Neutrino CP violating parameters from nontrivial quark-lepton correlation: a S3xGUT model

We investigate the prediction on the lepton phases in theories with a non trivial correlation between quark (CKM) and lepton (PMNS) mixing matrices. We show that the actual evidence, under the only assumption that the correlation matrix $V^M$ product of $CKM$ and $PMNS$ has a zero in the entry $(1,3)$, gives us a prediction for the three CP-violating invariants $J$, $S_1$, and $S_2$. A better determination of the lepton mixing angles will give a strong prediction of the CP-violating invariants in the lepton sector. These will be tested in the next generation experiments. To clarify how our prediction works, we show how a model based on a Grand Unified Theory and the permutation flavor symmetry $S_3$ predicts $V^M_{13}=0$.