EW one-loop corrections to the longitudinally polarized Drell--Yan scattering. (I). The Neutral current case

Complete one-loop electroweak corrections to neutral current Drell-Yan process $pp\to {\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}X$ are presented for the case of longitudinal polarization of initial particles. Cross sections for longitudinally polarized protons allow us to estimate different combinations of polarized quark distributions from single- and double-spin asymmetries. Numerical impact of electroweak next-order corrections to asymmetries as function of the vector boson rapidity and lepton pseudorapidities in the hadron-hadron centre-of-mass frame using the MC generator ReneSANCe is thoroughly studied.