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Evanescent Operators, Scheme Dependences and Double Insertions
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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.
Forward citations
Cited by 5 Pith papers
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Four-loop QCD mixing of current-current operators
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Three-loop perturbative corrections to B and D meson lifetime ratios are calculated, producing values that agree with experiment when using HQET sum rules or lattice inputs.
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Two-Loop Anomalous Dimensions in the LEFT: Dimension-Six Four-Fermion Operators in NDR
Derives the full two-loop ADM for four-fermion operators in LEFT in NDR scheme including O(α_s²), O(α_s α) and O(α²) terms, with results for 5/4/3 active flavors implemented in DsixTools.
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Inclusive Charmless Non-Leptonic B Decays at NLO within and beyond the Standard Model
Complete NLO QCD corrections to charmless inclusive non-leptonic B-decay widths are computed for the full BSM operator set, yielding 26 constrained directions in Wilson coefficient space.
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