Octant of \(\theta_{23}\), MH, \(0\nu\beta\beta\) decay and vacuum alignment of \( A_{4} \) flavour symmetry in an inverse seesaw model

Measurements of disappearance channel of long baseline accelerator based experiments (like NO\(\nu\)A) are inflicted with the problem of octant degeneracy. In these experiments, the mass hierarchy (MH) sensitivity depends upon the value of CP-violating phase \(\delta_{CP}\). Moreover, MH of light neutrino masses is still not fixed. Also, the flavour structure of fermions is yet not fully understood. We discuss all these issues, in a highly predictive, low-scale inverse seesaw (ISS) model within the framework of \(A_4\) flavour symmetry. Recent global analysis has shown a preference for normal hierarchy and higher octant of \(\theta_{23}\), and hence we discuss our results with reference to these, and find that the vacuum alignment of \(A_4\) triplet flavon (1,-1,-1) favours these results. Finally, we check if our very precise prediction on \(m_{ee}\) and the lightest neutrino mass falls within the range of sensitivities of the neutrinoless double beta decay (\(0\nu\beta\beta\)) experiments. We note that when octant of \(\theta_{23}\) and MH is fixed by more precise measurements of future experiments, then through our results, it would be possible to precisely identify the favourable vacuum alignment corresponding to the \(A_{4}\) triplet field as predicted in our model.