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

Abstract

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*} \sigma_{W^+ \to \mu^+ \nu_\mu} &= 300.9 \pm 2.4 \pm 3.8 \pm 6.0~\text{pb}, \\ \sigma_{W^- \to \mu^- \bar{\nu}_\mu} &= 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.