Neutrino masses and mixing in Type I+II Seesaw with $\Delta(27)$ Symmetry

In this article, we have discussed a minimal extension of the Standard Model (SM), in which the neutrino mass matrix is obtained from type-I and type-II seesaw with the assistance of the non-abelian discrete $\Delta(27)$ symmetry. In this model, we have added two Higgs doublets, which will give mass to the charged leptons and two right-handed neutrinos ($\nu_1, \nu_2$) and five scalar triplets $\Delta_i (i=1,2,...,5)$ to give masses to the neutrinos through type-I and type-II seesaw mechanism. The extra particle, one scalar singlet we have added to make the Lagrangian invariant and which will give the mass to the second neutrino. The massiveness of neutrino can be realized after introducing two right-handed neutrinos and three scalar triplets, these right handed neutrinos transform as a singlet under $SU(2)_L$, as $1_1$ and $1_2$ under $\Delta(27)$. Similarly, the scalar triplets are triplets under SM as well as under $\Delta(27)$ also. We further connote with the detailed numerical investigation of neutrino oscillation data like non-zero reactor mixing angle ($\theta_{13}$), Dirac CP-violating phase ($\delta_{CP}$), the sum of the light neutrino masses, two mass squared differences and its implication to neutrino-less double beta decay (NDBD).