Mixed QCD–electroweak O(αsα)O(αsα) corrections to Drell–Yan processes in the resonance region: Pole approximation and non-factorizable corrections

Drell–Yan-like W-boson and Z-boson production in the resonance region allows for high-precision measurements that are crucial to carry experimental tests of the Standard Model to the extremes, such as the determination of the W-boson mass and the effective weak mixing angle. In this article, we establish a framework for the calculation of the mixed QCD–electroweak O(αsα)O(αsα) corrections to Drell–Yan processes in the resonance region, which are one of the main remaining theoretical uncertainties. We describe how the Standard Model prediction can be successfully performed in terms of a consistent expansion about the resonance poles, which classifies the corrections in terms of factorizable and non-factorizable contributions. The former can be attributed to the W/ZW/Z production and decay subprocesses individually, while the latter link production and decay by soft-photon exchange. At next-to-leading order we compare the full electroweak corrections with the pole-expanded approximations, confirming the validity of the approximation. At O(αsα)O(αsα), we describe the concept of the expansion and explicitly give results on the non-factorizable contributions, which turn out to be phenomenologically negligible. Our results, thus, demonstrate that for phenomenological purposes the O(αsα)O(αsα) corrections can be factorized into terms associated with initial-state and/or final-state corrections. Moreover, we argue that the factorization properties of the non-factorizable corrections at O(αsα)O(αsα) from lower-order O(αs)O(αs) graphs generalize to any order in O(αsnα).