Neutrino Mixings and Leptonic CP Violation from CKM Matrix and Majorana Phases

Abstract

The high scale mixing unification hypothesis recently proposed by three of us (R. N. M., M. K. P. and G. R.) states that if at the seesaw scale, the quark and lepton mixing matrices are equal then for quasi-degenerate neutrinos, radiative corrections can lead to large solar and atmospheric mixings and small reactor angle at the weak scale in agreement with data. Evidence for quasi-degenerate neutrinos could, within this framework, be interpreted as a sign of quark-lepton unification at high scale. In the current work, we extend this model to show that the hypothesis works quite successfully in the presence of CP violating phases (which were set to zero in the first paper). In the case where the PMNS matrix is identical to the CKM matrix at the seesaw scale, with a Dirac phase but no Majorana phase, the low energy Dirac phase is predicted to be ($\simeq 0.3^{\circ}$) and leptonic CP-violation parameter $J_{CP} \simeq (4 - 8)\times 10^{-5}$ and $\theta_{13} = 3.5^{\circ}$. If on the other hand, the PMNS matrix is assumed to also have Majorana phases initially, the resulting theory damps radiative magnification phenomenon for a large range of parameters but nevertheless has enough parameter space to give the two necessary large neutrino mixing angles. In this case, one has $\theta_{13} = 3.5^{\circ} - 10^{\circ}$ and $|J_{CP}|$ as large as $0.02-0.04$ which are accessible to long baseline neutrino oscillation experiments.