Exploring Neutrino Mixing angles and Dirac and Majorana CP Violation Phases at GUT Scale

por Prof. Eiichi Takasugi

miércoles 31 jul. 2002 12:00 → 13:00 Europe/Madrid

Sala Seminarios IFIC (Edf. Institutos de Investigación)

The special aspect of the neutrino mixing matrix at $m_Z$ scale is (1) $V_{13}\sineq 0$ and (2) $\tan^2 \theta_{\rm atm}\simeq 1$. The recent SNO data implies that the solar mixing angle is far from the maximal value, $\tan^2 \theta_{\rm sol}\simeq 0.37$. From these data, it may be natural to assume that at GUT scale, the mixing angles would be such that (1) $$V_{13}=0$ and (2) $\tan^2 \theta_{\rm atm}\simeq 1$. Then, we explore what kind of solar mixing angle would be at the GUT scale. The model $V_{13}=0$ at GUT scale, the number of parameters in the neutrino mass matrix is three masses, two mixing angles and two Majorana phases. At $m_Z$ scale, $V_{13}$ as well as a Dirac phase is induced by the radiative correction. In particular, we found that $\sin^22\tilde\theta_{12}\leq \sin^22\theta_{\rm sol}$, where $\theta_{12}$ and $\theta_{\rm sol}$ are mixing angles at the GUT scale and at $m_Z$ scale resprctively. This means that if the solar mixing angle at $m_Z$ scale is really far from maximal, $\tan^2 \theta_{\rm sol}\simeq 0.37$, then the Bi-maximal scheme can not be a realistic model. We also discuss possible sizes of $V_{13}$ and a Dirac CP violation phase.We also comment on the relation between the CP violation phase and phases which appear in leptogenesis.