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, $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_{B-L}$. 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 $SU(4{)}_C\times SU(2{)}_L\times SU(2{)}_R$ 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 the Dirac mass to the right-handed Majorana mass.

• Received 27 March 2015

DOI:https://doi.org/10.1103/PhysRevD.92.033004