arXiv:1001.0481v2 [nucl-th] 12 Jul 2010 Analysis of the Q 2 dependence of charged-current quasielastic processes in neutrino-nucleus interactions Artur M. Ankowski, 1, 2, ∗ Omar Benhar, 2 and Nicola Farina 2 $^{1}$Institute of Theoretical Physics, University of WrocGLYPH<suppress>law, WrocGLYPH<suppress>law, Poland, $^{2}$INFN and Department of Physics,“Sapienza” Universit` a di Roma, I-00185 Roma, Italy (Dated: June 21, 2018) We discuss the observed disagreement between the Q 2 distributions of neutrino-nucleus quasielas- tic events, measured by a number of recent experiments, and the predictions of Monte Carlo sim- ulations based on the relativistic Fermi gas model. The results of our analysis suggest that these discrepancies are likely to be ascribable to both the breakdown of the impulse approximation and the limitations of the Fermi gas description. Several issues related to the extraction of the Q 2 distri- butions from the experimental data are also discussed, and new kinematical variables, which would allow for an improved analysis, are proposed. PACS numbers: 13.15.+g, 25.30.Pt I. INTRODUCTION A number of recent experiments reported a sizable disagreement between the measured Q 2 distributions of neutrino-nucleus scattering events and the results of Monte Carlo (MC) simulations [1–3]. The largest dis- crepancies occur in the region of low Q $^{2}$, typically Q 2 ≲ 0 . 2 GeV $^{2}$, where the observed number of charged-current quasielastic (CCQE) events is significantly lower than MC predictions. To account for this differences, the Mini- BooNE Collaboration introduced an additional parame- ter in the relativistic Fermi gas (RFG) model used in the MC code [2]. This procedure leads to a modification of the treatment of Pauli blocking, whose physical interpre- tation is quite questionable. In Ref. [2] it was also argued that a more refined treatment of nuclear effects may be needed. However, the results of Ref. [4] suggest that re- placing the RFG model with the approach based on the use of a realistic spectral function (SF) does not lead to a consistent description of low- and high- Q 2 data. Note that, although strictly speaking the spectral function can also be defined in the RFG model, in which case it re- duces to a collection of δ -function peaks, in the following we will use the acronym SF to indicate a spectral function obtained from more advanced dynamical models. The basic assumption underlying MC simulations is the validity of the impulse approximation (IA), imply- ing that the scattering process involves only one nucleon, while the remaining ( A − 1) particles act as spectators. This scheme is likely to be applicable if the space resolu- tion of the incoming neutrino, λ ∼ | q | − $^{1}$, where q is the momentum transfer, is small compared to the average separation between nucleons in the target nucleus. In this paper we analyze possible sources of the ob- served discrepancies, associated with both the breakdown ∗ Artur.Ankowski@roma1.infn.it The results of the calculations, carried out for a carbon target using both the RFG model, with Fermi momentum with Δ M 2 = M 2 n − M 2 $_{p}$, M$_{n}$ and M$_{p}$ being the neutron and proton mass, is the reconstructed energy of the in- coming neutrino. Note that Eqs. (1) and (2) have to be regarded as definitions of two quantities used in data analysis and should not be identified with the true Q 2 and neutrino energy. E rec ν = 2 E$_{µ}$ ( M$_{n}$ − ε ) − ( ε 2 − 2 M$_{n}$ε + m 2 µ + Δ M $^{2}$) 2( M$_{n}$ − ε − E$_{µ}$ + | k $^{′}$| cos θ ) , (2) where m$_{µ}$ , k $^{′}$, and θ denote the muon mass, momentum, and scattering angle, respectively. In the above equation Q 2 rec = − m 2 µ + 2 E rec ν ( E$_{µ}$ − | k $^{′}$| cos θ ) , (1) Consider the yield of CCQE events averaged over the MiniBooNE neutrino flux. We have compared the dis- tributions of events plotted as a function of Q 2 and its reconstructed value, defined as [1, 2] II. UNCERTAINTIES IN THE Q 2 RECONSTRUCTION In Section II we discuss the bias of the Q 2 reconstruc- tion from the kinematics of the CCQE events, while Sec- tion III is devoted to a quantitative investigation of the limits of applicability of the IA scheme. In Section IV we discuss the main difficulties involved in the comparison between theoretical calculations and experimental data, and put forth the proposal of new kinematical variables, whose use may allow for a more effective data analysis. Finally, in Section V, we summarize our results and state the conclusions. of the IA and the limitations of the RFG model, and point out some issues related to the extraction of the Q 2 distributions from the experimental data.