Minimal type II seesaw model

Abstract

We propose a minimal type II seesaw model by introducing only one right-handed neutrino besides the $SU(2{)}_{L}$ triplet Higgs to the standard model. In the usual type II seesaw models with several right-handed neutrinos, the contributions of the right-handed neutrinos and the triplet Higgs to the $CP$ asymmetry, which stems from the decay of the lightest right-handed neutrino, are proportional to their respective contributions to the light neutrino mass matrix. However, in our minimal type II seesaw model, this $CP$ asymmetry is just given by the one-loop vertex correction involving the triplet Higgs, even though the contribution of the triplet Higgs does not dominate the light neutrino masses. For illustration, the Fritzsch-type lepton mass matrices are considered.