below.

Normal Hierarchy
----------------

$$\includegraphics[height=5.5cm]{nhy1y2.pdf}
\includegraphics[height=5.5cm]{nhy1y3.pdf}$$

Here we first explore neutrino phenomenology for normal neutrino mass hierarchy. In left panel (right panel) of figure \[fig:nhy1y2\] we have shown the

$$\includegraphics[height=5.5cm]{nhapba.pdf}
\includegraphics[height=5.5cm]{nhmp.pdf}$$

allowed points for $y_1$ vs $y_2$ ($y_3$). All these points satisfy 3$\sigma$ allowed range for the three neutrino mixing angles, ratio of solar to atmospheric mass-squared differences [@Esteban:2018azc]. From the equation (\[m1\]) and equation (\[m2\]), one can easily obtain the common factor $|a|$ appearing in the absolute neutrino mass using $\Delta{m_{21}^{2}}={m_{2}^{2}-m_{1}^{2}}=2.43\times 10^{-5}$ eV$^2$. Therefore the parameter space can be further constrained using the cosmological upper limit on the sum of absolute neutrino masses $\sum_i \lvert m_i \rvert < 0.11$ eV [@Aghanim:2018eyx].

$$\includegraphics[height=5.5cm]{nhm1mall.pdf}
\includegraphics[height=5.5cm]{nhn0bb.png}$$

The allowed regions presented in figure \[fig:nhy1y2\] also satisfy this constraint. Now, in figure \[fig:nhapba\] left panel we have plotted the allowed regions in the $\alpha$-$\phi_{ba}$ plane. As mentioned earlier here $\alpha$ is the ratio of the two parameters appearing in the right handed neutrino mass matrix and $\phi_{ba}$ is their relative phase difference. This complex phase factor plays a crucial role in the present analysis in determination of the neutrino masses and the associated (Majorana) phases.

$$\includegraphics[height=5.5cm]{ihy1y2.pdf}
\includegraphics[height=5.5cm]{ihy1y3.pdf}$$

In the right panel of figure \[fig:nhapba\] 