Mixed EW-QCD two-loop amplitudes for $$ q\overline{q}\to {\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ and γ5 scheme independence of multi-loop corrections

Abstract

A bstract We perform a dedicated study of the $$ q\overline{q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> <mml:mover> <mml:mi>q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> -initiated two-loop electroweak-QCD Drell-Yan scattering amplitude in dimensional regularization schemes for vanishing light quark and lepton masses. For the relative order α and α s one-loop Standard Model corrections, details of our comparison to the original literature are given. The infrared pole terms of the mixed two-loop amplitude are governed by a known generalization of the dipole formula and we show explicitly that exactly the same two-loop polarized hard scattering functions are obtained in both the standard ’t Hooft-Veltman-Breitenlohner-Maison γ 5 scheme and Kreimer’s anticommuting γ 5 scheme.