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We present, in the context of dimensional regularization, a prescription torenormalize Feynman diagrams with an arbitrary number of external fermions.This prescription, which is based on the original t'Hooft-Veltman proposal tokeep external particles in four dimensions, is particularly useful to definethe 'renormalization' (in the context of effective Lagrangian) of physicalfour-quark operators without introducing any evanescent operator. The resultsobtained for $b\rightarrow s$ processes agree with those from the so-callednaive prescription, but disagree with the ones with the introduction ofevanescent operators in a renormalization group analysis. We also present anexplicit two loop calculation of the mixing of the evanescent operators withthe physical dimension five operators for the same processes. Particularattention is paid to the unboundedness nature of such mixing and how a formalfinite transformation is effected to decouple. The inevitable mass dependenceof one of these schemes in the literature is pointed out as the cause for thedifference mentioned.Comment: 39 pages plain TeX and 10 Postscript figures available upon request,  McGill/ 94-14 and UM-TH-94-2

Renormalization of four-quark operators, effective theory, and the role of evanescent operators