Lepton-pair production in association with a $b\bar{b}$ pair and the determination of the $W$ boson mass

We perform a study of lepton-pair production in association with bottom quarks at the LHC based on the predictions obtained at next-to-leading order in QCD, both at fixed order and matched with a QCD parton shower. We consider a comprehensive set of observables and estimate the associated theoretical uncertainties by studying the dependence on the perturbative QCD scales (renormalisation, factorisation and shower) and by comparing different parton-shower models (Pythia8 and Herwig++) and matching schemes (MadGraph5_aMC@NLO and POWHEG). Based on these results, we propose a simple procedure to include bottom-quark effects in neutral-current Drell-Yan production, going beyond the standard massless approximation. Focusing on the inclusive lepton-pair transverse-momentum distribution $p_{\bot}^{l^+l^-}$, we quantify the impact of such effects on the tuning of the simulation of charged-current Drell-Yan observables and the $W$-boson mass determination.