WBoson Production Cross Section at the Large Hadron Collider withO(αs2)Corrections

We compute the $\mathcal{O}({\alpha }_s^2)$ QCD corrections to the fully differential cross section $pp\to WX\to l\nu X$, 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 CERN Large Hadron Collider (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 in perturbation theory. These corrections are significantly larger than those obtained by parton-shower event generators merged with NLO calculations. Our result may be used to assess and significantly reduce the QCD uncertainties in the many studies of $W$ boson production planned at the LHC.