Leptogenesis, $\mu -\tau$ Symmetry and ${\theta }_{13}$

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 $\mu -\tau$ interchange symmetry, the primordial lepton asymmetry of the Universe, ${\epsilon }_l$ can be expressed in a simple form in terms of low energy neutrino oscillation parameters as ${\epsilon }_l=(a\Delta m_{\odot }^2+b\Delta m_A^2{\theta }_{13}^2)$, where $a$ and $b$ are parameters characterizing high scale physics and are each of order $\le 10^{-2}$ eV${}^{-2}$. We also find that for the case of two right handed neutrinos, ${\epsilon }_l\propto {\theta }_{13}^2$ as a result of which, the observed value of baryon to photon ratio implies a lower limit on ${\theta }_{13}$. For specific choices of the CP phase $\delta$ we find ${\theta }_{13}$ is predicted to be between $0.10-0.15$.

16 pages, one figure