Connecting Leptogenesis to CP Violation in Neutrino Mixings in a Tri-bimaximal Mixing model

We show that in a recently proposed $S_3$ model for tri-bimaximal mixing pattern for neutrinos, CP violating phases in neutrino mixings are directly responsible for lepton asymmetry $\epsilon_\ell$. In the exact tri-bimaximal limit, $\epsilon_\ell$ is proportional to one of the Majorana phases whereas in the presence of small deviations from tri-bimaximal pattern, there are two contributions, one being proportional to the Dirac phase and the other to one of the two Majorana phases. In the second case, $\theta_{13}$ is nonzero and correlated with the deviation from maximal atmospheric mixing