Speaker
Mr
Ivan Girardi
(SISSA)
Description
Using the fact that the neutrino mixing matrix $U = U^\dagger_{e}U_{\nu}$, where $U_{e}$ and $U_{\nu}$ result from the diagonalisation of the charged lepton and neutrino mass matrices, and assuming 3-neutrino mixing, we consider a number of forms of $U_{\nu}$ associated with a variety of flavour symmetries: i) tri-bimaximal (TBM) and
ii) bimaximal BM) forms , the forms corresponding iii) to the conservation of the lepton charge $L' = L_e - L_\mu - L_{\tau}$ (LC), iv) to golden ratio type A (GRA) mixing, v) golden ratio type B (GRB) mixing, and vi) to hexagonal (HG) mixing. In this approach to neutrino mixing one obtains exact predictions for the Dirac phase $\delta$ in the neutrino mixing matrix if the matrix $U_e$ has a minimal form in terms of angles and phases it contains that can provide the requisite corrections to $U_{\nu}$ so that the reactor, atmospheric and solar neutrino mixing angles $\theta_{13}$, $\theta_{23}$ and $\theta_{12}$ have values compatible with the current data. The predictions for $\delta$ depend on the angles $\theta_{13}$,
$\theta_{23}$ and $\theta_{12}$ and have also simple
"leading order" and "next-to-leading order" approximate
forms. We compare the exact predictions for $\delta$ with
those obtained in the "leading order" approximation.
We investigate also the variation of the predictions
of $\delta$ with the variation of the values of the neutrino mixing angles $\theta_{13}$, $\theta_{23}$ and $\theta_{12}$ in their
3$\sigma$ experimentally allowed ranges.
Finally, we discuss other forms for the matrices $U_e$ and $U_{\nu}$ which allow us to derive exact predictions for the CP violation phase $\delta$. A measurement of $\cos\delta$
can allow to descriminate between the different forms of
$U_{e}$ and $U_{\nu}$ considered in our study.
