Polarized $W^+W^-$ pairs at the LHC: Effects from bottom-quark induced processes at NLO QCD+EW

We investigate the effects of the bottom-quark induced processes on the doubly polarized cross sections of $W^+W^-$ pair production at the LHC. The method to extract the on-shell single-top contribution is provided. Results for phenomenological and experimental analyses are given at next-to-leading order (NLO) QCD+EW accuracy, with the leading contribution from the gluon-gluon and photon-photon fusion included. We found that the contribution of the bottom-quark induced processes, after the subtraction of the on-shell $tW$ channel, is largest for the doubly longitudinal polarization, being at the level of $9\%$ and $13\%$ (compared to the NLO value of the light-quark contribution, for integrated cross section) for two cut setups, with and without a jet veto, respectively. A bound of the $tW$ interference is calculated for various kinematic distributions, showing that this interference effect is, in general, smaller for the no jet veto case.