Probing the nucleon axial form factor via the $\vec{e}^{\,+} + {}^2\text{H} \rightarrow \barν_e + p + p$ reaction below the pion-production threshold
The nucleon axial form factor $F_A(Q^2)$ is a primary source of systematic uncertainty in charged-current quasielastic interactions, of critical importance for long-baseline neutrino-oscillation studies. Its low-$Q^2$ behavior is particularly problematic to pin down in neutrino measurements. To address this limitation, we investigate the weak process of polarized positron capture on the deuteron, $\vec{e}^{\,+} + {}^2\text{H} \rightarrow \barν_e + p + p$. Employing a relativistic momentum-space formalism, we present predictions for the total cross section. Focusing on the kinematic regime free from pion-production backgrounds, we analyze various differential cross sections and their sensitivity to the $F_A(Q^2)$ variation. Our results demonstrate that thanks to the positron upgrade, Jefferson Lab will gain a unique position to make inroads into determining the low-$Q^2$ behavior of the axial form factor.