Mixed NNLO QCD $\times$ electroweak corrections to single-Z production in pole approximation: differential distributions and forward-backward asymmetry

TL;DR

This paper advances the calculation of mixed QCD and electroweak corrections to Z-boson production, providing detailed differential distributions and asymmetry analysis crucial for precision measurements at the LHC.

Contribution

It completes previous calculations by including Z-production related corrections, enhancing the accuracy of theoretical predictions for Drell-Yan processes.

Findings

Initial-state QCD and electroweak final-state corrections dominate the mixed corrections.

The corrections significantly affect the forward-backward asymmetry in lepton-pair invariant mass.

Results improve the precision of weak mixing angle measurements at the LHC.

Abstract

Radiative corrections in pole approximation, which are based on the leading contribution in a systematic expansion of amplitudes about resonance poles, naturally decompose into factorizable corrections attributed to the production or decay of the resonance and non-factorizable corrections induced by soft photon (or gluon) exchange between those subprocesses. In this paper we complete an earlier calculation of mixed QCD$\times$electroweak corrections of $\mathcal{O}(\alpha_s\alpha)$ to the neutral-current Drell-Yan cross section in pole approximation by including the previously neglected corrections that are solely related to the Z-boson production process. We present numerical results both for differential distributions and for the forward-backward asymmetry differential in the lepton-pair invariant mass, which is the key observable in the measurement of the effective weak mixing angle at the LHC. Carefully disentangling the various types of factorizable and non-factorizable corrections, we find (as expected in our earlier work) that the by far most important contribution at $\mathcal{O}(\alpha_s\alpha)$ originates from the interplay of initial-state QCD corrections and electroweak final-state corrections.