Gauge invariance and dimensional regularization withγ5in flavor-changing neutral processes

We reexamine the calculation of the flavor-changing neutral effective vertices ${\mathit{bsZ}}^0$, bs${\mathrm{\chi }}^0$, and bsH (${\mathrm{\chi }}^0$ is the unphysical Higgs boson and H is the physical Higgs boson) at one loop in dimensional regularization in the ’t Hooft–Veltman (’tHV) method, comparing to naive dimensional regularization (NDR). We show that the differences between the Green functions in both schemes satisfy simplified Slavnov-Taylor identities (STI’s). The ’tHV scheme breaks chiral invariance, and hence gauge symmetry. Moreover, this scheme leaves room for ambiguities in the extension of the current to D dimensions; for some choices, the regularized bare quantities may even violate Hermiticity. However, we show that the STI’s can be satisfied in the ’tHV scheme by specific finite counterterms. In both methods, ’tHV and NDR, the flavor-changing neutral counterterms are uniquely determined through the STI’s and the on-shell renormalization conditions, fixing the renormalized Green functions on and off shell. A difference between both schemes is that in the physical amplitude the sum of all counterterms vanishes for NDR, while for the ’tHV scheme the sum of all counterterms does not vanish, and cancels the terms of the regularized vertices that arise from the violation of chiral invariance (and, in some cases, Hermiticity) in this scheme. Also, as expected, any finite difference between renormalization schemes that satisfy the STI’s leads to the same S-matrix elements. Although the renormalization algorithm needs neutral flavor-changing counterterms, the elecroweak theory is completely predictive in the flavor-changing neutral sector in both renormalization schemes.