Axial-vector dominance predictions in quasielastic neutrino-nucleus scattering

TL;DR

This paper models the axial form factor in quasielastic neutrino-nucleus scattering using axial-vector-meson dominance constrained by QCD, and tests it against MiniBooNE data, showing good agreement and identifying key sensitivity regions.

Contribution

It introduces a generalized axial-vector-meson-dominance model with QCD constraints and the half width rule to predict the axial form factor without free parameters.

Findings

The model reproduces MiniBooNE data with $/ ext{bins} = 0.81.

Uncertainties in $G_A(Q^2)$ are comparable to the half width rule estimates.

The most sensitive $Q^2$ region is between 0.2 and 0.6 GeV$^2$.

Abstract

The axial form factor plays a crucial role in quasielastic neutrino-nucleus scattering, but the error of the theoretical cross section due to uncertainties of $G_A$ remains to be established. Reversely, the extraction of $G_A$ from the neutrino nucleus cross section suffers from large systematic errors due to nuclear model dependencies, while the use of single parameter dipole fits underestimates the errors and prevents an identification of the relevant kinematics for this determination. We propose to use a generalized axial-vector-meson-dominance (AVMD) in conjunction with large-$N_c$ and high energy QCD constrains to model the nucleon axial form factor, as well as the half width rule as an a priori uncertainty estimate. The minimal hadronic ansatz comprises the sum of two monopoles corresponding to the lightest axial-vector mesons being coupled to the axial current. The parameters of the resulting axial form factor are the masses and widths of the two axial mesons as obtained from the averaged PDG values. By applying the half width rule in a Monte Carlo simulation, a distribution of theoretical predictions can then be generated for the neutrino-nucleus quasielastic cross section. We test the model by applying it to the $(\nu_\mu,\mu)$ quasielastic cross section from $^{12}$C for the kinematics of the MiniBooNE experiment. The resulting predictions have no free parameters. We find that the relativistic Fermi gas model globally reproduces the experimental data, giving $\chi^2/ \# bins = 0.81$. A $Q^2$-dependent error analysis of the neutrino data shows that the uncertainties in the axial form factor $G_A(Q^2)$ are comparable to the ones induced by the a priori half width rule. We identify the most sensitive region to be in the range $0.2 \lesssim Q^2 \lesssim 0.6 \,{\rm GeV}^2$.