Evanescent Operators, Scheme Dependences and Double Insertions

Details Evanescent Operators, Scheme Dependences and Double Insertions Evanescent Operators, Scheme Dependences and Double Insertions

1994-12-27

arxiv.org/abs/hep-ph/9412375v2

Nucl.Phys. B455 (1995) 39-58

Physics

High Energy Physics

High Energy Physics - Phenomenology

23 pages, LaTeX 2.09, uses packages epsf, rotate, a4. 3 figures included as PostScript files in a seperate uuencoded compresse

Scientific paper

The anomalous dimension matrix of dimensionally regularized four-quark operators is known to be affected by evanescent operators, which vanish in $D=4$ dimensions. Their definition, however, is not unique, as one can always redefine them by adding a term proportional to $(D-4)$ times a physical operator. In the present paper we compare different definitions used in the literature and find that they correspond to different renormalization schemes in the physical operator basis. The scheme transformation formulae for the Wilson coefficients and the anomalous dimension matrix are derived in the next-to-leading order. We further investigate the proper treatment of evanescent operators in processes appearing at second order in the effective four-fermion interaction such as particle-antiparticle mixing, rare hadron decays or inclusive decays.

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