Nucleon axial-vector form factor and radius from radiatively-corrected antineutrino scattering data

TL;DR

This paper develops and applies a QED radiative-corrections framework to extract the nucleon axial-vector form factor $G_A(Q^2)$ and the axial radius $r_A$ from elastic (anti)neutrino–nucleon scattering, notably MINERvA's antineutrino–hydrogen data. It employs a process-independent formalism, a $z$-expansion parameterization with physically constrained coefficients, and a fixed-order radiative-corrections treatment to convert predictions to the observed level, assessing impacts across current and future datasets. The results indicate that radiative corrections shift extracted axial quantities by amounts comparable to or larger than the experimental uncertainties in some fits, while deuterium data are comparatively less affected; the corrections will be essential for percent-level precision in upcoming oscillation experiments and LQCD comparisons. The work also discusses prospects for near-term improvements in both experimental analyses and lattice QCD to reach a coherent, high-precision understanding of the axial structure of the nucleon and its implications for neutrino–nucleon interactions.

Abstract

The nucleon axial-vector form factor, $G_A$, is critical to determine the electroweak interactions of leptons with nucleons. Important examples of processes influenced by $G_A$ are elastic (anti)neutrino-nucleon scattering and muon capture by the proton. Sparse experimental data results in a large uncertainty on the momentum dependence of $G_A$ and has motivated the consideration of new experimental probes and first-principles lattice quantum chromodynamics (QCD) evaluations. The comparison of new and precise theoretical predictions for $G_A$ with future experimental data necessitates the application of radiative corrections to experimentally-observable processes. We apply these corrections in the extraction of $G_A$ and the associated axial-vector radius from the recent MINERvA antineutrino-hydrogen data, compare the effects from radiative corrections to other uncertainties in neutrino scattering experiments, and discuss the comparison of lattice QCD evaluations to experimental measurements.

Figures (12)

• Figure 1: The ratio of the cross section with the radiative corrections to the leading-order cross section across $Q^2$ and $E_\nu$ for $\nu_\mu$ (left) and $\bar{\nu}_\mu$ (right).
• Figure 2: The ratio of the cross section after accounting for the radiative corrections relative the leading-order cross section as a function of $Q^2$, for the MINERvA (black solid line), BEBC (purple dash-dotted line), FNAL (red dashed line), ANL (green dotted line), and BNL (blue dash-dotted line) measurements. The black dashed line at $d\sigma/d\sigma_\textrm{LO}=1$ is intended to guide the eye.
• Figure 3: MINERvA muon antineutrino-hydrogen charged-current quasielastic data are compared to predictions with three different nucleon axial-vector form-factor choices from Refs. Bodek:2007viMeyer:2016oeg, where the BBBA07 form-factor choice is taken with and without the radiative corrections applied. The left figure shows the differential cross section in squared four-momentum transfer, and the right shows the data and calculations relative to the BBBA07 prediction without the radiative corrections. The calculated $\chi^2$ utilizes the covariance matrix provided by the MINERvA Collaboration.
• Figure 4: The nucleon axial-vector form factor $G_A \left( Q^2 \right)$ is shown as a function of the squared momentum transfer $Q^2$. The form factor is obtained from fitting recent MINERvA antineutrino-hydrogen data MINERvA:2023avz (i) using the BBBA2005 nucleon vector form factors Bradford:2006yz without the radiative corrections (blue solid lines with blue error band); (ii) using the Borah2020 nucleon vector form factors Borah:2020gte without the radiative corrections (black dashed lines and turquoise error band); and (iii) using the Borah2020 nucleon vector form factors Borah:2020gte with the radiative corrections Tomalak:2021hecTomalak:2022xup (red solid lines with the space between the outer two lines representing the unshaded error band).
• Figure 5: Antineutrino-hydrogen charged-current elastic cross-section data from MINERvA MINERvA:2023avz is compared with predictions based on the fits without the radiative corrections when the nucleon vector form factors are taken from Ref. Borah:2020gte, shown by the shorter turquoise bins, vs BBBA2005 fit Bradford:2006yz, shown by the red bins. Kinematic cuts in the MINERvA measurement are placed on the muon scattering angle $\theta_\mu \le 20^\circ$ and momentum $1.5~\mathrm{GeV} \le p_\mu \le 20~\mathrm{GeV}$. The thickness of the bin size in the panels represents the error, and the fifteenth bin is not shown. The two right panels zoom into the region $0.2~\mathrm{GeV}^2 \lesssim Q^2 \lesssim 1~\mathrm{GeV}^2$, and the region $Q^2 \gtrsim 1~\mathrm{GeV}^2$. Cross sections are evaluated with leading-order expressions.