Two-loop corrections to QCD θ angle from evanescent operator in the BMHV scheme

A bstract We study the renormalization of the QCD θ angle at the two-loop level focusing on divergent and finite CP -violating contributions from evanescent operators, using dimensional regularization with the BMHV scheme. When one considers the Lagrangian in d -dimensional space-time instead of four dimensions in dimensional regularization, evanescent operators that break the chiral symmetry are induced. Consequently, T -odd and P -odd fermion loops in the BMHV scheme generate evanescent contributions to the QCD θ angle. We carefully classify the evanescent contributions into two types: one originating from the evanescent operators at the one-loop level and the other directly produced by two-loop calculations. We show that renormalization of the parameters in the BMHV scheme keeps removing those unphysical contributions to the QCD θ angle at any scale at the two-loop level. We also discuss how the rephasing invariance of the radiative correction to the QCD θ angle is realized in the BMHV scheme.