with a precision tof = 180 ps on a distance of ∼ 10 m, which allows the separation at 90% C.L. of pions from protons and from kaons produced in the target up to 5.5 and 3 GeV/c momentum, respectively. This is complemented by the Cherenkov threshold detector, Ethr = 2.6 GeV for pion, which is used for hadron–electron and pion–proton/kaon separation below and above 2.5 GeV/c, respectively. The electromagnetic calorimeter is used only to separate hadrons from electrons below 2.5 GeV/c to study the Cherenkov performance. In addition, e/ separation by t.o.f measurements is provided by the RPC barrel surrounding the TPC. The secondary 0 measurement and beam muon identification were performed with an electromagnetic and a hadron calorimeter. First results from HARP have been obtained for a better understanding of the K2K beamline. The + production from 12.9 GeV/c protons impinging on a 5% interaction length Al target was measured in the 0.75 GeV/c < p < 6.5 GeV/c momentum range within 30 mrad < < 210 mrad polar angle well matched to the K2K experiment covering ∼ 80% and ∼ 65% of the space phase of interest for the neutrino flux at the near and far detector, respectively. Fig. 48 shows the projections of the double-differential + production cross-section d2 /dp d as a function of p in selected bins of , for p–Al data at 12.9 GeV/c. The overall error on the total cross-section is 5.8%. The average statistical error is 1.6% per point, while the average point-to-point full error is 8.2%. Data were fitted to the Sanford–Wang parameterization, the results of the fit are reported in Table 21. Globally, these data resulted compatible with but more precise than, older pion production Al data, allowing to improve the neutrino beam knowledge in the K2K experiment (see Fig. 49). The uncertainty of the neutrino flux prediction in K2K [16] was dominated by the precision in the forward + production arising from the interactions of the 12.9 GeV/c protons in the Al target. The HARP-based neutrino prediction
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102
Time of Flight Difference (ns)
dE/dx (KeV/cm)
10
10
1
10-1
1 10-1
0
1
1
2
3
Momentum (GeV/c)
4
5
6
7
8
9
10
Momentum (GeV)
1 0.999 0.998
Velocity (c units)
0.997 0.996 0.995 0.994 0.993 0.992 0.991 0.99 0
1
2
3
4
5
6
7
8
9
10
Momentum (GeV) Fig. 47. Particle identification methods in HARP: dE/dx (TPC), time of flight difference (TOF wall) and particle velocities in C4 F10 Cherenkov for , K and p as a function of the particle momentum.
was obtained by substituting the original + production cross-section assumed in the K2K beam Monte Carlo with the Sanford–Wang parameterization of the HARP data, while keeping unchanged all other ingredients of the K2K beam simulation. The resulting neutrino flux at the near and far detector sites (normalized to a unit area) and its ratio, resulted in good agreement to those from the original K2K Monte Carlo especially below 1.5 GeV neutrino energy (see Fig. 49). The current total systematic error attached to the far-to-near ratio in the K2K analysis is of the order of 7%. The error associated with the HARP measurement is below of 1% since most errors in the cross-section cancel in the ratio, giving the real possibility to achieve a considerable reduction of the total uncertainty with these HARP measurements.
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600
600 30-60 mrad
60-90 mrad
400
400
200
200
0
0 0
2
4
6
0
2
6
600
600 90-120 mrad d2σπ / (dp dΩ) (mb / (GeV/c sr))
4
120-150 mrad
400
400
200
200
0
0 0
2
4
6
0
2
4
6
600
600 150-180 mrad
180-210 mrad
400
400
200
200
0
0 0
2
4
6
0
2
4
6
p (GeV/c) Fig. 48. Projections of the double-differential + production cross-section as function of pion momentum in different bins of the pion polar angle for p–Al data at 12.9 GeV/c, as measured in HARP.
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Table 21 Sanford–Wang fit to HARP p–Al data at 12.9 GeV/c. The errors refer to the 68.27% C.L. for seven parameters C1
C2
C3
C4 = C5
C6
C7
C8
440 ± 130
0.85 ± 0.34
5.1 ± 1.3
1.78 ± 0.75
4.43 ± 0.31
0.135 ± 0.029
35.7 ± 9.6
p–Al
Φnear (a.u.)
0.25
2.5
0.2 0.15 2
0.1
0 0
0.5
1
1.5
2
2.5
3
Eν (GeV) 0.25
Φfar/Φnear (10-6)
0.05 1.5
1
Φfar (a.u.)
0.2 0.15 0.5
0.1 0.05 0 0
0.5
1
1.5 Eν (GeV)
2
2.5
3
0 0
0.5
1
1.5
2
2.5
3
Eν (GeV)
Fig. 49. Muon neutrino fluxes in the K2K near (top-left) and far (down-left) detector, unit-area normalized, and their far-to-near ratio (right) as a function of the neutrino energy as predicted by the default K2K Monte Carlo simulation (dotted histogram and empty squares with error boxes) and by including the HARP + production measurements (filled circles with error bars).
8.2. E907 (MIPP) The MIPP (FNAL-E907) experiment [89], approved in November 2001, started the data taking in 2005 after an engineering test-run. It make use of 5–80 GeV secondary beams of protons, anti-protons, ± , K ± from the 120 GeV main injector at Fermilab, to measure particle production cross-section on various nuclei. Its goals include: • a model independent understanding of neutrino production for MINOS at Numi, i.e. the study of meson production from a MINOS-like target at 120 GeV; • tuning of Monte Carlo simulation codes (GEANT, MARS, . . .) for atmospheric neutrino experiments, extensive air shower experiments; • low energy pion production for the design of Neutrino Factory/Muon Collider beams; • search for glueballs, non-perturbative QCD studies, nuclear scaling. The planned data taking is shown in Table 22 and has recently started. The hadroproduction spectrum on a MINOS target can be measured with the Main Injector Beam that closely matches the beam emittance used in NUMI. As MINOS will not build a hadronic hose [147], that would have improved the far/near flux ratio uncertainties, hadroproduction measurements such as the ones MIPP can provide are crucial. In addition, for the Neutrino Factory project and the atmospheric neutrinos, while HARP covers the low energy part of the spectrum, MIPP will cover the remaining energy range up to 100 GeV. To reduce costs, the MIPP experiment plans to re-use components from decommissioned experiments at FERMILAB and elsewhere, to reduce expenditures. A secondary beamline from the Main Injector will be tagged with two threshold Cherenkov counters in the experimental hall MC7, where the MIPP detector (shown in
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Table 22 Data taking foreseen for MIPP at Fermilab Beam
Target
Energy (GeV)
Events (106 )
, k, p , k, p , k, p
NO Be C Cu Pb H NuMI
5–110 5–110 5–110 120
18.0 30.0 18.0 9.9
p
Fig. 50. The MIPP apparatus.
Fig. 50) will be installed. Large angle target fragmentation particles will be measured by a TPC inside a large aperture magnet (the Jolly Green Giant 262 × 124 × 221 cm3 with a 7 KG field), while forward high momentum tracks will be measured by a system of chambers from the E690 experiment. The EOS-TPC, built at LBL for heavy ion studies, has been used in the E-910 particle production experiment at BNL and has good PID capabilities, through dE/dx measurements: a 3 /k separation up to 0.7 GeV/c and K/p separation up to 1.1 GeV/c. In the forward region PID will be obtained through a TOF system (between 1 and 2.5 GeV), a threshold Cherenkov from E-910 filled with Freon ( /K/p thresholds are at 2.5/7.5/17.5 GeV/c) and above 7.5 GeV from a SELEX-type Rich counter [148] filled with Neon ( /K/p thresholds are at 12/42/80 GeV/c). The main limits of the MIPP experiment are connected to a low data taking rate, mainly due to the use of old re-used devices. As an example, the EOS TPC electronics is limited to 30 Hz readout speed, to be compared to the 3 kHz of the HARP TPC. An upgrade of the TPC related electronics is being considered to cope with the need for high statistics. 8.3. Future measurements Some interest has been raised about the possibility to do a hadroproduction experiment at CERN SPS for a precise understanding of the neutrino beam in construction at JPARC for the T2K experiment [149]. Contrary to what happened in K2K, a pion monitor to measure the hadron spectrum may be impossible at least at higher momenta. This will imply an even higher dependence on MC hadron production models for the beamline simulation, increasing the systematic
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error on the far/near ratio R. The minimum needs will be some good quality data taken with the same material of the T2K target with a 5%, 50% and 100%I target. A conceptual design of such an experiment would require a detector with good tracking and PID capabilities. Two options for an experiment at CERN SPS have been considered. The first uses the NA49 detector [150] that is mainly limited by the low speed of the DAQ ( 50 triggers/spill), while the second aims at the use of the COMPASS detector [151]. This more recent setup can be used for hadroproduction measurements with an angular acceptance ± 180 mrad, good momentum measurement for p 2.5 GeV/c, good PID for pions above ∼ 3 GeV/c and kaons above ∼ 9 GeV/c and a high speed DAQ capable of recording 5 × 104 triggers/spill. The low momentum PID capabilities can be supplemented by adding a dedicated TOF detector similar to the Harp TOFW detector [146]. 9. Conclusions Hadroproduction for neutrino experiments is a well established field since the 1970s. From the former neutrino experiments, measurements were required to calculate the neutrino beam fluxes. In the future, the search for small-sized effects like the subleading → e oscillations for the 13 mixing angle measurement and the claimed high precision era for the next generation of long-baseline neutrino oscillation experiments requires data with low systematic uncertainties for a full understanding of the beam systematics. New interesting data are expected from the recent open geometry HARP experiment at the CERN PS and from the MIPP experimental FNAL. These ancillary experiments will be of utmost importance in this context, also for the design of the foreseen long-term new neutrino facilities, such as the neutrino factory. Acknowledgments We would like to thank all our colleagues of the NA56/SPY and HARP experiments for many enlightening discussions on the subject: in particular K. Elsener, that by inviting us to NBI02 and NBI03, triggered the first draft of this work. We acknowledge also the generous help in advice, careful reading of the manuscript and discussions from L. DiLella and Jeff Wyss. We are indebted to M. Baldo-Ceolin and A. Pullia who raised our interest in neutrino physics. The support of the European Community-Research Infrastructure Activity under the FP6 “Structuring the European Research Area” program (CARE, Contract no. RII3-CT-2003-506395) is acknowledged. References [1] L. Wolfenstein, Phys. Rev. D 17 (1978) 2369; S.P. Mikheev, A.Y. Smirnov, Nuovo Cim. C 9 (1986) 17. [2] K. Kimura, A. Takamura, H. Yokomakura, Phys. Rev. D 66 (2002) 073005 [arXiv:hep-ph/0205295]; E.K. Akhmedov, R. Johansson, M. Lindner, T. Ohlsson, T. Schwetz, JHEP 0404 (2004) 078 [arXiv:hep-ph/0402175]; M. Freund, Phys. Rev. D 64 (2001) 053003 [arXiv:hep-ph/0103300] [3] B.T. Cleveland, et al., [Homestake Collaboration], Astrophys. J. 496 (1998) 505. [4] W. Hampel, et al., [Gallex Collaboration], Phys. Lett. B 447 (1999) 127; M. Altmann, et al., [GNO Collaboration], Phys. Lett. B 490 (2000) 16 [arXiv:hep-ex/0006034] [5] J.N. Abdurashitov, et al., [SAGE Collaboration], J. Exp. Theor. Phys. 95 (2002) 181 [Zh. Eksp. Teor. Fiz. 122 (2002) 211] [arXiv:astroph/0204245]. [6] S. Fukuda, et al., [Super-Kamiokande Collaboration], Phys. Lett. B 539 (2002) 179 [arXiv:hep-ex/0205075]. [7] S.N. Ahmed, et al., [SNO Collaboration], Phys. Rev. Lett. 92 (2004) 181301 [arXiv:nucl-ex/0309004]. [8] K. Eguchi, et al., [KamLAND Collaboration], Phys. Rev. Lett. 90 (2003) 021802 [arXiv:hep-ex/0212021]. [9] T. Araki, et al., [KamLAND Collaboration], Phys. Rev. Lett. 94 (2005) 081801 [arXiv:hep-ex/0406035]. [10] Y. Fukuda, et al., [Super-Kamiokande Collaboration], Phys. Rev. Lett. 81 (1998) 1562 [arXiv:hep-ex/9807003]. [11] M.C. Sanchez, et al., [Soudan 2 Collaboration], Phys. Rev. D 68 (2003) 113004 [arXiv:hep-ex/0307069]. [12] M. Ambrosio, et al., [MACRO Collaboration], Phys. Lett. B 566 (2003) 35 [arXiv:hep-ex/0304037]. [13] Y. Ashie, et al., [Super-Kamiokande Collaboration], Phys. Rev. Lett. 93 (2004) 101801 [arXiv:hep-ex/0404034]. [14] S. Fukuda, et al., [Super-Kamiokande Collaboration], Phys. Rev. Lett. 85 (2000) 3999 [arXiv:hep-ex/0009001]. [15] Y. Ashie, et al., [Super-Kamiokande Collaboration], Phys. Rev. D 71 (2005) 112005 [arXiv:hep-ex/0501064]. [16] E. Aliu, et al., [K2K Collaboration], Phys. Rev. Lett. 94 (2005) 081802 [arXiv:hep-ex/0411038]. [17] M. Apollonio, et al., [CHOOZ Collaboration], Eur. Phys. J. C 27 (2003) 331 [arXiv:hep-ex/0301017]. [18] A. Aguilar, et al., [LSND Collaboration], Phys. Rev. D 64 (2001) 112007 [arXiv:hep-ex/0104049]. [19] E. Church, et al., [BooNe Collaboration], Preprint arXiv:nucl-ex/9706011.
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