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Mixed EW-QCD two-loop amplitudes for $q\bar{q} \to \ell^+\ell^-$ and $γ_5$ scheme independence of multi-loop corrections

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 $α$ 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.