The W boson production cross section at the LHC through O(alpha_s^2)

We compute the O(alpha_s^2) QCD corrections to the fully differential cross-section pp \to W X \to l \nu X, retaining all effects from spin correlations. The knowledge of these corrections makes it possible to calculate with high precision the W boson production rate and acceptance at the LHC, subject to realistic cuts on the lepton and missing energy distributions. For certain choices of cuts we find large corrections when going from next-to-leading order (NLO) to next-to-next-to-leading order (NNLO) in perturbation theory. These corrections are significantly larger than those obtained by parton-shower event generators merged with NLO calculations. Our calculation may be used to assess and significantly reduce the QCD uncertainties in the many studies of $W$ boson production planned at the LHC.