Quark mixing angles and weak CP-violating phase vs quark masses: potential approach

Abstract

It is shown that following experimentally viable expressions for quark mixing angles ${\theta }_{12}$, ${\theta }_{23}$, ${\theta }_{13}$ and CP-violating phase $\delta$: $\sin {\theta }_{12}=\sqrt{m_d/|m_s|}$, $\sin {\theta }_{23}=2|m_s|/m_b$, $\sin {\theta }_{13}\approx 2m_d/m_b$, $\tan \delta =m_b^2{m}_c/6m_t{m}_s^2$ may be derived as stable points of certain 4-th power in $V_{CKM}$ flavor-invariant potentials built with traces of 3x3 quark up and down mass matrices and the Jarlskog invariant. There is no fine-tuning, potentials' dimensionless constants are the integer numbers not above 10.

Comments: 13 pages. arXiv admin note: substantial text overlap with arXiv:2210.09780