QCD nonleading corrections to weak decays in dimensional regularization and 't Hooft-Veltman schemes

Abstract

We calculate next-to-leading QCD corrections to the effective hamiltonian for weak decays in the limit of massless quarks using three regularization schemes with different treatment of γ5: (i) dimensional regularization (anticommuting γ5 in D ≠ 4), (ii) 't Hooft-Veltman scheme (non-anticommuting γ5 in D ≠ 4) and (iii) dimensional reduction (γ5 in D = 4). The main part of the calculation is the evaluation of the two-loop anomalous dimensions of relevant four-quark operators. Although all three schemes give rather different results at the intermediate stages of the calculation, the final result for the complete next-to-leading order corrections turns out to be the same in all schemes considered and to be equal to the one of Altarelli et al. obtained previously in the dimensional reduction scheme. This result follows after a subtle analysis of operator mixing.