Dominant $\mathcal{O}(\alpha_s\alpha)$ corrections to Drell-Yan processes in the resonance region

Apart from the well-known NNLO QCD and NLO electroweak corrections to W- and Z-boson production at hadron colliders, the most important fixed-order corrections are given by the mixed QCD-electroweak corrections of $\mathcal{O}(\alpha_s\alpha)$. The knowledge of these corrections is of particular importance to control the theoretical uncertainties in the upcoming high-precision measurements of the W-boson mass and the effective weak mixing angle at the LHC. Since these observables are dominated by the phase-space regions of resonant W/Z bosons, we address the $\mathcal{O}(\alpha_s\alpha)$ corrections in the framework of an expansion about the W/Z poles. Retaining only the leading, resonant contribution in the so-called pole approximation, the corrections can be classified into factorizable and non-factorizable contributions. In this article we review our calculation of the numerically dominant corrections which arise from factorizable corrections of "initial-final" type, i.e. they combine the QCD corrections to the production with the large electroweak corrections to the decay of the W/Z boson. Moreover, we compare our results to simpler approximate combinations of electroweak and QCD corrections based on naive products of NLO QCD and electroweak correction factors and using leading-logarithmic approximations for QED final-state radiation. Finally, we estimate the shift in the W-boson mass that results from the $\mathcal{O}(\alpha_s\alpha)$ corrections to the transverse-mass distribution.