Neutrino Scattering Physics at Neutrino Factories

Nuclear Physics B (Proc. Suppl.) 149 (2005) 39–43 www.elsevierphysics.com

Neutrino Scattering Physics at Neutrino Factories Y. Miyachi a a

Tokyo Institute of Technology, Oookayama 2-12-1, Meguro, Tokyo, 152-8851, Japan

Lepton-nucleon scattering is one of most powerful tools to explore the structure of the nucleon. Recent experimental and theoretical developments extends our understanding of the nucleon structure over very wide kinematic range. Physics case in the coming super beam and neutrino factory will be discussed, along with the present achievements in the lepton nucleon scattering experiments.

1. Introduction Lepton-nucleon scattering experiments have been used to investigate the nucleon internal structure. The elastic scattering experiments have revealed the spatial distributions of several elemental properties in terms of a nucleon form factor as shown in Figure 1. The axial current interaction in the neutrino scattering allows us to study the spin structure of nucleon. Especially the strange axial form factor GsA has attracted interests for years.

Figure 1. Conceptual diagrams of lepton-nucleon elastic scattering (left) and a deep inelastic scattering (right) are shown.

∆Σ = ∆u + ∆u¯ + ∆d + ∆d¯ + ∆s + ∆s¯

(1)

can be decomposed into the quark spin ∆Σ, the gluon spin ∆G and their orbital angular momentum contributions Lq,g . EMC extracted ∆Σ = 0.12 ± 0.09 ± 0.14, contrary to the value about 0.6 expected from SU(3) flavor symmetry. The spin structure of nucleon has been studied using several different experimental methods, inclusive and semi-inclusive measurements of deep inelastic scattering and polarized proton-proton collisions at RHIC. It is certainly valuable to study it using neutrinos in the future super beams and neutrino factories. In order to describe the nucleon structure covering both the nucleon form factor and structure functions, the parton distribution function has been generalized into the off-forward condition. Generalized Parton Distribution (GPD) has been measured through hard exclusive productions in the electron scattering experiments. Neutrino scattering will provide valuable informations on the axial property of GPD. In this paper, physics cases in super beams and neutrino factories will be discussed, especially focusing on the spin structure of nucleon. 2. Deep Inelastic Scattering

Highly virtual photon can dissolve the nucleon into its building blocks, ”parton”, whose transverse size is characterized with the inverse of the virtual photon four momentum. There have been extensive theoretical and experimental developments achieved after EMC reported their surprising results on the spin structure of proton [1,2]. The spin of proton 1 2

=

1 ∆Σ + Lq + ∆G + Lg 2

0920-5632/$ – see front matter © 2005 Published by Elsevier B.V. doi:10.1016/j.nuclphysbps.2005.05.007

An energetic incoming lepton can interact with a part of nucleon, known as a parton. In a deep inelastic scattering, where the four momentum square of the virtual photon Q2 and the final state hadronic system W 2 are large enough, the scattered parton can exit from the nucelon without interacting with the target remnants. In such condition, the scattered lepton carries information on the structure functions of nucleon F1, 2, 3 (x, Q2 ) which are built on the basis of pa-

40

Y. Miyachi / Nuclear Physics B (Proc. Suppl.) 149 (2005) 39–43

tron distribution functions (PDF) q(x) [3]. These structure functions have been measured with the various fixed targets, the electron proton collider and also the Drell-Yan experiments. Using high energy neutrinos, the neutrino DIS experiments have been carried at various laboratories. All the available data on the structure functions are compiled in [4]. Preliminary results on F2 and F3 structure functions from the NuTeV experiments were reported [5]. Based on all the available data, the parton distributions have been extracted. The resulting sets of PDF parameterization are collected in [6]. PDF has been calculated with various low energy effective models of QCD. The experimental clarification is essential for the understanding QCD.

0.03(sta.) ± 0.01(sys.) [11]. The results from the inclusive measurements and also several theoretical calculations including lattice QCD have indicated the negative moment of helicity distribution of sea quarks. The further experimental results are awaited.

x⋅∆u 0.2 0

x⋅∆d 0 -0.2

2.1. Polarized Deep Inelastic Scattering Following the EMC experiment, extensive efforts have been put in both theoretical and experimental developments. The inclusive measurements of the charged lepton DIS at CERN, DESY and SLAC have extracted the spin dependent structure function g1, 2 (x, Q2 ) of proton, deuteron and neutron, covering the different kinematic regions. All the available measured results with references can be found in [6]. The Q2 dependence of the collected data allow us to extract the quark helicity distributions under certain assumptions, such as a SU(3) quark flavor symmetry and a shape of the distribution function (one of recent analyses can be found in [7]). The extracted quark contribution to the nucleon spin confirmed the EMC results. A large positive ∆G were also obtained from such phenomenological analyses and also extracted from the high pT hadron pair event analyses [8,9]. However the statistical and systematic uncertainties on the extracted ∆G are relatively large. COMPASS and RICH-Spin program have started to measure ∆G precisely and will clarify in the near future. The positive gluon moment means that there can be negatively polarized sea quarks inside. HERMES identifies pions, kaons and protons from 2 to 15 GeV/c using RICH [10]. The semi-inclusive measurement, identifying more than one hadron in coincidence with the scattered lepton, determined the quark helicity distributions for each flavor as shown in Figure 2, without assumptions mentioned above. The partial moment of the strange quark helicity dis
0.3 ∆s(x)dx = +0.03 ± tribution was extracted as 0.023

Q2 = 2.5 GeV2 0 GRSV2000 LO std BB01 LO

–

x⋅∆u -0.1 –

x⋅∆d

0

-0.1

0 x⋅∆s

-0.1

0.03

0.1

0.6

x

Figure 2. The extracted quark helicity distributions for each flavor by the HERMES experiment are shown. This figure is taken from [11].

There are structure functions so far unmeasured, g3, 4, 5 (x, Q2 ), which can be accessed via the neutrino DIS with the polarized nucleon target. The expected physics and their precision have been discussed. Some details can be found in [12]. The hadron coincident experiment plays important roles also in the neutrino scattering. In the electron scatter-

Y. Miyachi / Nuclear Physics B (Proc. Suppl.) 149 (2005) 39–43

41

ing the sensitivity to the strange quark component is reduced due to the u-quark dominance even using the flavor tagging technique. Combination of the flavor selectivity of the neutrino interaction and the flavor tagging by the hadron identification will improve the sensitivity. 3. Nucleon Form Factor 3.1. Electric and Magnetic Form Factor The electric and magnetic form factors of proton have been studied, covering the Q2 range from 0.1 to 9.6 GeV2 , using the electron nucleon elastic scattering. The observed large deviation in the ratio of the electric and magnetic form factor between two different experimental methods, the Rosenbluth technique and the polarization transfer measurements, have been one of most important topics in these years. The detailed discussions can be found in [13]. It was suggested that two-photon exchange contributions to the electron elastic cross section can partially restore the difference [14]. Further experiments have been started and been planned in Jefferson laboratory. 3.2. Strange Form Factor The strange form factor have been measured in the several experiments. Parity violating electron scattering is one of the promising experiments, which aim to extract GsE and GsM through an interference between a virtual photon and a neutral weak boson. Recently HAPPEX [15] and SAMPLE [16] reported their results. The extrapolation of these form factors to Q2 = 0 provide information on the charge radius and the magnetic moment of the strange quark. The theoretical estimations have been made [17]. The magnetic moment contains the orbital angular moment and the quark tensor charge contributions [18]. It is interesting to compare them with the results from the quark transversity and Sivers function measurements by HERMES. Neutral current cross sections for ν µ + p → νµ + p and ν¯ µ + p → ν¯ µ + p were measured as shown in Figure 3. Through the neutral current interaction, the strange axial form factor GsA was extracted [20]. At Q2 = 0 GeV2 , GsA (0) becomes the first moment of strange helicity distribution. The 90% confidence level region was extracted as −0.25 ≤ GsA (0) ≤ 0 in the recent reanalysis [21], in which a strong corre-

Figure 3. Neutral current cross sections measured by E734 are taken from [19].

lation between GsA (0) and the axial mass MA was pointed out. The global analysis based on both the parity violating electron scattering and the neutrino scattering experiment have been also performed. The result indicated that the improvement on the neutrino scattering data is crucial on the determination of GsA [22]. There are several proposal to measure GsA at the next generation neutrino beam lines (for example [23]). The experimental clarification of ∆s both from DIS and the neutrino elastic scattering will be essential for understanding of the spin structure nucleon. 4. Generalized Parton Distribution (GPD) Great attentions have been given to the global understanding of nucleon structure combining both PDF and the form factor. DIS can be considered as a forward scattering of the virtual photon absorption process. By extending into the off-forward region, where the final state photon momentum differs from the in-

42

Y. Miyachi / Nuclear Physics B (Proc. Suppl.) 149 (2005) 39–43

coming one. As an analogy of the form factor measurements, the momentum transfer to the nucleon system provides the spatial information of the quantity probed by the incoming virtual photon. Parton distribution functions are now generalized to have the momentum transfer t, which introduce additional dependence on a “skewedness” ξ . The details can be found in the recent review [24], and GPD are tabulated in Table 1. 4.1. Deeply Virtual Compton Scattering (DVCS)

background known as Bethe-Heitler process (right diagram in Figure 4). As described in [26], the DVCS amplitude can be measured through the interference term between the DVCS and BH processes. The DVCS amplitude measurements have been performed by the various experiments [26,27]. In Figure 5, the beam spin azimuthal asymmetry measured by HERMES is shown.

ALU

Table 1 GPD and its relation with PDF and form factors are tabulated.
GPD t →0 dxG(x, ξ ,t) q H q (x, ξ ,t) q(x) F1 (t) q q E (x, ξ ,t) F2 (t) GqA (t) H˜ q (x, ξ ,t) ∆q(x) q hA (t) E˜ q (x, ξ ,t)

0.6 0.4 0.2 0 -0.2 -0.4 -0.6

e


e

e

γ

e


-3

γ

-2

N

-1

0

1

2

3

φ (rad)

γ∗

N


N

N


Figure 5. The DVCS beam spin azimuthal asymmetry measured by HERMES is taken from [26]. Figure 4. Deeply Virtual Compton Scattering (left) and Bethe-Heitler processes (right) are shown. GPD can be measured through the interfarence of these two terms.

4.2. Deeply Virtual Neutrino Scattering (DVNS) As one of physics cases in the neutrino factory, one can consider a “Deeply Virtual Neutrino Scattering (DVNS)” experiment

GPD can be experimentally accessible through “Deeply Virtual Compton Scattering” [25],

ν + N → ν
+ γ + N
.

e + N → e
+ γ + N
.

Now the incoming neutrino scatters off a nucleon. The out-coming real photon is detected, keeping the target intact. The cross section of DVNS was calculated to be order of 10−5 nb, which is similar size of other processes involved [28]. As discussed in the semi-inclusive DIS measurement, DVCS is also dominated by the scattering on u quark. By the DVNS

(2)

The scattered parton will be put back to the nucleon, emitting a real photon exclusively as shown in Figure 4. If the scattering is hard enough, Q2 > 1.0 GeV2 , the virtual photon interacts with one parton inside nucleon as in DIS. There is an indistinguishable

(3)

Y. Miyachi / Nuclear Physics B (Proc. Suppl.) 149 (2005) 39–43

ν

N

ν
γ

N


Figure 6. Deeply Virtual Neutrino Scattering diagram is shown. Intense neutrino beam available in the neutrino factories allows us to measure GPDs by the DVNS process.

measurement, GPD can be mapped effectively for each quark flavor. 5. Summary Lepton scattering experiments have revealed that the nucleon indeed has a complex structure. Especially sea quark components are important to understand QCD which is the basic principle for describing the hadron structure. The accelerator technique and the quality of the neutrino beam will be rapidly increased. In the coming generation of neutrino facilities, the strange components to the nucleon form factors will be precisely measured. Neutrino factories allow us to open the experimental possibilities to the first neutrino DIS experiment using the polarized nucleon target. Recently several DVCS amplitude measurements have been carried out to measure GPD. Probing GPD using the neutrino interaction will certainly help global understanding the nucleon structure. REFERENCES 1. J. Ashman et al. [European Muon Collaboration], Phys. Lett. B 206 (1988) 364. 2. J. Ashman et al. [European Muon Collaboration], Nucl. Phys. B 328 (1989) 1. 3. R. Devenish and A. Cooper-Sarkar, OXFORD University Press, ISBN 0-19-850671-6.

43

4. S. Eidelman et al. [Particle Data Group Collaboration], Phys. Lett. B 592 (2004) 1. 5. D. Naples et al. [NuTeV Collaboration], arXiv:hep-ex/0307005. 6. The Durham HEP Databases at Durham University, http://durpdg.dur.ac.uk/HEPDATA/ 7. J. Blumlein and H. Bottcher, Nucl. Phys. B 636 (2002) 225. 8. B. Adeva et al., Phys. Rev. D 70 (2004) 012002. 9. A. Airapetian et al. [HERMES Collaboration], Phys. Rev. Lett. 84 (2000) 2584. 10. K. Ackerstaff et al. [HERMES Collaboration], Nucl. Instrum. Meth. A 417 (1998) 230. 11. A. Airapetian et al. [HERMES Collaboration], Phys. Rev. Lett. 92 (2004) 012005. 12. S. Forte, M. L. Mangano and G. Ridolfi, Nucl. Phys. B 602 (2001) 585. 13. J. Arrington, Phys. Rev. C 68 (2003) 034325. 14. P. G. Blunden, W. Melnitchouk and J. A. Tjon, Phys. Rev. Lett. 91 (2003) 142304. 15. K. A. Aniol et al. [HAPPEX Collaboration], Phys. Rev. C 69 (2004) 065501. 16. D. T. Spayde et al. [SAMPLE Collaboration], Phys. Lett. B 583 (2004) 79. 17. V. E. Lyubovitskij, P. Wang, T. Gutsche and A. Faessler, Phys. Rev. C 66 (2002) 055204. 18. X. S. Chen, D. Qing, W. M. Sun, H. S. Zong and F. Wang, Phys. Rev. C 69 (2004) 045201. 19. L. A. Ahrens et al., Phys. Rev. D 35 (1987) 785. 20. G. T. Garvey, W. C. Louis and D. H. White, Phys. Rev. C 48 (1993) 761. 21. W. M. Alberico, S. M. Bilenky and C. Maieron, Phys. Rept. 358 (2002) 227. 22. S. F. Pate, Phys. Rev. Lett. 92 (2004) 082002. 23. L. Bugel et al. [FINeSSE Collaboration], arXiv:hep-ex/0402007. 24. P. A. M. Guichon and M. Vanderhaeghen, Prog. Part. Nucl. Phys. 41 (1998) 125. 25. X. D. Ji, Phys. Rev. D 55 (1997) 7114. 26. A. Airapetian et al. [HERMES Collaboration], Phys. Rev. Lett. 87 (2001) 182001. 27. S. Stepanyan et al. [CLAS Collaboration], Phys. Rev. Lett. 87 (2001) 182002. 28. P. Amore, C. Coriano and M. Guzzi, arXiv:hepph/0404121.