Measurement of the forward $W$ boson cross-section in $pp$ collisions at $\sqrt{s} = 7 {\rm \, TeV}$

A measurement of the inclusive $W \to μν$ production cross-section using data from $pp$ collisions at a centre-of-mass energy of $\sqrt{s} = 7 {\rm \, TeV}$ is presented. The analysis is based on an integrated luminosity of about $1.0 {\rm \, fb}^{-1}$ recorded with the LHCb detector. Results are reported for muons with a transverse momentum greater than $20 {\rm \, Ge\kern -0.1em V\!/}c$ and pseudorapidity between 2.0 and 4.5. The $W^{+}$ and $W^{-}$ production cross-sections are measured to be $$σ_{W^{+} \to μ^{+}ν} = 861.0 \pm 2.0 \pm 11.2 \pm 14.7 {\rm \, pb},$$ $$σ_{W^{-} \to μ^{-}\overlineν} = 675.8 \pm 1.9 \pm 8.8 \pm 11.6 {\rm \, pb},$$ 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 $$\frac{σ_{W^{+} \to μ^{+}ν}}{σ_{W^{-} \to μ^{-}\overlineν}} = 1.274 \pm 0.005 \pm 0.009,$$ 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.