Mixed QCD-EW corrections to $\boldsymbol{pp\!\to\!\ell\nu_\ell\!+\!X}$ at the LHC

TL;DR

This paper presents a comprehensive calculation of mixed QCD-EW corrections to W boson production with leptons at the LHC, including all real and virtual contributions, providing the first full prediction across the entire lepton transverse momentum range.

Contribution

It introduces a novel, fully consistent computation of mixed QCD-EW corrections for W production, extending previous approximations and covering the entire kinematic spectrum.

Findings

Corrections are negative and grow with lepton pT, reaching about -20% at 500 GeV.

The calculation is reliable in on-shell and off-shell regions, matching factorized approaches.

Provides the first complete prediction of mixed QCD-EW effects in this process.

Abstract

We consider the hadroproduction of a massive charged lepton plus the corresponding neutrino through the Drell-Yan mechanism. We present a new computation of the mixed QCD-EW corrections to this process. The cancellation of soft and collinear singularities is achieved by using a formulation of the $q_T$ subtraction formalism derived from the next-to-next-to-leading order QCD calculation for heavy-quark production. For the first time, all the real and virtual contributions due to initial- and final-state radiation are consistently included without any approximation, except for the finite part of the two-loop virtual correction, which is computed in the pole approximation and suitably improved through a reweighting procedure. We demonstrate that our calculation is reliable in both on-shell and off-shell regions, thereby providing the first prediction of the mixed QCD-EW corrections in the entire region of the lepton transverse momentum. The computed corrections are in qualitative agreement with what we obtain in a factorised approach of QCD and EW corrections. At large values of the lepton $p_T$, the mixed QCD-EW corrections are negative and increase in size, to about $-20\%$ with respect to the next-to-leading order QCD result at $p_T=500\,$GeV.