Renormalization of four-quark operators, effective theory, and the role of evanescent operators
- Department of Physics, McGill University, Montreal, Quebec (Canada) H3A 2T8
- Randall Laboratory of Physics, University of Michigan, Ann Arbor, Michigan 48109 (United States)
We present, in the context of dimensional regularization, a presscription to renormalize Feynman diagrams with an arbitrary number of external fermions. This prescription, which is based on the original {close_quote}t Hooft{endash}Veltman proposal to keep external particles in four dimensions, is particularly useful to define the {open_quote}{open_quote}renormalization{close_quote}{close_quote} (in the context of effective Lagrangian) of physical four-quark operators without introducing any evanescent operator. The results obtained for {ital b}{implies}{ital s} processes agree with those from the so-called naive prescription, but disagree with the ones with the introduction of evanescent operators in a renormalization group analysis. We also present an explicit two loop calculation of the mixing of the evanescent operators with the physical dimension-five operators for the same processes. Particular attention is paid to the unboundedness nature of such mixing and how a formal finite transformation is effected to decouple. The inevitable mass dependence of one of these schemes in the literature is pointed out as the cause for the difference mentioned. {copyright} {ital 1995 The American Physical Society.}
- OSTI ID:
- 253525
- Journal Information:
- Physical Review, D, Vol. 53, Issue 1; Other Information: PBD: Jan 1996
- Country of Publication:
- United States
- Language:
- English
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