Abstract
The flavor-changing amplitudes \ensuremath{\gamma}${q}_{i}$${q}_{j}$ and ${\mathrm{Zq}}_{i}$${q}_{j}$ are computed for off-shell particles and without approximations. The calculations are done in the 't Hooft\char21{}Feynman gauge, and the on-shell renormalization scheme is used. The Ward-Slavnov-Taylor identities are derived and used to check the results. Putting the external quarks on shell, we found that the corresponding flavor-changing S-matrix elements are not renormalized, i.e., the sum of all counterterms vanishes. Using the renormalization scheme proposed by Sirlin the meaning of this cancellation is clarified.
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