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. At the integrated cross section level, using a fiducial ATLAS cut with a jet veto, the effect is $9\%$ compared to the NLO value of the light-quark contribution. It increases to $13\%$ after removing the jet veto. 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. Relevant scale uncertainties are calculated to help us decide on the importance of this interference.