Connecting Leptonic CP Violation, Lightest Neutrino Mass and Baryon Asymmetry Through Type II Seesaw

We study the possibility of connecting leptonic Dirac CP phase $\delta$, lightest neutrino mass and baryon asymmetry of the Universe within the framework of a model where both type I and type II seesaw mechanisms contribute to neutrino mass. Type I seesaw gives rise to Tri-Bimaximal (TBM) type neutrino mixing whereas type II seesaw acts as a correction in order to generate non-zero $\theta_{13}$. We derive the most general form of type II seesaw mass matrix which can not only give rise to correct neutrino mixing angles but also can generate non-trivial value of $\delta$. Considering both the cases where type II seesaw is sub-leading and is equally dominant compared to type I seesaw, we correlate the type II seesaw term with $\delta$ and lightest neutrino mass. We further constrain the Dirac CP phase $\delta$ and hence the type II seesaw mass matrix from the requirement of producing the observed baryon asymmetry through the mechanism of leptogenesis.