轻子质量矩阵中的奥卡姆剃刀--宇宙重子不对称性的标志
Occam's Razor in Lepton Mass Matrices - The Sign of Universe's Baryon Asymmetry -
摘要：
在跷跷板机制的框架下，基于奥卡姆剃刀方法讨论了中微子质量矩阵。我们在狄拉克中微子质量矩阵中加入了四个零，这使得观测到的中微子质量和轻子混合角所需的参数数最少，而带电轻子质量矩阵和右手Majorana中微子质量矩阵被取为实对角矩阵。低能中微子质量矩阵只有7个物理参数。利用中微子质量平方差、混合角$θ_{23}$和混合角$θ_{12}$的实验数据，成功地预言了中微子正常质量等级下的混合角$θ_{13}$和CP破坏相$δ_{CP}$. $\sinθ_{13}$最受青睐的区域在$0.13\sim 0.15$周围，这与观察值完全一致。CP违反相位$δ_{CP}$倾向于接近$\pm π/2$。我们还讨论了无中微子双β衰变$m_{ee}$的Majorana相和有效中微子质量，它大约是$7\sim 8$ meV。非常了不起的是，我们可以进行一个“完整的实验”来确定低能中微子质量矩阵，因为我们只有七个物理参数的中微子质量矩阵。特别地，中微子质量矩阵中的两个CP破坏相直接由高能下的两个CP破坏相给出。因此，在轻生假设下，我们可以从中微子质量矩阵的低能实验中确定宇宙重子的符号。
英文摘要：
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 $θ_{13}$ and the CP violating phase $δ_{CP}$ with the normal mass hierarchy of neutrinos by using the experimental data on the neutrino mass squared differences, the mixing angles $θ_{12}$ and $θ_{23}$. The most favored region of $\sinθ_{13}$ is around $0.13\sim 0.15$, which is completely consistent with the observed value. The CP violating phase $δ_{CP}$ is favored to be close to $\pm π/2$. 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.
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