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The precision measurement of the W boson mass is an important milestone forthe LHC physics program in the coming years. An accurate measurement of $M_W$allows to perform stringent consistency tests of the Standard Model by means ofglobal electroweak fits, which in turn are sensitive to New Physics at scalespotentially higher than the ones explored in direct searches. From thetheoretical point of view, our limited knowledge of PDFs will be one of thedominant sources of uncertainty in ongoing and future LHC determinations of$M_W$. In this whitepaper, we have quantified the impact of PDF uncertaintiesin the W mass extractions from the transverse mass distribution at the LHC. Thecalculation has been performed using the NNPDF2.3 set, which includes directconstrains on the W boson production kinematics with data for electroweak gaugeboson production from the LHC. Our results confirm previous estimates that PDFuncertainties in the determination of $M_W$ from the $m_W^T$ distribution aremoderate, around 10 MeV at most. We briefly discuss also the case of the lepton$p_T$ distribution.

PDF uncertainties in the extraction of the W mass at LHC: a Snowmass Whitepaper