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

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 ${\cal O}(α_{EW} α_s)$ precision is desired.

Figures (2)

• Figure 1: Mixed QCD-electroweak corrections to dilepton rapidity and transverse momentum distributions at the $13~{\rm TeV}$ LHC. Left pane includes corrections to both production and decay whereas right pane includes corrections to the production stage only. See text for details.
• Figure 2: Mixed QCD-electroweak corrections to dilepton rapidity and transverse momentum distributions at the $13~{\rm TeV}$ LHC. Left pane includes corrections to both production and decay whereas right pane includes corrections to the production stage only. See text for details.