Lepton mixing in gauge models

Abstract

We reexamine lepton mixing in gauge models by considering two theories within the type I seesaw mechanism, the Extended Standard Model, i.e. SU(2)_L \times U(1)_Y with singlet right-handed heavy neutrinos, and the Left-Right Model SU(2)_L x SU(2)_R x U(1)_{B-L}. The former is often used as a simple heuristic approach to masses and mixing of light neutrinos and to leptogenesis, while we consider the latter as an introduction to other left-right symmetric gauge theories like SO(10). We compare lepton mixing in both theories for general parameter space and discuss also some particular cases. In the electroweak broken phase, we study in parallel both models in the "current basis" (diagonal gauge interactions), and in the "mass basis" (diagonal mass matrices and mixing in the interaction), and perform the counting of CP conserving and CP violating parameters in both bases. We extend the analysis to the Pati-Salam model SU(4)_C x SU(2)_L x SU(2)_R and to SO(10). Although specifying the Higgs sector increases the predictive power, in the most general case one has the same parameter structure in the lepton sector for all the left-right symmetric gauge models. We make explicit the differences between the Extended Standard Model and the left-right models, in particular CP violating and lepton-number violating new terms involving the W_R gauge bosons. As expected, at low energy, the differences in the light neutrino spectrum and mixing appear only beyond leading order in the ratio of Dirac mass to right-handed Majorana mass.