Measurement of the forward $W$ boson cross-section in $pp$ collisions at $\sqrt{s}=7\mathrm{T}\mathrm{e}\mathrm{V}$

A measurement of the inclusive $W\to \mu \nu$ production cross-section using data from $pp$ collisions at a centre-of-mass energy of $\sqrt{s} = 7 {\rm , TeV}$ispresented\mathrm{.}Theanalysisisbasedonanintegratedluminosityofabout$1.0 {\rm , fb}^{-1}$ recorded with the LHCb detector. Results are reported for muons with a transverse momentum greater than $20 {\rm , Ge\kern -0.1em V!/}c$andpseudorapiditybetween2.0and\mathrm{4.5.}The$W^{+}$and$W^{-}$productioncross-sectionsaremeasuredtobe$$\sigma_{W^{+} \to \mu^{+}\nu} = 861.0 \pm 2.0 \pm 11.2 \pm 14.7 {\rm , pb},$$ $${\sigma }_{W^{-}\to {\mu }^{-}\bar{\nu }}=675.8\pm 1.9\pm 8.8\pm 11.6\mathrm{p}\mathrm{b},$$ where the first uncertainty is statistical, the second is systematic and the third is due to the luminosity determination. Cross-section ratios and differential distributions as functions of the muon pseudorapidity are also presented. The ratio of $W^{+}$ to $W^{-}$ cross-sections in the same fiducial kinematic region is determined to be $$\frac{{\sigma }_{W^{+}\to {\mu }^{+}\nu }}{{\sigma }_{W^{-}\to {\mu }^{-}\bar{\nu }}}=1.274\pm 0.005\pm 0.009,$$ where the uncertainties are statistical and systematic, respectively. Results are in good agreement with theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics.