Scalar Dark Matter in $A_4$ based texture one-zero neutrino mass model within Inverse Seesaw Mechanism

In this paper, we present a model based on $A_4$ discrete flavor symmetry implementing inverse and type-II seesaw mechanisms to have LHC accessible TeV scale right-handed neutrino mass and texture one-zero in the resulting Majorana neutrino mass matrix, respectively. We investigate neutrino and dark matter sectors of the model. Non-Abelian discrete $A_{4}$ symmetry spontaneously breaks into $Z_{2}$ subgroup and hence provide stable dark matter candidate. To constrain the Yukawa Lagrangian of our model, we imposed $Z'_2$, $Z_3$ and $Z_4$ cyclic symmetries in addition to the $A_4$ flavor symmetry. In this work we used the recently updated data on cosmological parameters from PLANCK 2018. For the dark matter candidate mass around 45 GeV-55 GeV, we obtain the mediator particle mass(right-handed neutrinos) ranging from 138 GeV to 155 GeV. The Yukawa couplings is found to be in the range 0.995-1 to have observed relic abundance of dark matter. We, further, obtain inverse ($X\equiv\frac{F^2n}{z^2}$) and type-II ($X^{'}\equiv f_1 v_{\Delta_{1}}$) seesaw contributions to $0\nu\beta\beta$ decay amplitude $|M_{ee}|$, while model being consistent with low energy experimental constraints. In particular, we emphasize that type-II seesaw contribution to $|M_{ee}|$ is large as compared to inverse seesaw contribution for normally ordered(NO) neutrino masses.