CP nonconservation in the leptonic sector

Abstract

In this paper we use an exact method to impose unitarity on moduli of the neutrino PMNS matrix recently determined, and show how one could obtain information on CP non-conservation from a limited experimental information. One suggests a novel type of global fit by expressing all the theoretical quantities in terms of convention independent parameters: the Jarlskog invariant $J$ and the moduli $|U_{\alpha i}|$, able to resolve the positivity problem of $|U_{e 3}|$. In this way the fit will directly provide a value for $J$, and if it is different from zero it will prove the existence of CP violation in the available experimental data. If the best fit result, $|U_{e3}|^2<0$, from M. Maltoni {\em et al}, New J.Phys. {\bf 6} (2004) 122 is confirmed, it will imply a new physics in the leptonic sector.