Parton density function uncertainties on the W boson mass measurement from the lepton transverse momentum distribution

We study the charged-current Drell-Yan process, and we evaluate the proton parton densities uncertainties on the lepton transverse momentum distribution and their impact on the determination of the W boson mass. We consider the global parton density function sets CT10, MSTW2008CPdeut, NNPDF2.3, NNPDF3.0, and MMHT2014 and apply the PDF4LHC recipe to combine the individual results, obtaining an uncertainty on m(W) that ranges between +/- 18 and +/- 24 MeV, depending on the final state, collider energy, and kind. We discuss the dependence of the uncertainty on the acceptance cuts and the role of the individual parton densities in the final result. We remark that some parton density function sets predict an uncertainty on m(W) of O(10 MeV); this encouraging result is spoiled, in the combined analysis of the different sets, by an important spread of the central values predicted by each group.