Mean field approach to reconstructed neutrino energy distributions in accelerator-based experiments

Background: The reconstruction of the neutrino energy is crucial in oscillation experiments that use interactions with nuclei to detect the neutrino. The common reconstruction procedure is based on the kinematics of the final-state lepton. The interpretation of the reconstructed energy in terms of the real neutrino energy must rely on a model for the neutrino-nucleus interaction. The relativistic Fermi gas (RFG) model is frequently used in these analyses. Purpose: We examine the effects of nuclear structure and dynamics going beyond a Fermi gas model on the reconstruction procedure. Method: In the Hartree-Fock (HF) model for a quasielastic nucleon knockout, the bound nucleon wave functions are obtained through a calculation using an effective nucleon-nucleon force. The final-state wave function is constructed from continuum states in the same potential which have the correct asymptotic behavior. The continuum random-phase approximation (CRPA) model extends the HF approach taking long-range correlations into account in a self-consistent way. Results: Considering only single-nucleon processes, the distributions of (reconstructed) neutrino energies obtained within the HF-CRPA approach are compared with the results of the RFG, a relativistic plane-wave impulse approximation calculation, and the RPA+np-nh model of Martini et al. [Phys. Rev. C 80, 065501 (2009)PRVCAN0556-281310.1103/PhysRevC.80.065501]. Conclusions: We find that the distributions of reconstructed energies for a fixed incoming energy in the HF-CRPA display additional strength in the lower reconstructed energy tails compared to models without elastic distortion of the outgoing nucleon and the mean-field description of the initial nucleon. This asymmetry redistributes strength from higher to lower values of the reconstructed energy. The mean-field description of the nuclear dynamics results in a reshaping of the reconstructed energy distribution that cannot be accounted for in a plane-wave impulse approximation model even by modifying ad hoc parameters, such as the binding energy. In particular, it is shown that in the RFG calculations there is no value of the binding energy which is able to reproduce the entire νμ oscillated spectrum of the T2K experiment as calculated in HF-CRPA.