Consequences of minimal seesaw with complex \u03bc\u03c4 antisymmetry of neutrinos

Abstract

We propose a complex extension of μτ permutation antisymmetry in the neutrino Majorana matrix Mν. The latter can be realized for the Lagrangian by appropriate CP transformations on the neutrino fields. The resultant form of Mν is shown to be simply related to that with a complex (CP) extension of μτ permutation symmetry, with identical phenomenological consequences, though their group theoretic origins are quite different. We investigate those consequences in detail for the minimal seesaw induced by two strongly hierarchical right-chiral neutrinos N1 and N2 with the result that the Dirac phase is maximal while the two Majorana phases are either 0 or π. We further provide an uptodate discussion of the ββ0ν process vis-a-vis ongoing and forthcoming experiments. Finally, a thorough treatment is given of baryogenesis via leptogenesis in this scenario, primarily with the assumption that the lepton asymmetry produced by the decays of N1 only matters here with the asymmetry produced by N2 being washed out. Tight upper and lower bounds on the mass of N1 are obtained from the constraint of obtaining the correct observed range of the baryon asymmetry parameter and the role played by N2 is elucidated thereafter. The mildly hierarchical right-chiral neutrino case (including the quasidegenerate possibility) is discussed in an appendix.