Polarization observables and T-noninvariance in the weak charged current induced electron proton scattering

In this work, we have studied the total scattering cross section ($sigma$), differential scattering cross section ($dsigma/dQ^2$) as well as the longitudinal ($P_L(E_e,Q^2)$), perpendicular ($P_P(E_e,Q^2)$), and transverse ($P_T(E_e,Q^2)$) components of the polarization of the final hadron ($n$, $ Lambda$ and $Sigma^0$) produced in the electron proton scattering induced by the weak charged current. We have not assumed T-invariance which allows the transverse component of the hadron polarization perpendicular to the production plane to be non-zero. The numerical results are presented for all the above observables and their dependence on the axial vector form factor and the weak electric form factor are discussed. The present study enables the determination of the axial vector nucleon-hyperon transition form factors at high $ Q^2$ in the strangeness sector which can provide test of the symmetries of the weak hadronic currents like T-invariance and SU(3) symmetry while assuming the hypothesis of conserved vector current and partial conservation of axial vector current.