EW one-loop corrections to the longitudinally polarized Drell-Yan process. Charged-current case II

Complete one-loop electroweak radiative corrections to the charged-current Drell-Yan processes $pp\to {\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}(+X)$ and $pp\to {\mathrm{\ell }}^{-}{\bar{\nu }}_{\mathrm{\ell }}(+X)$ are presented for the case of longitudinal polarization of initial particles. The results can be used to obtain precise predictions for the kinematic distributions of polarized $W^{\pm }$ production cross sections, and single- and double-spin asymmetries. Numerical results are obtained using the Monte-Carlo generator {\tt ReneSANCe}. This research contributes to a global next-to-leading order analysis of polarized parton distributions in proton-proton collisions at RHIC. We proved that the impact of the one-loop electroweak radiative corrections to single- and double-spin asymmetries is negligible.