Mixed EW-QCD two-loop amplitudes for $q\bar{q}\to {\ell }^{+}{\ell }^{-}$ and ${\gamma }_5$ scheme independence of multi-loop corrections

Abstract

We perform a dedicated study of the $q\bar{q}$-initiated two-loop electroweak-QCD Drell-Yan scattering amplitude in dimensional regularization schemes for vanishing light quark and lepton masses. For the relative order $\alpha$ and ${\alpha }_s$ 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 ${\gamma }_5$ scheme and Kreimer's anticommuting ${\gamma }_5$ scheme.

65 pages, 6 figures; ancillary files with results

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• Mixed strong$-$electroweak corrections to the Drell$-$Yan process
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
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