Precision Calculations for Electroweak Physics at Hadron Colliders
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Electroweak (EW) corrections can be enhanced at high energies due to the soft or collinear radiation of virtual and real W and Z bosons that result in Sudakov-like corrections of the form α W l log n (Q 2 /M V 2 ), where α W = α/(4πsin 2 &thetas; W ) and n ≤ 2l – 1. Here M V denotes the W or Z boson mass, &thetas; w the weak mixing angle and Q 2 a typical energy scale of the hard process under consideration. The inclusion of EW corrections in predictions for the CERN Large Hadron Collider (LHC) is therefore especially important when searching for signals of possible new physics in distributions probing the kinematic regime Q 2 » M V 2 . Next-to-leading order (NLO) EW corrections should also be taken into account when their size (O(α)) is comparable to that of QCD corrections at next-to-next-to-leading order (NNLO) (O(α s 2 )). To this end we have calculated and implemented in the parton-level Monte-Carlo program MCFM the NLO weak corrections to three key processes at the LHC: the Neutral-Current Drell-Yan process, top-quark pair production and di-jet production. This enables a study of their effects on LHC observables combined with the already available QCD corrections at NLO and NNLO. We provide both the full NLO weak corrections and their Sudakov approximation, since the latter is often used for a fast evaluation of weak effects at high energies and can be extended to higher orders. With both the exact and approximate results at hand, the validity of the Sudakov approximation can be readily quantified. In the case of top-quark pair production at the LHC we also calculated the NLO QED corrections.