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We consider the hadroproduction of a massive charged lepton plus thecorresponding neutrino through the Drell-Yan mechanism. We present a newcomputation of the mixed QCD-EW corrections to this process. The cancellationof 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 QCDcalculation for heavy-quark production. For the first time, all the real andvirtual contributions due to initial- and final-state radiation areconsistently included without any approximation, except for the finite part ofthe two-loop virtual correction, which is computed in the pole approximationand suitably improved through a reweighting procedure. We demonstrate that ourcalculation is reliable in both on-shell and off-shell regions, therebyproviding the first prediction of the mixed QCD-EW corrections in the entireregion of the lepton transverse momentum. The computed corrections are inqualitative agreement with what we obtain in a factorised approach of QCD andEW corrections. At large values of the lepton $p_T$, the mixed QCD-EWcorrections are negative and increase in size, to about $-20\%$ with respect tothe next-to-leading order QCD result at $p_T=500\,$GeV.

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