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 $\delta$: $\sin\theta_{12} = \sqrt{m_{d} / |m_{s}|}$, $\sin\theta_{23} = 2 \, |m_{s}| / m_{b}$, $\sin\theta_{13} \approx 2 \, m_{d} / m_{b}$, $\tan\delta = m_{b}^{2} \, m_{c} / 6 \, m_{t} \, m_{s}^{2}$ 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.