Occam's Razor in Lepton Mass Matrices - The Sign of Universe's Baryon Asymmetry -

Abstract

We discuss the neutrino mass matrix based on the Occam's Razor approach in the framework of the seesaw mechanism. We impose four zeros in the Dirac neutrino mass matrix, which give the minimum number of parameters needed for the observed neutrino masses and lepton mixing angles, while the charged lepton mass matrix and the right-handed Majorana neutrino mass matrix are taken to be real diagonal ones. The low-energy neutrino mass matrix has only seven physical parameters. We show successful predictions for the mixing angle $\theta_{13}$ and the CP violating phase $\delta_{CP}$ with the normal mass hierarchy of neutrinos by using the experimental data on the neutrino mass squared differences, the mixing angles $\theta_{12}$ and $\theta_{23}$. The most favored region of $\sin\theta_{13}$ is around $0.13\sim 0.15$, which is completely consistent with the observed value. The CP violating phase $\delta_{CP}$ is favored to be close to $\pm \pi/2$. We also discuss the Majorana phases as well as the effective neutrino mass for the neutrinoless double-beta decay $m_{ee}$, which is around $7\sim 8$ meV. It is extremely remarkable that we can perform a "complete experiment" to determine the low-energy neutrino mass matrix, since we have only seven physical parameters in the neutrino mass matrix. In particular, two CP violating phases in the neutrino mass matrix are directly given by two CP violating phases at high energy. Thus, assuming the leptogenesis we can determine the sign of the cosmic baryon in the universe from the low-energy experiments for the neutrino mass matrix.