Measurement of the $W\to \mu {\nu }_{\mu }$ cross-sections as a function of the muon transverse momentum in $pp$ collisions at 5.02 TeV

The $pp\to W^{\pm }(\to {\mu }^{\pm }{\nu }_{\mu })X$ cross-sections are measured at a proton-proton centre-of-mass energy $\sqrt{s}=5.02$ TeV using a dataset corresponding to an integrated luminosity of 100 pb${}^{-1}$ recorded by the LHCb experiment. Considering muons in the pseudorapidity range $2.2<\eta <4.4$, the cross-sections are measured differentially in twelve intervals of muon transverse momentum between $28<p_{\mathrm{T}}<52$ GeV. Integrated over $p_{\mathrm{T}}$, the measured cross-sections are \begin{align*} σ_{W^+ \to μ^+ ν_μ} &= 300.9 \pm 2.4 \pm 3.8 \pm 6.0~$\text{pb}$, \ σ_{W^- \to μ^- \barν_μ} &= 236.9 \pm 2.1 \pm 2.7 \pm 4.7~$\text{pb}$, \end{align*} where the first uncertainties are statistical, the second are systematic, and the third are associated with the luminosity calibration. These integrated results are consistent with theoretical predictions. This analysis introduces a new method to determine the $W$-boson mass using the measured differential cross-sections corrected for detector effects. The measurement is performed on this statistically limited dataset as a proof of principle and yields \begin{align*} m_W = 80369 \pm 130 \pm 33~$\text{MeV}$, \end{align*} where the first uncertainty is experimental and the second is theoretical.