QCD non-leading corrections to weak decays as an application of regularization by dimensional reduction

Abstract

We compute in QCD with massless quarks the two-loop anomalous dimensions of the four-fermion operators relevant to weak non-leptonic amplitudes and discuss the physical implications for strange and charm particle decays. Our main goal was to derive the complete order α corrections to the inclusive decay width of a charm (or heavier) quark. We find that the correction terms in the effective hamiltonian show the same enhancement-suppression pattern as the leading terms. Also, for a free c quark, the non-leptonic decay width is further increased (and the semileptonic branching ratio further depleted) with respect to the leading approximation. Implications for D (especially D +) decays are discussed. The calculation was completely done by a recently proposed variant of dimensional regularization called dimensional reduction. Much of this paper is devoted to exposing and resolving (within two loops) the field theoretic subtleties associated with this method which was particularly suited to this computation.