Two Particle-Hole Excitations in Charged Current Quasielastic Antineutrino--Nucleus Scattering
aa r X i v : . [ h e p - ph ] F e b July 4, 2018
Two Particle-Hole Excitations in Charged Current Quasielastic Antineutrino–NucleusScattering
J. Nieves, I. Ruiz Simo, and M. J. Vicente Vacas Instituto de F´ısica Corpuscular (IFIC), Centro Mixto Universidad de Valencia-CSIC,Institutos de Investigaci´on de Paterna, E-46071 Valencia, Spain Dipartimento di Fisica, Universit`a di Trento, I-38123 Trento, Italy Departamento de F´ısica Te´orica and IFIC, Centro Mixto Universidad de Valencia-CSIC,Institutos de Investigaci´on de Paterna, E-46071 Valencia, Spain
We evaluate the quasielastic and multinucleon contributions to the antineutrino nucleus scatteringcross section and compare our results with the recent MiniBooNE data. We use a local Fermi gasmodel that includes RPA correlations and gets the multinucleon part from a systematic many bodyexpansion of the W boson selfenergy in the nuclear medium. The same model had been quitesuccessful for the neutrino cross section and contains no new parameters. We have also analysedthe relevance of 2p2h events for the antineutrino energy reconstruction. PACS numbers: 25.30.Pt,13.15.+g, 24.10.Cn,21.60.Jz
Neutrino (antineutrino) charged-current (CC) scattering on nuclei without emitted pions is a crucial detectionchannel for many neutrino experiments [1–3] and has been extensively studied by several theoretical groups [4–21].It has been customary to take for granted that most of those events could be attributed to the quasielastic (QE)scattering of the weak probe on a nucleon. Hence, the initial neutrino(antineutrino) energy could be approximatelydetermined from the energy and angle of the final lepton assuming QE kinematics.This assumption soon led to some puzzling results. In particular, neutrino MiniBooNE data [3] were quite chal-lenging showing substantially larger cross sections than the theoretical predictions [22, 23]. A simple way out was tomodify in the calculations some standard hadronic parameters, such as the nucleon axial mass M A [3, 11, 17], to fitdata. However, the large obtained values (e.g. M A = 1 . ± .
17 GeV in [3]) were in clear conflict with other electronand even neutrino experiments which result in a value very close to one ( M A = 1 . ± .
014 GeV in [24]).A more natural solution came from the incorporation of some standard nuclear effects such as RPA and multinucleonmechanisms. The importance of these effects in the non mesonic neutrino nucleus scattering was first explored inRefs. [8, 9] and later in Refs. [12, 18, 19]. Some of these more complete models were found to describe well even theMiniBooNE double differential cross section while using standard values for all parameters of the calculations [19]. Inthese models, a substantial part of the cross section measured in Ref. [3] corresponds to events in which at least twonucleons are emitted.The relevance of the multinucleon mechanisms has some unwanted consequences. Obviously, the neutrino energyreconstruction, based on the QE kinematics is not so reliable [20, 25–27] and that implies larger systematic uncer-tainties in the experiments analysis. Furthermore, a clear separation of quasielastic and multinucleon events is notstraightforward from the experimental point of view, even if final nucleons were detected, due to the energy thresholdsand to the strong final state interaction of the nucleons in their way out of the nucleus. It is evident the need forcomprehensive and theoretically well founded models that provide a good description for single and multinucleonprocesses. Only with their help, one could approach the tasks of disentangling the genuine QE events and properlyreconstruct the neutrino energy. Of particular interest are the atomic number and the neutrino energy dependence ofthe reactions, the quest for kinematical regions with minimal multinucleon contamination and the relative importanceof multinucleon mechanisms for neutrino versus antineutrino induced reactions. In fact, the latter observable couldbe an stringent test for the available models [16, 28]. Furthermore, if the contribution of multinucleon mechanisms issubstantially different in neutrinos and antineutrinos, as predicted for instance in Refs. [9, 13] and this is not properlyunderstood, it could lead to an asymmetry between ν and ¯ ν which could be misinterpreted as a consequence of CPviolation.Our approach for the study of QE and multinucleon processes induced by neutrinos was developed in Refs. [5, 6, 18–20]. The model starts from a local Fermi gas (LFG) picture for the nucleus. The purely QE contribution for bothneutrinos and antineutrinos was studied in Refs. [5, 6] incorporating among other nuclear effects Pauli blocking, Fermimotion and the long range correlations (RPA). A correct energy balance is imposed using the experimental Q values. After subtraction of some background, such as pion production followed by absorption.
Of the various options discussed in those papers, we will use here the fully relativistic model of Ref. [5]. Multinucleonmechanisms (not properly QE) in the neutrino nucleus scattering were studied in Ref. [18]. The approach is based ona systematic many body expansion of the W boson absorption modes that includes one, two and even three nucleonmechanisms, as well as the excitation of ∆ isobars followed by their absorption and the production of pions. Theparameters of the calculation had been previously fixed in the study of photon, electron and pion interactions withnuclei. The model successfully describes [19] the published MiniBooNE neutrino CCQE-like data, finding a largecontribution of two nucleon excitation mechanisms or, using the usual many body naming, 2 particle – 2 hole (2p2h)channels. In a latter work [20], we investigated the energy reconstruction procedure with the aim of determiningthe influence of the multinucleon excitations on the extraction of neutrino energy unfolded cross sections from themeasured flux-average data. We found that the 2p2h contribution strongly distorts the shape of the total CCQE-likeflux unfolded cross section for neutrino beams.In this work, we apply the same model [19] for QE plus multinucleon mechanisms to antineutrino nucleus scatteringand compare with the recent MiniBooNE data [29]. The differences with the neutrino calculation are straightforward.The sign of the antisymmetric piece of the leptonic tensor is changed and that implies a change on the sign of the parityviolating pieces. In terms of the nuclear structure functions, this means a change of sign in the pieces proportional to W in the differential cross section, following the notation of Ref. [5]. The W + boson selfenergy in the nuclear mediumis replaced by that of the W − . This is achieved by exchanging the role of protons and neutrons in all formulae. Finally,proper care has to be taken with the energy balance because of the different Q values. We will always use the sameaxial mass of our previous papers ( M A = 1 .
049 GeV).The results presented in this paper correspond to QE and 2p2h contributions to the ¯ ν µ + C → µ + + X process.Scattering on other nuclei like O or Fe produce similar cross sections per nucleon. Apart from the ¯ ν , ν energydependence of the cross sections and their ratio and the muon angular distribution, we will also show results of thedouble differential cross section d σ/dcos θ µ dT µ folded with the MiniBooNE ¯ ν µ flux. σ / Z ( - c m ) QE2p2hQE+2p2h appx QE appx appx QE+2p2h ν µ + C FIG. 1: Cross section contributions divided by the number of protons for ¯ ν + C scattering as a function of the antineutrinoenergy. Curves labeled appx correspond to the approximated unfolded cross section for the MiniBooNE flux. Experimentalpoints from Ref. [29]. The results are shown in Figs. 1-4. In Fig. 1, we show the energy dependence of the QE and the 2p2h contributionsto the ¯ ν µ + C cross section. The cross sections are smaller than for neutrinos. In this case, 2p2h channels alsoprovide an important contribution which cannot be neglected. One of the relevant questions is to assess the quality ofthe standard procedures of energy reconstruction. Our results are similar to those obtained for the neutrino case. Inthe figure, we have labeled appx the approximated unfolded cross sections . We observe that for genuine QE eventsthe curve is hardly modified. However, for 2p2h events there is a substantial displacement towards low energies thatis also reflected in the summed cross section. In other words, some “high” energy antineutrinos would be identified as“low” energy ones. Although this statement is of a general validity, the detailed distortion of the cross section curvedepends on the antineutrino flux. The full model for the unfolded σ appx agrees well with the experimental data ,whereas the pure QE contribution predicts lower values for the cross section. σ ν µ / σ ν µ QEQE+2p2h appx
QE+2p2h
FIG. 2: Ratios of neutrino versus antineutrino cross sections in C as a function of the energy. Solid line: QE + 2p2h.Dash-dotted line: QE. Triangles: Ratio obtained with the MiniBooNE flux using the unfolding procedure of Ref. [20]. Fig. 2, shows the ratio between the neutrino and the antineutrino induced reactions. The inclusion of the 2p2hmechanisms slightly reduces the ratio (by less than a ten percent at the peak) without much affecting the shape. Thus,in our model the relative importance of the 2p2h channel is somehow larger for antineutrinos. A similar trend, althoughwith a stronger reduction, has been found by Amaro et al. [13] in the superscaling approximation and by Meucci etal. [21] in the EDAI option of the relativistic Green’s function model, which agrees well with the ν µ MiniBooNE data.Other works like Ref. [16], which reaches agreement with MiniBooNE QE neutrino data by modifying the magneticform factors of the bound nucleons, and Ref. [9] lead to larger values for this ratio. This latter reference is of particular See Ref. [20] for details on the unfolding procedure For this observable, there is an additional 17.2% normalization uncertainty not shown in the figure. interest as it is the closest to our approach and contains a microscopical evaluation of 2p2h mechanisms similar toours. However, there are some important differences which amount to a more comprehensive inclusion of mechanismsin our scheme and some approximations used in the calculations. A detailed discussion on these differences can befound in Ref. [18]. Finally, we find that the unfolding procedure respects the σ ν /σ ¯ ν ratio for energies above 0.6 GeVbut produces a strong distortion at lower energies.In Fig. 3, we present the muon angular distribution for 1 GeV neutrinos (antineutrinos). The ¯ ν scattering is moreforward peaked than the ν one for both the QE and the 2p2h contributions. This is due to the different sign of thepiece proportional to the W structure function (cf. Eq. (10) of Ref. [5]) which leads to a negative interference forthe ¯ ν case. cos θ µ d σ / d c o s θ µ ( - c m ) ν QE ν ν QE+2ph ν QE ν ν QE+2ph ν µ , ν µ + C E ν = 1.0 GeV FIG. 3: Muon angular distributions for 1 GeV neutrinos (antineutrinos) scattering on C. As discussed in Ref. [19], excluded the observation of final hadrons, a good observable to compare with theoreticalmodels is the double differential cross section corresponding to the energy and angle of the final muon, because itavoids the problems of energy reconstruction and depends just on directly measured quantities. In Fig. 4, we showour results for that cross section for the muonic antineutrino flux of MiniBooNE. In general terms, we successfullydescribe these data. For all angular windows 2p2h mechanisms play an important role and lead to a much betteragreement with data. Their contribution tends to concentrate at low muon energies so that more energy is transferredto the nucleus than in pure QE events. Comparing this plot with its neutrino counterpart [3, 19], we observe a quitedifferent pattern because of the more forward peaked character of the antineutrino induced reaction. There are alsosome changes concerning the antimuon energy distribution that are mostly due to the lower average energies of theMiniBooNE ¯ ν flux.In summary, we have studied non mesonic antineutrino nucleus cross sections in a model that starts from a relativisticlocal Fermi gas description of the nucleus, includes RPA correlations and multinucleon effects finding a good agreementwith experimental data. The same model had been quite successful for the neutrino cross section and contains no d σ / d T µ d c o s θ µ / Z ( - c m G e V )
012 01 010 0.5 1 1.5 20510 0 0.5 1 1.5 2 T µ (GeV)
012 0 0.5 1 1.5 201 0 0.5 1 1.5 201cos θ=0.95 ν µ + C FIG. 4: Muon angle and energy distribution d σ/dcosθ µ dT µ per proton on a C target folded with the MiniBooNE muonantineutrino flux. Different panels correspond to the various angular bins labeled by their cosinus central value. Black-solidline is the full model including QE (relativistic and with RPA) and 2p2h mechanisms. Red-dash-dotted curve corresponds toQE and blue-dashed curve to 2p2h events. Data from Ref. [29], errors only account for the shape uncertainty. Besides, thereis an additional normalization uncertainty of 17.2%. free parameters. The effects of multinucleon events are seen to be larger, relative to the QE contribution, than forthe neutrino case and considerably improve the agreement with experiment. We have also found that the size of the2p2h cross section limits the reliability of the unfolding procedures based on the assumption of QE kinematics for thenon mesonic events.
Acknowledgments
This research was supported by the Spanish Ministerio de Econom´ıa y Competitividad and European FEDER fundsunder the contracts FIS2011-28853-C02-01 and FIS2011-28853-C02-02, by Generalitat Valenciana under contractPROMETEO/2009/0090 and by the EU Hadron-Physics2 project, grant agreement no. 227431. [1] R. Gran et al. [K2K Collaboration], Phys. Rev. D , 052002 (2006).[2] V. Lyubushkin et al. [NOMAD Collaboration], Eur. Phys. J. C (2009) 355.[3] A. A. Aguilar-Arevalo et al. [MiniBooNE Collaboration], Phys. Rev. D (2010) 092005.[4] O. Benhar, N. Farina, H. Nakamura, M. Sakuda and R. Seki, Phys. Rev. D , 053005 (2005).[5] J. Nieves, J. E. Amaro and M. Valverde, Phys. Rev. C (2004) 055503 [Erratum-ibid. C (2005) 019902].[6] J. Nieves, M. Valverde and M. J. Vicente Vacas, Phys. Rev. C (2006) 025504.[7] T. Leitner, L. Alvarez-Ruso and U. Mosel, Phys. Rev. C , 065502 (2006).[8] M. Martini, M. Ericson, G. Chanfray and J. Marteau, Phys. Rev. C , 065501 (2009).[9] M. Martini, M. Ericson, G. Chanfray and J. Marteau, Phys. Rev. C , 045502 (2010).[10] T. Leitner and U. Mosel, Phys. Rev. C (2010) 064614.[11] O. Benhar, P. Coletti and D. Meloni, Phys. Rev. Lett. (2010) 132301.[12] J. E. Amaro, M. B. Barbaro, J. A. Caballero, T. W. Donnelly and C. F. Williamson, Phys. Lett. B (2011) 151.[13] J. E. Amaro, M. B. Barbaro, J. A. Caballero and T. W. Donnelly, Phys. Rev. Lett. , 152501 (2012) [arXiv:1112.2123[nucl-th]].[14] J. E. Amaro, M. B. Barbaro, J. A. Caballero, T. W. Donnelly and J. M. Udias, Phys. Rev. D , 033004 (2011).[15] C. Juszczak, J. T. Sobczyk and J. Zmuda, Phys. Rev. C (2010) 045502.[16] A. Bodek, H. S. Budd and M. E. Christy, Eur. Phys. J. C , 1726 (2011).[17] A. V. Butkevich, Phys. Rev. C (2010) 055501.[18] J. Nieves, I. Ruiz Simo and M. J. Vicente Vacas, Phys. Rev. C (2011) 045501.[19] J. Nieves, I. Ruiz Simo and M. J. Vicente Vacas, Phys. Lett. B (2012) 72.[20] J. Nieves, F. Sanchez, I. Ruiz Simo and M. J. Vicente Vacas, Phys. Rev. D , 113008 (2012).[21] A. Meucci and C. Giusti, Phys. Rev. D , 093002 (2012) [arXiv:1202.4312 [nucl-th]].[22] S. Boyd, S. Dytman, E. Hernandez, J. Sobczyk and R. Tacik, AIP Conf. Proc. (2009) 60.[23] L. Alvarez-Ruso, arXiv:1012.3871 [nucl-th].[24] A. Bodek, S. Avvakumov, R. Bradford and H. S. Budd, Eur. Phys. J. C , 349 (2008).[25] M. Martini, M. Ericson and G. Chanfray, Phys. Rev. D , 093012 (2012).[26] O. Lalakulich and U. Mosel, Phys. Rev. C , 054606 (2012).[27] M. Martini, M. Ericson and G. Chanfray, arXiv:1211.1523 [hep-ph].[28] O. Lalakulich, K. Gallmeister and U. Mosel, Phys. Rev. C , 014614 (2012).[29] A. A. Aguilar-Arevalo, B. C. Brown, L. Bugel, G. Cheng, E. D. Church, J. M. Conrad, R. Dharmapalan and Z. Djurcic etal.etal.