Charged current induced electron-proton scattering and the axial vector form factor

Abstract

We investigate the total scattering cross section ($σ$), differential cross section ($\frac{dσ}{dQ^2}$), the longitudinal ($A_L(E_e,Q^2)$) and perpendicular ($A_P(E_e,Q^2)$) spin asymmetries of the polarized target proton, as well as the longitudinal ($P_L(E_e,Q^2)$), perpendicular ($P_P(E_e,Q^2)$), and transverse ($P_T(E_e,Q^2)$) polarization components of the final neutron, in the weak charged current induced electron-proton scattering relevant to the experiments being performed at the Thomas Jefferson National Accelerator Facility (JLab) and Mainz Microtron (MAMI). The analysis is performed assuming time-reversal (T) invariance as well as without assuming T invariance, allowing for a nonvanishing transverse polarization component of the final nucleon, perpendicular to the production plane. Numerical results are presented for all observables, and their sensitivities to the axial vector and weak electric form factors are examined. This study may be useful in the neutrino oscillation experiments to provide an alternative constrain on the parameterization of axial vector form factor, which currently has large uncertainties.

Figures (20)

• Figure 1: Feynman diagram for the process $e^-(k) + p(p) \rightarrow \nu_e(k^\prime) + n(p^{\prime})$. The quantities in the bracket represent four momenta of the corresponding particles.
• Figure 3: Diagrammatic representation of the process $e^-(\vec{k}) + p(\vec{p}=0) \rightarrow \nu_e(\vec{k^\prime}) + n(\vec{p}^{~\prime})$, and the longitudinal and perpendicular directions of the polarized proton (left panel). The longitudinal, perpendicular and transverse directions with respect to the momentum of the final nucleon (right panel).
• Figure 4: Total cross section $\sigma$ as a function of $E_{e}$ for the process $e^- + p \longrightarrow \nu_{e} + n$, when the initial electron is polarized. (Left panel) shows the results for the different parameterizations of $g_{1}(Q^2)$ viz. the dipole parameterization with $M_{A} = 1.026$ GeV shown by solid lines with circle, the lattice gauge parameterization of Robert and Chen Chen:2021guoChen:2022odn shown by the dash-dotted line, the $z$ expansion for the MINERvA hydrogen, LQCD, deuterium, and combined hydrogen-LQCD fits are represented by double-dot-dashed line, double dash-dotted line, dashed line and dotted line, respectively. (Middle panel) shows the results for $\sigma$ using the different values of the axial dipole mass $M_{A}$ viz. $M_{A} =1.026$ GeV (dashed line), 1.1 GeV (dash-dotted line), 1.2 GeV (double-dot-dashed line), and 1.35 GeV (double-dash-dotted line). (Right panel) shows the results for $\sigma$ obtained using the different values of $g_{2}(0)$ assuming T-invariance viz. $g_{2}^{R} (0)=0$ (solid line), +1 (dashed line), +2 (dash-dotted line), $-1$ (double-dot-dashed line), and $-2$ (double-dash-dotted line).
• Figure 5: $g_2^R(0)-M_A$ correlation for $\sigma$ for the process $e^- + p \longrightarrow \nu_{e} + n$, when the initial electron is polarized at $E_{e}=855$ MeV (left panel), 1.1 GeV (middle panel), and 2.2 GeV (right panel).
• Figure 6: $\frac{d\sigma}{dQ^2}$ as a function of $Q^2$ at $E_{e}=855$ MeV (left panel), 1.1 GeV (middle panel), and 2.2 GeV (right panel) for the process $e^- + p \longrightarrow \nu_{e} + n$, when the initial electron is polarized for the different parameterizations of $g_{1}(Q^2)$. Lines and points have the same meaning as in Fig. \ref{['sigma:delta1']}.