Mixed QCD-electroweak corrections to on-shell Z production at the LHC

TL;DR

This paper provides the first complete calculation of mixed QCD-electroweak corrections for on-shell Z boson production at the LHC, highlighting their subtle interplay and importance for precision measurements.

Contribution

It introduces a fully differential computation of mixed QCD-electroweak corrections for Z production, enabling precise predictions for LHC observables.

Findings

Mixed corrections are small, about per mill level.

Interplay between QCD-QED and QCD-weak contributions is subtle.

Both corrections are necessary for ${\cal O}(\alpha_{EW} \alpha_s)$ precision.

Abstract

We present the first complete calculation of mixed QCD-electroweak corrections to the production of on-shell $Z$ bosons in hadron collisions and their decays to massless charged leptons. Our computation is fully differential with respect to final state QCD partons and resolved photons, allowing us to compute any infra-red safe observable pertinent to the $pp \to Z \to l^+ l^-$ process in the approximation that the $Z$ boson is on shell. Although mixed QCD-electroweak corrections are small, at about the per mill level, we observe that the interplay between QCD-QED and QCD-weak contributions is subtle and observable-dependent. It is therefore not possible to avoid computing one or the other if ${\cal O}(\alpha_{EW} \alpha_s)$ precision is desired.