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

We investigate the total scattering cross section($\sigma$), the differential cross section$\left(\frac{d\sigma}{dQ^2}\right)$, 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 future experiments 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 the above mentioned observables, and their sensitivities to the various parameterizations of the axial vector form factor $g_1(Q^2)$ and a nonzero weak electric form factor $g_2(Q^2)$ are examined. We find that the cross section depends strongly on the parameterizations used for the axial vector form factor. Moreover, the dipole parameterization of $g_1(Q^2)$ with a higher value of the axial dipole mass $M_A$ simulates the apparent enhancement in $\sigma$ obtained using the non-dipole parameterizations like the $z$-expansion and Faddeev equation form. The cross sections are found to depend only weakly on the weak electric form factor $g_2(Q^2)$, which is associated with the violation of G-invariance. On the contrary, the spin observables both $A_{L,P}(E_e, Q^2)$ and $P_{L,P}(E_e, Q^2)$ are found to be strongly dependent on $g_2(Q^2)$. This study may be useful in the analysis of the neutrino oscillation experiments to provide an alternative constrain on the parameterization of axial vector form factor, which currently has large uncertainties.