Scalar dark matter in the A₄-based texture one-zero neutrino mass model within the inverse seesaw mechanism

In this paper, we present a model based on A₄ 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 the neutrino and dark matter sectors of the model. Non-Abelian discrete A₄ symmetry spontaneously breaks into the Z₂ subgroup and hence provides a stable dark matter candidate. To constrain the Yukawa Lagrangian of our model, we impose $Z_2^{\prime }$, Z₃, and Z₄ cyclic symmetries in addition to the A₄ flavor symmetry. In this work we use the recently updated data on cosmological parameters from the Planck Collaboration [N. Aghanim et al. [Planck Collaboration], Astron. Astrophys. A6, 641 (2020)]. For the dark matter candidate mass around 45-55 GeV, we obtain a mediator particle mass (right-handed neutrinos) ranging from 138-155 GeV. The Yukawa couplings are found to be in the range 0.995-1 to have observed the relic abundance of dark matter. We further obtain inverse ($X\equiv \frac{F^{2}n}{z^2}$) and type-II ($X^{\prime }\equiv f_1{v}_{{\Delta }_1}$) seesaw contributions to the 0νββ decay amplitude |M_ee|, with the model being consistent with low-energy experimental constraints. In particular, we emphasize that the type-II seesaw contribution to |M_ee| is large compared to the inverse seesaw contribution for normally ordered (NO) neutrino masses.