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

The precision measurement of the W boson mass is an important milestone for the 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 of global electroweak fits, which in turn are sensitive to New Physics at scales potentially higher than the ones explored in direct searches. From the theoretical point of view, our limited knowledge of PDFs will be one of the dominant sources of uncertainty in ongoing and future LHC determinations of $M_W$. In this whitepaper, we have quantified the impact of PDF uncertainties in the W mass extractions from the transverse mass distribution at the LHC. The calculation has been performed using the NNPDF2.3 set, which includes direct constrains on the W boson production kinematics with data for electroweak gauge boson production from the LHC. Our results confirm previous estimates that PDF uncertainties in the determination of $M_W$ from the $m_W^T$ distribution are moderate, around 10 MeV at most. We briefly discuss also the case of the lepton $p_T$ distribution.