Impact of the parton distribution function uncertainties on the measurement of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math>boson mass at the Tevatron and the LHC

We study at a quantitative level the impact of the uncertainties on the value of the $W$ boson mass measured at hadron colliders due to: i) the proton parton distribution functions (PDFs), ii) the value of the strong coupling constant ${\ensuremath{\alpha}}_{s}$ and iii) the value of the charm mass used in the PDF determination. The value of the $W$ boson mass is extracted, by means of a template fit technique, from the lepton-pair transverse mass distribution measured in the charged current Drell-Yan process. We study the determination of ${m}_{W}$ at the Tevatron and at the LHC with 7 and 14 TeV of center-of-mass energy in a realistic experimental setup. The analysis has been done at the Born level using the event generator HORACE and at NLO-QCD using the event generators DYNNLO and ResBos. We consider the three global PDF sets, CTEQ6.6, MSTW2008, and NNPDF2.1. We estimate that the total PDF uncertainty on ${m}_{W}$ is below 10 MeV both at the Tevatron and at the LHC for all energies and final states. We conclude that PDF uncertainties do not challenge a measurement of the $W$ boson mass at the level of 10 MeV accuracy.