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

Abstract

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.