Charged-current quasielastic neutrino cross sections on $^{12}$C with realistic spectral and scaling functions

Abstract

Charge-current quasielastic (CCQE) (anti)neutrino scattering cross sections on a $^{12}$C target are analyzed using a spectral function $S(p,{\cal E})$ that gives a scaling function in accordance with the ($e,e'$) scattering data. The spectral function accounts for the nucleon-nucleon (NN) correlations, it has a realistic energy dependence and natural orbitals (NO's) from the Jastrow correlation method are used in its construction. In all calculations the standard value of the axial mass $M_A= 1.032$ GeV/c$^2$ is used. The results are compared with those when NN correlations are not included, as in the Relativistic Fermi Gas (RFG) model, or when harmonic-oscillator (HO) single-particle wave functions are used instead of NO's. The role of the final-state interactions (FSI) on the theoretical spectral and scaling functions, as well as on the cross sections is accounted for. A comparison of the results for the cases with and without FSI, as well as to results from the phenomenological scaling function obtained from the superscaling analysis (SuSA) is carried out. Our calculations based on the impulse approximation (IA) underpredict the MiniBooNE data, but agree with the data from the NOMAD experiment. The possible missing ingredients in the considered theoretical models are discussed.