Analysis of flux-integrated cross sections for quasi-elastic neutrino charged-current scattering off $^{12}$C at MiniBooNE energies

TL;DR

This paper compares flux-integrated cross sections for neutrino scattering off carbon with experimental data, showing model independence of flux-integrated differential cross sections and analyzing the axial mass parameter within different nuclear models.

Contribution

It demonstrates the nuclear model independence of flux-integrated differential cross sections and evaluates the axial mass using relativistic models against MiniBooNE data.

Findings

Flux-integrated differential cross sections are model-independent.

Relativistic models yield an axial mass consistent with MiniBooNE.

Fermi gas model fails at low muon energies and angles.

Abstract

Flux-averaged and flux-integrated cross sections for quasi-elastic neutrino charged-current scattering on nucleus are analyzed. It is shown that the flux-integrated differential cross sections are nuclear model-independent. We calculate these cross sections using the relativistic distorted-wave impulse approximation and relativistic Fermi gas model with the Booster Neutrino Beamline flux and compare results with the recent MiniBooNE experiment data. Within these models an axial mass $M_A$ is extracted from a fit of the measured $d\sigma/dQ^2$ cross section. The extracted value of $M_A$ is consistent with the MiniBooNE result. The measured and calculated double differential cross sections $d\sigma/dTd\cos\theta$ generally agree within the error of the experiment. But the Fermi gas model predictions are completely off of the data in the region of low muon energies and scattering angles.