On-Mass-Shell Renormalization of Fermion Mixing Matrices

Abstract

We consider favourable extensions of the standard model (SM) where the lepton sector contains Majorana neutrinos with vanishing left-handed mass terms, thus allowing for the see-saw mechanism to operate, and propose physical on-mass-shell (OS) renormalization conditions for the lepton mixing matrices that comply with ultraviolet finiteness, gauge-parameter independence, and (pseudo)unitarity. A crucial feature is that the texture zero in the neutrino mass matrix is preserved by renormalization, which is not automatically the case for possible generalizations of existing renormalization prescriptions for the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix in the SM. Our renormalization prescription also applies to the special case of the SM and leads to a physical OS definition of the renormalized CKM matrix.