Prospects for improving the LHC W boson mass measurement with forward muons

Measurements of the $W$ boson mass are planned by the ATLAS and CMS experiments, but for the time being, these may be unable to compete with the current world average precision of 15~MeV, due to uncertainties in the PDFs. We discuss the potential of a measurement by the LHCb experiment based on the charged lepton transverse momentum $p_T^{\ell}$ spectrum in $W \to \mu\nu$ decays. The unique forward acceptance of LHCb means that the PDF uncertainties would be anti-correlated with those of $p_T^{\ell}$ based measurements by ATLAS and CMS. We compute an average of ATLAS, CMS and LHCb measurements of $m_W$ from the $p_T^{\ell}$ distribution. Considering PDF uncertainties, this average is a factor of 1.3 more precise than an average of ATLAS and CMS alone. Despite the relatively low rate of $W$ production in LHCb, we estimate that with the Run-II dataset, a measurement could be performed with sufficient experimental precision to exploit this anti-correlation in PDF uncertainties. The modelling of the lepton-pair transverse momentum distribution in the neutral current Drell-Yan process could be a limiting factor of this measurement and will deserve further studies.