Dimensional taming of mass singularities in QCD corrections to weak radiative decays of quarks

Lowest order QCD corrections to the rate of the b→sγ decay induced by effective weak-interaction dipole operators are calculated by using dimensional regularization. The existing calculations of the rate all appear to have had recourse to dimensional reduction as a way of regularization. It is shown that the rate does not depend on which one of the two methods of regularization is used as long as the s quark is considered massive, because both regularizations give rise to the same on-shell wave function renormalization and because of the validity of the Bloch–Nordsieck theorem. In the heavy b-quark limit, realized by treating the s quark as massless, however, the two regularization methods give different results. It is argued that only dimensional regularization leads to correct results unless some unconventional on-shell wave function renormalization of massless fermion fields is adopted.