Measurement of the $W$-boson production cross-sections in $pp$ collisions at $\sqrt{s}$ = 13 TeV in the forward region

A precision measurement of the $W$-boson production cross-section is performed using the $W\to \mu \nu$ decay channel, based on a sample of proton-proton collision data collected by the LHCb experiment at $\sqrt{s}$ = 13 TeV and corresponding to an integrated luminosity of 5.1 $f{b}^{-1}$. The cross-section is measured for muons with transverse momentum between 25 and 55 GeV and pseudorapidity between 2.0 and 4.5. The integrated production cross-sections of $W$ bosons are measured to be $$\begin{array}{lcl}{\sigma }_{W^{+}\to {\mu }^{+}\nu }& =& 1754.2\pm 1.5\pm 11.9\pm 35.1\text{ pb}\\ {\sigma }_{W^{-}\to {\mu }^{-}\bar{\nu }}& =& 1178.1\pm 1.3\pm 9.7\pm 23.6\text{ pb}\end{array}$$ where uncertainties are statistical, systematic, and due to the luminosity determination, respectively. Results are in good agreement with theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics. This measurement is significantly more precise than previous results in this kinematic regime.