RENORMALIZATION OF 4-QUARK OPERATORS, EFFECTIVE THEORY, AND THE ROLE OF EVANESCENT OPERATORS

We present, in the context of dimensional regularization, a prescripti on to renormalize Feynman diagrams with an arbitrary number of externa l fermions. This prescription, which is based on the original 't Hooft -Veltman proposal to keep external particles in four dimensions, is pa rticularly useful to define the ''renormalization'' (in the context of effective Lagrangian) of physical four-quark operators without introd ucing any evanescent operator. The results obtained for b --> s proces ses agree with those from the so-called naive prescription, but disagr ee with the ones with the introduction of evanescent operators in a re normalization group analysis. We also present an explicit two loop cal culation of the mixing of the evanescent operators with the physical d imension-five operators for the same processes. Particular attention i s paid to the unboundedness nature of such mixing and how a formal fin ite transformation is effected to decouple. The inevitable mass depend ence of one of these schemes in the literature is pointed out as the c ause for the difference mentioned.