μ−τsymmetry, sterile right-handed neutrinos, and leptogenesis

Abstract

Leptogenesis is studied in a seesaw model with $\ensuremath{\mu}\ensuremath{-}\ensuremath{\tau}$ symmetry for $S{U}_{L}(2)$-singlet right-handed neutrinos. It is shown that lepton asymmetry is not zero and is given by the square of the solar neutrino mass difference and can be of the right order of magnitude. Further it involves the same Majorana phase which appears in the neutrinoless double $\ensuremath{\beta}$-decay. In this framework one of the right-handed seesaw partners of light neutrinos can be made massless. This can be identified with a sterile neutrino, once it acquires a tiny mass ($\ensuremath{\approx}1\text{ }\text{ }\mathrm{eV}$) when $\ensuremath{\mu}\ensuremath{-}\ensuremath{\tau}$ symmetry is broken in the right-handed neutrino sector. The above mentioned sterile neutrino together with another one can be identified to explain the MiniBooNE and LSND results. The light $5\ifmmode\times\else\texttimes\fi{}5$ neutrino mass matrix is completely fixed if $CP$ is conserved and so is the effective mass for neutrinoless double $\ensuremath{\beta}$-decay.