A comparative study of type-II, inverse and linear seesaw mechanisms with $ A_{4} $ flavour symmetry

In this work, we present a comparative study of the three of the seesaw models, viz., type II, inverse and linear seesaw models, to investigate about light neutrino masses and mixings, flavour structure, neutrinoless double beta decay ($ 0 u beta beta $) and charged lepton flavour violation (cLFV) decay ($murightarrow egamma$). We consider the $ A_{4} $ flavour symmetry, while some other symmetries, like $U(1)_{X}$, $Z_4$ and $Z_5$ are also included to forbid unwanted terms in the Lagrangian. Taking into account the present experimental data for the known light neutrino parameters from recent global fit data, we compute the currently unknown neutrino parameters such as the lightest neutrino mass ($m_1$), CPV phase (Dirac and Majorana), and effective light neutrino mass in the neutrinoless double beta decay, by considering different VEV alignments of the triplet scalar flavon fields. We also elucidate on the octant of atmospheric neutrino mixing angle, $theta_{23}$, in the light of our predicted results. Finally, we present the region of parameter spaces of $m_1$, CPV phases, octant of $theta_{23}$ and effective mass measurable in of neutrino less double beta decay experiments, that can be tested in future experiments. We observe that the branching ratio of ($murightarrow egamma$) can help discriminate the three seesaw models. Further, the favoured Octant of the atmospheric mixing angle $theta_{23}$ changes with the VEV alignment of the triplet flavon field - i.e., the internal flavour structure of the neutrinos is reflected in their composition (mixing). The constant F determining the scale of flavour symmetry breaking, seesaw scale and coupling constants of the three seesaw models has also been computed, which puts a constraint among them allowed by the present experimental results.