The Nucleon Axial Form Factor from Elementary Target Data

TL;DR

This work scrutinizes the nucleon axial form factor $F_A(Q^2)$ using elementary-target data from MINERvA hydrogen, deuterium bubble chambers, BEBC, and LQCD inputs, employing a $z$-expansion with regularization to extract $F_A$ and its uncertainties. It finds notable tension between hydrogen (MINERvA) and deuterium data, with deuterium data showing strong sensitivity to prior choices and potentially underestimating uncertainties. The analysis favors a modern, theory-grounded parameterization based on $k_{ m max}=6$ fits, with strong support from LQCD and MINERvA, and recommends deprioritizing deuterium data until systematic issues are resolved. The resulting axial-radius values and form-factor shapes imply slower $Q^2$ falloff in single-nucleon constraints than traditional dipole fits, impacting neutrino-oscillation predictions and Monte Carlo tuning, and highlighting the value of combining free-nucleon data with LQCD constraints for robust axial form-factor determinations.

Abstract

Precise neutrino-nucleon amplitudes are essential ingredients for predicting neutrino event rates in current and upcoming long-baseline neutrino oscillation experiments. A common neutrino interaction with a low reaction threshold and with most of the energy carried by two final state particles is quasielastic scattering, for which the nucleon axial form factor, $F_{A}(Q^{2})$, is a dominant source of uncertainty. Improvements to the nucleon axial form factor rely on neutrino scattering data with elementary targets to reduce or eliminate the need for nuclear modeling systematics. This work examines constraints on the nucleon axial form factor that can be achieved from datasets of neutrino scattering on deuterium targets, Lattice QCD predictions, and from the recent hydrogen target data from the MINERvA Collaboration. Significant tension is found between hydrogen and deuterium target data, suggesting that extractions from deuterium underestimate both the central value and uncertainty of the form factor. Parameterizations for and uncertainties of the nucleon axial form factor using the $z$ expansion are provided.

Figures (12)

• Figure 1: L-curve obtained from fitting only the MINERvA dataset. The left plot shows the full range $\lambda \in [0,1]$, and the right plot is zoomed in on the region with minimum radius of curvature. The numbers superimposed on the plot indicate the value of $\lambda$.
• Figure 2: L-curve obtained from fitting all of the deuterium datasets together. The left plot shows the $Q^{2}_{\rm min}=0.06~{\rm GeV}^{2}$ cut, and the right plot the $Q^{2}_{\rm min}=0.20~{\rm GeV}^{2}$ cut.
• Figure 3: Plots of the axial form factor as a function of the 4-momentum transfer $Q^{2}$. The left panel shows the regularized fits with $\lambda=1$ and $k_{\rm max}=7$. The right panel shows the unregularized fits with $\lambda=0$ and $k_{\rm max}=6$. The cut at $Q^{2}_{\rm min}=0.06~{\rm GeV}^{2}$ is given by the teal shaded region bounded by a dashed line, and the cut at $Q^{2}_{\rm min}=0.20~{\rm GeV}^{2}$ by the orange shaded region bounded by the dot-dashed line. The result from Ref. Meyer:2016oeg, which has $k_{\rm max}=8$ and $\lambda=1$, is given by the unfilled region bounded by solid black lines.
• Figure 4: The fit axial form factors both before and after the addition of the BEBC dataset to the other event distributions. In these fits, $k_{\rm max}=6$ is chosen and the $z$ expansion parameters are unregularized ($\lambda=0$). The left (right) panel shows the form factors obtained when the $0.06~{\rm GeV}^{2}$ ($0.20~{\rm GeV}^{2}$) cuts are applied to the event distribution datasets. The teal shaded region bounded by dashed lines indicates the fit only to the BEBC dataset (the same in both panels). The orange shaded region bounded by the dot-dashed line indicates the event-distribution datasets that were shown in the right panel of Fig. \ref{['fig:lambda_dependence']}. The blue-violet shaded region bounded by the dotted line is the combined fit including both the event-distribution datasets and the BEBC dataset. The result from Ref. Meyer:2016oeg is given by the unfilled region bounded by solid black lines.
• Figure 5: The fit axial form factors for the BEBC dataset in isolation (teal shading, bounded by dashed line) and the combined fit with the event distribution datasets. The orange shaded region bounded by the dot-dashed line is the same joint-fit result shown in the left panel of Fig. \ref{['fig:addition_bebc']}. The blue-violet shaded region bounded by the dotted line is the same joint-fit result shown in the right panel of Fig. \ref{['fig:addition_bebc']}.