We study all possible texture zeros in the Majorana neutrino mass matrix which are allowed from neutrino oscillation as well as cosmology data when the charged lepton mass matrix is assumed to take the diagonal form. In case of one-zero texture, we write down the Majorana phases which are assumed to be equal and the lightest neutrino mass as a function of the Dirac CP phase. In case of two-zero texture, we numerically evaluate all the three CP phases and lightest neutrino mass by solving four real constraint equations. We then constrain texture zero mass matrices from the requirement of producing correct baryon asymmetry through the mechanism of leptogenesis.Adopting a type I seesaw framework, we consider the CP violating out of equilibrium decay of the lightest right handed neutrino as the source of lepton asymmetry. Apart from discriminating between the texture zero mass matrices and light neutrino mass hierarchy, we also constrain the Dirac and Majorana CP phases so that the observed baryon asymmetry can be produced. In two-zero texture, we further constrain the diagonal form of Dirac neutrino mass matrix from the requirement of producing correct baryon asymmetry.

We study the possibility of generating non-zero reactor mixing angle θ 13 by perturbing the µ − τ symmetric neutrino mass matrix. The leading order µ − τ symmetric neutrino mass matrix originates from type I seesaw mechanism whereas the perturbations to µ − τ symmetry originate from type II seesaw term. We consider four different realizations of µ − τ symmetry: Bimaximal Mixing(BM), Tri-bimaximal Mixing (TBM), Hexagonal Mixing (HM) and Golden Ratio Mixing (GRM) all giving rise to θ 13 = 0, θ 23 = π 4 but different non-zero values of solar mixing angle θ 12 . We assume a minimal µ − τ symmetry breaking type II seesaw mass matrix as a perturbation and calculate the neutrino oscillation parameters as a function of type II seesaw strength. We then consider the origin of non-trivial leptonic CP phase in the charged lepton sector and calculate the lepton asymmetry arising from the lightest right handed neutrino decay by incorporating the presence of both type I and type II seesaw. We constrain the type II seesaw strength as well as leptonic CP phase (and hence the charged lepton sector) by comparing our results with experimental neutrino oscillation parameters as well as Planck bound on baryon to photon ratio.Finally, we extend our analysis on lepton flavour violating decays like µ → eγ and µ → eee due to exchange of TeV scale Higgs triplet scalar within the low scale type II seesaw framework. The branching ratios for these lepton flavour processes are examined with the small type II perturbation term ω and the estimated values are very close to the experimental bound coming from current search experiments.

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