Mixed strong$-$electroweak corrections to the Drell$-$Yan process

TL;DR

This work delivers the first complete calculation of mixed QCD–EW corrections to neutral-current Drell–Yan production, valid across the full dilepton invariant-mass spectrum. It combines a two-loop virtual amplitude, real and real–virtual emissions, and a q_T subtraction framework adapted for final-state charged leptons to control infrared singularities. The results show a small net mixed correction at the fiducial level but reveal significant impacts in high-p_T and high-mass regions, underscoring the importance of exact computations beyond resonance approximations. The approach provides a fully differential, infrared-safe prediction that can support precision EW parameter extractions and searches for new physics in DY tails.

Abstract

We report on the first complete computation of the mixed QCD$-$electroweak (EW) corrections to the neutral-current Drell$-$Yan process. Superseding previously applied approximations, our calculation provides the first result at this order that is valid in the entire range of dilepton invariant masses. The two-loop virtual contribution is computed by using semi-analytical techniques, overcoming the technical problems in the evaluation of the relevant master integrals. The cancellation of soft and collinear singularities is achieved by a formulation of the $q_T$ subtraction formalism valid in presence of charged massive particles in the final state. We present numerical results for the fiducial cross section and selected kinematical distributions. At large values of the lepton $p_T$ the mixed QCD$-$EW corrections are negative and increase in size, to about $-15\%$ with respect to the next-to-leading-order QCD result at $p_T=500\,$GeV. Up to dilepton invariant masses of 1 TeV the computed corrections amount to about $-1.5\%$ with respect to the next-to-leading-order QCD result.

Figures (2)

• Figure 1: Complete ${\cal O}(\alpha_{\mathrm{S}}\alpha)$ correction to the differential cross section $d\sigma^{(1,1)}$ in the anti-muon $p_T$ compared to the corresponding result in the pole approximation and to the factorised approximation $d\sigma^{(1,1)}_{\rm fact}$. The top panels show the absolute predictions, while the central (bottom) panels display the ${\cal O}(\alpha_{\mathrm{S}}\alpha)$ correction normalized to the LO (NLO QCD) result. For the full result the ratios also display our estimate of the numerical uncertainties, obtained as described in the text.
• Figure 2: As Fig. \ref{['fig:pt']}, but for the di-muon invariant mass.