On-shell renormalization of the mixing matrices in Majorana neutrino theories

We generalize a recently proposed on-shell approach to renormalize the Cabibbo–Kobayashi–Maskawa quark-mixing matrix to the case of an extended leptonic sector that includes Dirac and Majorana neutrinos in the framework of the seesaw mechanism. An important property of this formulation is the gauge independence of both the renormalized and bare lepton mixing matrices. Also, the texture zero in the neutrino mass matrix is preserved.