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

TL;DR

This paper calculates the dominant mixed QCD-electroweak corrections to W/Z boson production at hadron colliders, crucial for high-precision measurements of fundamental parameters like the W-boson mass.

Contribution

It provides a detailed calculation of the factorizable $ ext{O}( ext{ extalpha}_s ext{ extalpha})$ corrections in the resonance region using the pole approximation, including comparisons to approximate methods.

Findings

Dominant factorizable corrections identified and computed.

Comparison shows the importance of exact calculations over naive approximations.

Estimated shift in W-boson mass due to these corrections.

Abstract

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.