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 \rightarrow \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.