夸克质量矩阵中的奥卡姆剃刀
Occam's Razor in Quark Mass Matrices
摘要：
从奥卡姆剃刀方法的角度出发，我们考虑了成功的CKM混合和CP破坏所需的夸克质量矩阵中的最小参数数。我们在下夸克质量矩阵中加入三个零点，取对角上夸克质量矩阵，以减少自由参数的数目。这三个零点是最大零点，以便在夸克质量矩阵中具有CP破坏相位。这样，就只剩下六个实参数和一个CP破坏相，这是再现下夸克质量和CKM参数观测数据的最小数目。检查了带有三个零的二十个纹理。其中，13种织构对下夸克质量矩阵是可行的。作为这些纹理的代表，我们详细讨论了纹理$M_d^{(1)}$。利用$\sin 2β$、$θ_{13}$和$θ_{23}$的实验数据，结合夸克质量的观测值，预测了Cabibbo角与实验数据的接近性.据发现，这一令人惊讶的结果保持不变，在所有其他可行的纹理。我们还研究了$|V_{ub}/V_{cb}|$、$\sin 2β$和$J_{CP}$之间的相关性。对于所有织构，比值$|V_{ub}/V_{cb}|$的最大值为$0.09$，其小于实验数据的上限$0.094$。我们希望这一预测将在未来的实验中得到验证。
英文摘要：
On the standpoint of Occam's Razor approach, we consider the minimum number of parameters in the quark mass matrices needed for the successful CKM mixing and CP violation. We impose three zeros in the down-quark mass matrix with taking the diagonal up-quark mass matrix to reduce the number of free parameters. The three zeros are maximal zeros in order to have a CP violating phase in the quark mass matrix. Then, there remain six real parameters and one CP violating phase, which is the minimal number to reproduce the observed data of the down-quark masses and the CKM parameters. The twenty textures with three zeros are examined. Among them, the thirteen textures are viable for the down-quark mass matrix. As a representative of these textures, we discuss a texture $M_d^{(1)}$ in details. By using the experimental data on $\sin 2β$, $θ_{13}$ and $θ_{23}$ together with the observed quark masses, the Cabibbo angle is predicted to be close to the experimental data. It is found that this surprising result remains unchanged in all other viable textures. We also investigate the correlations among $|V_{ub}/V_{cb}|$, $\sin 2β$ and $J_{CP}$. For all textures, the maximal value of the ratio $|V_{ub}/V_{cb}|$ is $0.09$, which is smaller than the upper-bound of the experimental data, $0.094$. We hope that this prediction will be tested in future experiments.
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