Neutrino mixings and leptonicCPviolation 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 quasidegenerate 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 quasidegenerate neutrinos could, within this framework, be interpreted as being consistent with 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 Pontecorvo-Maki-Nakagawa-Sakata matrix is identical to the Cabibbo-Kobayashi-Maskawa quark-mixing matrix at the seesaw scale, with a Dirac phase but no Majorana phase, the low energy Dirac phase is predicted to be ($\ensuremath{\simeq}0.3\ifmmode^\circ\else\textdegree\fi{}$) and leptonic $CP$-violation parameter ${J}_{CP}\ensuremath{\simeq}(4\ensuremath{-}8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and ${\ensuremath{\theta}}_{13}=3.5\ifmmode^\circ\else\textdegree\fi{}$. If on the other hand, the Pontecorvo-Maki-Nakagawa-Sakata matrix is assumed to also have non-negligible Majorana phase(s) 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 ${\ensuremath{\theta}}_{13}=3.5\ifmmode^\circ\else\textdegree\fi{}--10\ifmmode^\circ\else\textdegree\fi{}$ and $|{J}_{CP}|$ as large as 0.02--0.04 which are accessible to long baseline neutrino oscillation experiments.