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Recent experimental results on Coherent Pion production in neutrino interactions
Available online at www.sciencedirect.com
Nuclear Physics B (Proc. Suppl.) 229–232 (2012) 191–195 www.elsevier.com/locate/npbps
Recent experimental results on Coherent Pion production in neutrino interactions L. Camilleri Columbia University, Nevis Labs Irvington on Hudson, New York 10533, USA
Abstract Recent experimental results on charged current (π+ ) coherent production by KEK and SciBooNE and neutral current (π ) production by MiniBooNE, SciBooNE and NOMAD will be discussed. The NOMAD results are at an average neutrino energy of 25 GeV whereas the energies of the other experiments are in an average energy range of 1-2 GeV. A comparison with some theoretical models will be presented. 0
Keywords: Coherent pions
1. Introduction Several experiments have studied coherent pion production in recent years. They are listed in Table 1, together with the nature of the target they used, the neutrino energy they ran at and the reactions they were sensitive to. In coherent pion production the neutrino interacts with the target nucleus as a whole, without breaking it up. This implies that the momentum transfer to the nucleus must be small and the consequences are that no other particle emerges from the reaction other than the scattered lepton and the pion, and that these are produced in the forward direction. The charged (CC) and neutral (NC) current reactions (Fig.1) are, respectively: νμ +A = μ− +A+π+ and νμ +A = νμ +A+π0 . Most experiments use the model of Rein and Sehgal [6] to describe coherent production in their simulation programs. The process is dominated by the axial vector current. Its calculation can use Adler’s PCAC theorem [7] and, at Q2 = 0, is related to the differential πA elastic cross sections as shown in Fig. 2. These πA cross sections are related to the π-nucleon elastic cross-sections and to an absorbtion in nuclear matter term which, themselves, can be related to the total and inelastic cross sections. Isospin considerations imply that σ(CC : π+ ) = 2σ(NC : π0 ). In a later paper [8] they extended this model to take into 0920-5632/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2012.09.031
account a non-zero lepton mass in CC reactions. The model can also be extended to non-zero Q2 by including an axial vector form factor: G A = MA2 /(Q2 + MA2 ).
Figure 1: The principle of coherent pion production in neutrino interactions
At low energy, the main background is the production of resonances, mainly the Δ, decaying to πN in which the nucleon is not reconstructed. For CC reactions, an additional background is quasi-elastic (QEL) events in which the proton is misidentified as a π+ . At high energy deep-inelastic (DIS) interactions constitute the major background. Interactions occuring outside the
192
L. Camilleri / Nuclear Physics B (Proc. Suppl.) 229–232 (2012) 191–195
Table 1: Coherent pion experiments: their laboratory, target, neutrino beam average energy and the reactions they studied
Experiment K2K [1] MiniBooNE [2] SciBooNE [3] [4] NOMAD [5]
Lab KEK Fermilab Fermilab CERN
Target Plastic scint. (CH) Mineral oil (CH2 ) Plastic scint. (CH) Drift Chambers C (A=12.8)
Energy (GeV) 1.3 1.1 1.1,2.2,0.8 24.8
Reactions CC NC CC,NC NC
detector producing a single π with its decay photons entering the detector are also a problem. The other difficulty is accounting for the reinteractions of final state hadrons which can destroy or produce a pion. 0
2. Charged Current Coherent π+ Two experiments, the K2K near detector [1] and SciBooNE [3], have recently published results for this reaction. They use the same fully active tracking detector (SciBar) consisting of 64 planes of horizontal scintillator strips interleaved with 64 planes of vertical strips. This is followed in both cases by a muon range detector (MRD) consisting of iron plates interleaved with active detector planes. Coherent π+ events were defined as two-track events, one of which penetrates into the MRD. SciBooNE divides their data into 2 samples: one in which the muon stops in the MRD (mean Eν = 1.1 GeV) and the other in which the muon traverses the MRD ( mean Eν = 2.2 GeV). QEL events are rejected using a likelihood that discriminates between protons and pions based on the candidate track ionization in SciBar. In addition the candidate pion track direction must be inconsistent with the proton direction of a potential QEL event as computed, using QEL kinematics, from the muon direction and energy. Events in which
Data CC coherent CC 1, DIS, NC CC QE
120 80 40 0
0
0.2
0.4
0.6
0.8 1 1.2 q2rec (GeV/c)2
Figure 3: The K2K charged current coherent π+ Q2 distribution showing good agreement of the data with the background with no need for a coherent contribution.
Entries / 0.025 (GeV/c)2
Figure 2: Neutral current π0 production showing the nucleus emerging unchanged after interaction with a Pomeron and the connection between this process and pion elastic scattering.
Entries / 0.05(GeV/c)2
unreconstructed vertex activity amounts to more than 10 MeV are rejected to minimize the Δ background in which the proton is not reconstructed. Finally the pion candidate must be in the forward direction. Neither experiment sees any evidence for π+ coherent production. This can be seen in the Q2 distribution of the K2K data (Fig.3) and of the 2.2 GeV neutrino energy bin of SciBooNE (Fig.4). They obtain the results and limits at 90% C.L. shown in Table 2.
40
DATA
30
CC coherent CC resonant Other
20
CC QE
10
0 0
0.1
0.2
0.3
0.4 0.5 Q2 (GeV/c)2
Figure 4: The higher neutrino energy SciBooNE charged current coherent π+ Q2 distribution. Only a small coherent contribution is needed.
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L. Camilleri / Nuclear Physics B (Proc. Suppl.) 229–232 (2012) 191–195
Table 2: Charged Current Coherent π+ results
Experiment
Energy (GeV)
σ(coh π+ )/σ(νμ CC)
σ(coh π+ )/σ(νμ CC) at 90% C.L.
K2K
1.3
[0.04 ± 0.29(stat)+0.32 (syst)] × 10−2 −0.35
0.60 × 10−2
SciBooNE
1.1
[0.16 ± 0.32(stat)+0.30 (syst)] × 10−2 −0.27
0.67 × 10−2
SciBooNE
2.2
[0.68 ± 0.32(stat)+0.39 (syst)] × 10−2 −0.25
1.36 × 10−2
3. Neutral Current Coherent π0 Three experiments have contributed to this subject lately. MiniBooNE [2] is an 800 ton mineral oil detector which records and identifies particles using their Cerenkov ring. This allows them to identify pizeros as two rings of electromagnetic origin (fuzzy edges). SciBooNE [4] identifies pizeros as two separated tracks in SciBar. NOMAD [5] reconstructs a π0 as two photons converting in their 2.7 ton drift chamber target consisting mostly of carbon. This target being in a magnetic field the conversion positrons and electrons open up. MiniBooNE identifies coherent π0 ’s of energy Eπ and direction θπ as events with no muon and two photon-like Cerenkov rings. They then fit the distributions of the reconstructed di-photon mass, mγγ (Fig.5), and of the forwardness, ζπ = Eπ (1 − cosθπ ), to templates of Monte Carlo distributions of coherent and incoherent π0 ’s and of all other backgrounds. They observe a definite signal and quote their result in terms of the total number of single π0 observed: coh/(coh + incoh) = [19.5 ± 1.1(stat) ± 2.5(syst)]% whereas their NUANCE-based simulation program predicts this ratio to be 30%. SciBooNE identifies coherent π0 ’s as events with no proton, defined as events having a vertex activity smaller than 2 MeV, and with small four-momentum transfer to the nucleus approximated as ζπ smaller than 100 MeV. They fit the ζπ distribution of surviving events with and without the vertex activity cut to templates of coherent, incoherent and of all other backgrounds. The data clearly includes coherent pions and their result is: σ(cohπ0 )/σ(νμ CC) = [1.16 ± 0.24] × 10−2 This is in very good agreement with 1.21 × 10−2 , the Rein and Sehgal prediction as calculated with their Monte Carlo program. In NOMAD coherent π0 ’s are identified as two converted photons and no other particle in the event. They
use four variables in their analysis, mγγ , the forwardness of each of the two photons, ζγ1 , ζγ2 and the opening angle of the two photons, θ12 . The main background is neutral current DIS events and it is estimated by normalizing the Monte Carlo prediction to the region with mγγ larger than 0.2 GeV/c2 and with ζγ1 and ζγ2 larger than 0.05. The neutrino interaction vertex is taken to be the position at which the distance of closest approach of the two photons is minimal. Only events with an interaction vertex within the fiducial volume are retained. However some events can be due to neutrino interactions upstream of the detector. The fraction of the retained candidates that are due to this background is calculated using another sample of events containing charged tracks in addition to two converting γ’s from which the neutrino interaction vertex is found to be outside the detector. Having calculated the backgrounds from the data themselves, the coherent π0 contribution to the final sample is obtained by fitting the two-dimensional ζγ1 , ζγ2 distribution and the θ12 distribution (Fig.6) to the sum of the calculated backgrounds augmented by a coherent π0 contribution calculated using the Rein and Sehgal model but multiplied by a factor α. The best fit yields α = 0.985 ±0.113, from which NOMAD finds the ratio of σ(coh π0 )/σ(νμCC) to be: = [3.21 ± 0.36(stat) ± 0.29(syst)] × 10−3 Using the νμ CC cross sections measured [9] in their own experiment they compute σ(coh π0 ) to be: = [72.7 ± 8.1(stat) ± 6.9(syst)] × 10−40 cm−2 /nucleus again in excellent agreement with the Rein and Sehgal prediction. 4. Comparison with newer models Extensions to the Rein and Sehgal models have been proposed recently by Berger and Sehgal [10]. In Extension I they use the latest π-Nucleon differential cross
L. Camilleri / Nuclear Physics B (Proc. Suppl.) 229–232 (2012) 191–195
1600
Number of Events
2
Events/(5 MeV/c )
194
a) Data Full MC Fit Resonant Coherent Background
1400 1200 1000 800
70
60
50
600 40
400 200 0
30
0.1
0.2
Mass
0.3
0.4
GeV/c
2
Figure 5: The MiniBooNE γγ invariant mass showing a clear π0 peak and the coherent π0 contribution to the sample.
sections. In Extension II, in order to avoid modelling nuclear processes, they use measured π-Carbon elastic cross sections. This latter calculation yields significantly lower cross sections than the original Rein and Sehgal calculation and also lower than those of Extension I. This is seen in Fig. 7, which shows the νC coherent pion cross sections calculated with both Extensions. The low energy experimental data discussed above is also displayed in this figure. All the experiments used the original Rein and Sehgal model to calculate their efficiencies and to determine whether they agreed with expectations or not. Therefore Extension I of [10], which is the closest to the original Rein and Sehgal, was used whenever needed to convert the quoted results into an absolute cross section. The most striking feature of this comparison is the lack of CC coh π+ signal. The upper end of the error bars on these data are barely consistent with the lowest prediction. However the NC coherent π0 data, including the earlier Aachen-Padova data [11] which used an aluminium target but is shown scaled to Carbon, are in good agreement with Extension I. SciBooNE has measured both π+ and π0 coherent production and the ratio of these measurements, 0.14+0.30 , is −0.28 much lower than the value of ∼ 1.5 expected from [10]. Note that, at high energy, the NOMAD data is in very good agreement with the original Rein and Sehgal calculation, which is close to Extension I, and so were the earlier high energy coherent π+ and π0 data as shown in [12] and [13] respectively. Several other models are available such as the models of Alvarez-Ruso et al [14] and [15] and of S.K.Singh et al [16] which are based on Δ production modified for the nuclear medium. Their
20
10
0
0
0.1
0.2
Θ12
0.3
0.4
0.5
Figure 6: The NOMAD distribution of the opening angle between the two γ’s showing the coherent π0 contribution in the hatched blue histogram.
predictions are also shown in Fig. 7. 5. Conclusions At energies above 2 GeV the Rein and Sehgal model agrees well with all the available data on both π+ and π0 coherent production. Below 2 GeV π0 coherent production has been observed by SciBooNE, MiniBooNE and Aachen-Padova. Their measured rate tends to favour models with a high π0 yield. However π+ coherent production has not been observed by K2K and SciBooNE, although their upper limits are consistent with models predicting a low coherent π+ yield. Efficiency calculations and conclusions could be affected by the different simulation codes used by the experiments. New low energy data from Minerva [17] and MicroBooNE [18] will be very welcome. 6. Ackowledgements I would like to thank the organizers, and in particular Georges Tzanakos, for a very interesting conference. The experimenters have been very helpful in supplying me with their data and plots.
L. Camilleri / Nuclear Physics B (Proc. Suppl.) 229–232 (2012) 191–195
195
[16] S.K. Singh et al, Phys. Rev. Lett. 96 (2006) 241801. [17] Proposal to Perform a High-Statistics Neutrino Scattering Experiment Using a Fine Grained Detector in the NuMI Beam:arXiv 0405002v1 hep-ex [18] A Proposal for a new experiment Using the Booster and NuMI Beamlines: MicroBooNE 2007 Fermilab Proposal P974 and http:// www-microboone.fnal.gov.
Figure 7: Data-Theory coherent cross section comparison. a) NC coherent π0 . b) CC coherent π+ . Data: SciBooNE open circles, MiniBooNE full circle, K2K full triangle, Aachen Padova full square. Theory: black points and asterix Berger and Sehgal Extensions I and II respectively. Solid and open stars Alvarez-Ruso with two different form factors, inverted full triangles Singh et al.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
M. Hasegawa et al, Phys. Rev. Lett. 95 (2005) 252301. A.A. Aguilar-Arevalo et al, Phys. Lett. B664 (2008) 41. K. Hiraide et al, Phys. Rev. D78 (2008) 112004. Y. Kurimoto et al, arXiv: 1005.0059 hep-ex. C.T. Kullenberg et al, Phys. Lett. B682 (2009) 177. D. Rein and L.M. Sehgal, Nucl. Phys. B223 (1983) 29. S.L. Adler, Phys. Rev. 135 (1964) B693. D. Rein and L.M. Sehgal, Phys. Lett. B67 (1987) 207. Q. Wu et al, Phys. Lett. B660 (2008) 19. Ch. Berger and L.M. Sehgal, Phys. Rev. D79 (2009) 053003. H. Faissner et al, Phys. Lett. B125 (1983) 230. F. Bergsma et al, Phys. Lett.B157 (1985) 469. P. Vilain et al, Phys. Lett. B313 (19930 267. L. Alvarez-Ruso et al, Phys. Rev. C75 (2007) 055501. L. Alvarez-Ruso et al, Phys. Rev. C76 (2007) 068501.
Nuclear Physics B (Proc. Suppl.) 229–232 (2012) 191–195 www.elsevier.com/locate/npbps
Recent experimental results on Coherent Pion production in neutrino interactions L. Camilleri Columbia University, Nevis Labs Irvington on Hudson, New York 10533, USA
Abstract Recent experimental results on charged current (π+ ) coherent production by KEK and SciBooNE and neutral current (π ) production by MiniBooNE, SciBooNE and NOMAD will be discussed. The NOMAD results are at an average neutrino energy of 25 GeV whereas the energies of the other experiments are in an average energy range of 1-2 GeV. A comparison with some theoretical models will be presented. 0
Keywords: Coherent pions
1. Introduction Several experiments have studied coherent pion production in recent years. They are listed in Table 1, together with the nature of the target they used, the neutrino energy they ran at and the reactions they were sensitive to. In coherent pion production the neutrino interacts with the target nucleus as a whole, without breaking it up. This implies that the momentum transfer to the nucleus must be small and the consequences are that no other particle emerges from the reaction other than the scattered lepton and the pion, and that these are produced in the forward direction. The charged (CC) and neutral (NC) current reactions (Fig.1) are, respectively: νμ +A = μ− +A+π+ and νμ +A = νμ +A+π0 . Most experiments use the model of Rein and Sehgal [6] to describe coherent production in their simulation programs. The process is dominated by the axial vector current. Its calculation can use Adler’s PCAC theorem [7] and, at Q2 = 0, is related to the differential πA elastic cross sections as shown in Fig. 2. These πA cross sections are related to the π-nucleon elastic cross-sections and to an absorbtion in nuclear matter term which, themselves, can be related to the total and inelastic cross sections. Isospin considerations imply that σ(CC : π+ ) = 2σ(NC : π0 ). In a later paper [8] they extended this model to take into 0920-5632/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2012.09.031
account a non-zero lepton mass in CC reactions. The model can also be extended to non-zero Q2 by including an axial vector form factor: G A = MA2 /(Q2 + MA2 ).
Figure 1: The principle of coherent pion production in neutrino interactions
At low energy, the main background is the production of resonances, mainly the Δ, decaying to πN in which the nucleon is not reconstructed. For CC reactions, an additional background is quasi-elastic (QEL) events in which the proton is misidentified as a π+ . At high energy deep-inelastic (DIS) interactions constitute the major background. Interactions occuring outside the
192
L. Camilleri / Nuclear Physics B (Proc. Suppl.) 229–232 (2012) 191–195
Table 1: Coherent pion experiments: their laboratory, target, neutrino beam average energy and the reactions they studied
Experiment K2K [1] MiniBooNE [2] SciBooNE [3] [4] NOMAD [5]
Lab KEK Fermilab Fermilab CERN
Target Plastic scint. (CH) Mineral oil (CH2 ) Plastic scint. (CH) Drift Chambers C (A=12.8)
Energy (GeV) 1.3 1.1 1.1,2.2,0.8 24.8
Reactions CC NC CC,NC NC
detector producing a single π with its decay photons entering the detector are also a problem. The other difficulty is accounting for the reinteractions of final state hadrons which can destroy or produce a pion. 0
2. Charged Current Coherent π+ Two experiments, the K2K near detector [1] and SciBooNE [3], have recently published results for this reaction. They use the same fully active tracking detector (SciBar) consisting of 64 planes of horizontal scintillator strips interleaved with 64 planes of vertical strips. This is followed in both cases by a muon range detector (MRD) consisting of iron plates interleaved with active detector planes. Coherent π+ events were defined as two-track events, one of which penetrates into the MRD. SciBooNE divides their data into 2 samples: one in which the muon stops in the MRD (mean Eν = 1.1 GeV) and the other in which the muon traverses the MRD ( mean Eν = 2.2 GeV). QEL events are rejected using a likelihood that discriminates between protons and pions based on the candidate track ionization in SciBar. In addition the candidate pion track direction must be inconsistent with the proton direction of a potential QEL event as computed, using QEL kinematics, from the muon direction and energy. Events in which
Data CC coherent CC 1, DIS, NC CC QE
120 80 40 0
0
0.2
0.4
0.6
0.8 1 1.2 q2rec (GeV/c)2
Figure 3: The K2K charged current coherent π+ Q2 distribution showing good agreement of the data with the background with no need for a coherent contribution.
Entries / 0.025 (GeV/c)2
Figure 2: Neutral current π0 production showing the nucleus emerging unchanged after interaction with a Pomeron and the connection between this process and pion elastic scattering.
Entries / 0.05(GeV/c)2
unreconstructed vertex activity amounts to more than 10 MeV are rejected to minimize the Δ background in which the proton is not reconstructed. Finally the pion candidate must be in the forward direction. Neither experiment sees any evidence for π+ coherent production. This can be seen in the Q2 distribution of the K2K data (Fig.3) and of the 2.2 GeV neutrino energy bin of SciBooNE (Fig.4). They obtain the results and limits at 90% C.L. shown in Table 2.
40
DATA
30
CC coherent CC resonant Other
20
CC QE
10
0 0
0.1
0.2
0.3
0.4 0.5 Q2 (GeV/c)2
Figure 4: The higher neutrino energy SciBooNE charged current coherent π+ Q2 distribution. Only a small coherent contribution is needed.
193
L. Camilleri / Nuclear Physics B (Proc. Suppl.) 229–232 (2012) 191–195
Table 2: Charged Current Coherent π+ results
Experiment
Energy (GeV)
σ(coh π+ )/σ(νμ CC)
σ(coh π+ )/σ(νμ CC) at 90% C.L.
K2K
1.3
[0.04 ± 0.29(stat)+0.32 (syst)] × 10−2 −0.35
0.60 × 10−2
SciBooNE
1.1
[0.16 ± 0.32(stat)+0.30 (syst)] × 10−2 −0.27
0.67 × 10−2
SciBooNE
2.2
[0.68 ± 0.32(stat)+0.39 (syst)] × 10−2 −0.25
1.36 × 10−2
3. Neutral Current Coherent π0 Three experiments have contributed to this subject lately. MiniBooNE [2] is an 800 ton mineral oil detector which records and identifies particles using their Cerenkov ring. This allows them to identify pizeros as two rings of electromagnetic origin (fuzzy edges). SciBooNE [4] identifies pizeros as two separated tracks in SciBar. NOMAD [5] reconstructs a π0 as two photons converting in their 2.7 ton drift chamber target consisting mostly of carbon. This target being in a magnetic field the conversion positrons and electrons open up. MiniBooNE identifies coherent π0 ’s of energy Eπ and direction θπ as events with no muon and two photon-like Cerenkov rings. They then fit the distributions of the reconstructed di-photon mass, mγγ (Fig.5), and of the forwardness, ζπ = Eπ (1 − cosθπ ), to templates of Monte Carlo distributions of coherent and incoherent π0 ’s and of all other backgrounds. They observe a definite signal and quote their result in terms of the total number of single π0 observed: coh/(coh + incoh) = [19.5 ± 1.1(stat) ± 2.5(syst)]% whereas their NUANCE-based simulation program predicts this ratio to be 30%. SciBooNE identifies coherent π0 ’s as events with no proton, defined as events having a vertex activity smaller than 2 MeV, and with small four-momentum transfer to the nucleus approximated as ζπ smaller than 100 MeV. They fit the ζπ distribution of surviving events with and without the vertex activity cut to templates of coherent, incoherent and of all other backgrounds. The data clearly includes coherent pions and their result is: σ(cohπ0 )/σ(νμ CC) = [1.16 ± 0.24] × 10−2 This is in very good agreement with 1.21 × 10−2 , the Rein and Sehgal prediction as calculated with their Monte Carlo program. In NOMAD coherent π0 ’s are identified as two converted photons and no other particle in the event. They
use four variables in their analysis, mγγ , the forwardness of each of the two photons, ζγ1 , ζγ2 and the opening angle of the two photons, θ12 . The main background is neutral current DIS events and it is estimated by normalizing the Monte Carlo prediction to the region with mγγ larger than 0.2 GeV/c2 and with ζγ1 and ζγ2 larger than 0.05. The neutrino interaction vertex is taken to be the position at which the distance of closest approach of the two photons is minimal. Only events with an interaction vertex within the fiducial volume are retained. However some events can be due to neutrino interactions upstream of the detector. The fraction of the retained candidates that are due to this background is calculated using another sample of events containing charged tracks in addition to two converting γ’s from which the neutrino interaction vertex is found to be outside the detector. Having calculated the backgrounds from the data themselves, the coherent π0 contribution to the final sample is obtained by fitting the two-dimensional ζγ1 , ζγ2 distribution and the θ12 distribution (Fig.6) to the sum of the calculated backgrounds augmented by a coherent π0 contribution calculated using the Rein and Sehgal model but multiplied by a factor α. The best fit yields α = 0.985 ±0.113, from which NOMAD finds the ratio of σ(coh π0 )/σ(νμCC) to be: = [3.21 ± 0.36(stat) ± 0.29(syst)] × 10−3 Using the νμ CC cross sections measured [9] in their own experiment they compute σ(coh π0 ) to be: = [72.7 ± 8.1(stat) ± 6.9(syst)] × 10−40 cm−2 /nucleus again in excellent agreement with the Rein and Sehgal prediction. 4. Comparison with newer models Extensions to the Rein and Sehgal models have been proposed recently by Berger and Sehgal [10]. In Extension I they use the latest π-Nucleon differential cross
L. Camilleri / Nuclear Physics B (Proc. Suppl.) 229–232 (2012) 191–195
1600
Number of Events
2
Events/(5 MeV/c )
194
a) Data Full MC Fit Resonant Coherent Background
1400 1200 1000 800
70
60
50
600 40
400 200 0
30
0.1
0.2
Mass
0.3
0.4
GeV/c
2
Figure 5: The MiniBooNE γγ invariant mass showing a clear π0 peak and the coherent π0 contribution to the sample.
sections. In Extension II, in order to avoid modelling nuclear processes, they use measured π-Carbon elastic cross sections. This latter calculation yields significantly lower cross sections than the original Rein and Sehgal calculation and also lower than those of Extension I. This is seen in Fig. 7, which shows the νC coherent pion cross sections calculated with both Extensions. The low energy experimental data discussed above is also displayed in this figure. All the experiments used the original Rein and Sehgal model to calculate their efficiencies and to determine whether they agreed with expectations or not. Therefore Extension I of [10], which is the closest to the original Rein and Sehgal, was used whenever needed to convert the quoted results into an absolute cross section. The most striking feature of this comparison is the lack of CC coh π+ signal. The upper end of the error bars on these data are barely consistent with the lowest prediction. However the NC coherent π0 data, including the earlier Aachen-Padova data [11] which used an aluminium target but is shown scaled to Carbon, are in good agreement with Extension I. SciBooNE has measured both π+ and π0 coherent production and the ratio of these measurements, 0.14+0.30 , is −0.28 much lower than the value of ∼ 1.5 expected from [10]. Note that, at high energy, the NOMAD data is in very good agreement with the original Rein and Sehgal calculation, which is close to Extension I, and so were the earlier high energy coherent π+ and π0 data as shown in [12] and [13] respectively. Several other models are available such as the models of Alvarez-Ruso et al [14] and [15] and of S.K.Singh et al [16] which are based on Δ production modified for the nuclear medium. Their
20
10
0
0
0.1
0.2
Θ12
0.3
0.4
0.5
Figure 6: The NOMAD distribution of the opening angle between the two γ’s showing the coherent π0 contribution in the hatched blue histogram.
predictions are also shown in Fig. 7. 5. Conclusions At energies above 2 GeV the Rein and Sehgal model agrees well with all the available data on both π+ and π0 coherent production. Below 2 GeV π0 coherent production has been observed by SciBooNE, MiniBooNE and Aachen-Padova. Their measured rate tends to favour models with a high π0 yield. However π+ coherent production has not been observed by K2K and SciBooNE, although their upper limits are consistent with models predicting a low coherent π+ yield. Efficiency calculations and conclusions could be affected by the different simulation codes used by the experiments. New low energy data from Minerva [17] and MicroBooNE [18] will be very welcome. 6. Ackowledgements I would like to thank the organizers, and in particular Georges Tzanakos, for a very interesting conference. The experimenters have been very helpful in supplying me with their data and plots.
L. Camilleri / Nuclear Physics B (Proc. Suppl.) 229–232 (2012) 191–195
195
[16] S.K. Singh et al, Phys. Rev. Lett. 96 (2006) 241801. [17] Proposal to Perform a High-Statistics Neutrino Scattering Experiment Using a Fine Grained Detector in the NuMI Beam:arXiv 0405002v1 hep-ex [18] A Proposal for a new experiment Using the Booster and NuMI Beamlines: MicroBooNE 2007 Fermilab Proposal P974 and http:// www-microboone.fnal.gov.
Figure 7: Data-Theory coherent cross section comparison. a) NC coherent π0 . b) CC coherent π+ . Data: SciBooNE open circles, MiniBooNE full circle, K2K full triangle, Aachen Padova full square. Theory: black points and asterix Berger and Sehgal Extensions I and II respectively. Solid and open stars Alvarez-Ruso with two different form factors, inverted full triangles Singh et al.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
M. Hasegawa et al, Phys. Rev. Lett. 95 (2005) 252301. A.A. Aguilar-Arevalo et al, Phys. Lett. B664 (2008) 41. K. Hiraide et al, Phys. Rev. D78 (2008) 112004. Y. Kurimoto et al, arXiv: 1005.0059 hep-ex. C.T. Kullenberg et al, Phys. Lett. B682 (2009) 177. D. Rein and L.M. Sehgal, Nucl. Phys. B223 (1983) 29. S.L. Adler, Phys. Rev. 135 (1964) B693. D. Rein and L.M. Sehgal, Phys. Lett. B67 (1987) 207. Q. Wu et al, Phys. Lett. B660 (2008) 19. Ch. Berger and L.M. Sehgal, Phys. Rev. D79 (2009) 053003. H. Faissner et al, Phys. Lett. B125 (1983) 230. F. Bergsma et al, Phys. Lett.B157 (1985) 469. P. Vilain et al, Phys. Lett. B313 (19930 267. L. Alvarez-Ruso et al, Phys. Rev. C75 (2007) 055501. L. Alvarez-Ruso et al, Phys. Rev. C76 (2007) 068501.