Leptogenesis, $μ-τ$ Symmetry and $θ_{13}$

Abstract

We show that in theories where neutrino masses arise from type I seesaw formula with three right handed neutrinos and where large atmospheric mixing angle owes its origin to an approximate leptonic $μ-τ$ interchange symmetry, the primordial lepton asymmetry of the Universe, $ε_l$ can be expressed in a simple form in terms of low energy neutrino oscillation parameters as $ε_l = (a Δm^2_\odot+ b Δm^2_A θ^2_{13})$, where $a$ and $b$ are parameters characterizing high scale physics and are each of order $\leq 10^{-2} $ eV$^{-2}$. We also find that for the case of two right handed neutrinos, $ε_l \propto θ^2_{13}$ as a result of which, the observed value of baryon to photon ratio implies a lower limit on $θ_{13}$. For specific choices of the CP phase $δ$ we find $θ_{13}$ is predicted to be between $0.10-0.15$.