the neutrino masses in terms of the mass squared differences in the [*normal hierarchy*]{} are $$m_1 = 0, \quad m_2 = \sqrt{\Delta m_{21}^2},\quad m_3 = \sqrt{\Delta m_{31}^2},
\label{b2}$$ while in the [*inverted hierarchy*]{} one has $$m_1 = \sqrt{\Delta m_{31}^2}, \quad m_2 = \sqrt{ \Delta m_{31}^2+\Delta m_{21}^2 },\quad m_3 = 0.
\label{b3}$$ The current values for the parameters in and , are given in [@Tortola:2012te; @GonzalezGarcia:2012sz; @Fogli:2012ua]. We use the most recent values [@nufit] from the collaboration of reference [@GonzalezGarcia:2012sz], which at one sigma are given by $$\begin{aligned}
\begin{split}
\label{nu.data}
    \sin^2 &\theta_{12} =  0.306^{+0.012}_{-0.012}, \quad 
    \sin^2 \theta_{23} = 0.446^{+0.007}_{-0.007} \text{ \ or \ } 0.587^{+0.032}_{-0.037}, \quad
    \sin^2 \theta_{13} = 0.0229^{+0.0020}_{-0.0019}, 
\\
    & \Delta m_{21}^2 (10^{-5} \text{ eV}^2)= 7.45^{+0.19}_{-0.16}, \quad
    \Delta m_{31}^2 (10^{-3} \text{ eV}^2)= 2.417^{+0.013}_{-0.013}, \quad
    \delta (^\circ) = 265^{+56}_{-61}.
\end{split}\end{aligned}$$

Note that at three sigma, $\delta$ spans its full range of $0^\circ - 360^\circ$ and that $\alpha$ has not been measured. The two values of $\theta_{23}$ represent a degeneracy in the best fit to the data.

One can solve for the flavorful parameters $\epsilon_i$ and ${v_L}_i$ by requiring that the diagonalization of the neutrino mass matrix, Eq. (\[nu.mass.1\]), yields the correct neutrino data specified in Eq. (\[nu.data\]). A procedure for 