Gauge and scheme dependence of mixing matrix renormalization

We reexamine the issue of mixing matrix renormalization in theories that include Dirac or Majorana fermions. We show how a gauge-variant on-shell renormalized mixing matrix can be related to a manifestly gauge-independent one within a generalized (MS) over bar scheme of renormalization. This scheme-dependent relation is a consequence of the fact that in any scheme of renormalization, the gauge-dependent part of the mixing-matrix counterterm is ultraviolet safe and has a pure dispersive form. Employing the unitarity properties of the theory, we can successfully utilize the aforementioned scheme-dependent relation to preserve basic global or local symmetries of the bare Lagrangian through the entire process of renormalization. As an immediate application of our study, we derive the gauge-independent renormalization-group equations of mixing matrices in a minimal extension of the standard model with isosinglet neutrinos.