Mixed QCD$\otimes$QED corrections to on-shell $Z$ boson production at the LHC

TL;DR

The paper presents a fully-exclusive calculation of mixed QCD⊗QED corrections to on-shell $Z$ production at the LHC, extending NNLO QCD via an abelianised nested soft-collinear subtraction framework to account for initial-initial and initial-final contributions, including $Z$ decay effects. It uses NNPDF3.1luxQED inputs and explores inclusive, fiducial, and differential observables, quantifying the mixed corrections with Delta ratios. The results show that mixed corrections are generally at the permille level with initial-final contributions often playing a larger role than initial-initial ones, and photon-induced channels can be non-negligible due to cancellations in the partonic channels. This work provides a precise benchmark for QCD⊗QED effects in on-shell $Z$ production and lays the groundwork for future mixed corrections to off-shell Drell–Yan and $W$ production.

Abstract

We compute the mixed QCD$\otimes$QED corrections to the production of on-shell $Z$ bosons at the LHC at a fully-exclusive level. We also include the factorised NLO QCD correction to $Z$ boson production and NLO QED correction to $Z$ boson decay into two leptons. We make use of an abelianised version of the nested soft-collinear subtraction formalism to perform this computation. We study the phenomenological impact of the mixed QCD$\otimes$QED corrections for a number of observables relevant for LHC phenomenology.

Figures (6)

• Figure 1: Contributions to the colour factors $C_FT_R$ (left) and $C_AC_F$ (right).
• Figure 2: Contributions to the colour factor $C_F^2$ and their abelianised counterparts.
• Figure 3: Contributions to the colour factor $C_F^2$ and their abelianised counterparts.
• Figure 4: Relative differential corrections $\Delta$ for the transverse momentum (left) and rapidity (right) of the dilepton system, $p_{\perp,\ell \ell}$ and $y_{\ell \ell}$. See text for further details.
• Figure 5: Relative differential corrections $\Delta$ for the transverse momentum of the leading (left) and subleading (right) lepton, $p_{\perp,\ell_1}$ and $p_{\perp,\ell_2}$. See text for further details.