The CP violating phase \delta_{13} and the quark mixing angles \theta_{13}, \theta_{23} and \theta_{12} from flavour permutational symmetry breaking

TL;DR

This paper derives explicit formulas for quark mixing angles and CP violation phase from flavour permutational symmetry breaking, matching experimental data closely, and linking these parameters to quark mass ratios and symmetry breaking parameters.

Contribution

It provides exact analytical expressions for mixing parameters based on symmetry breaking, connecting them directly to quark masses and symmetry parameters, which is a novel approach.

Findings

Derived explicit formulas for mixing angles and CP phase.

Computed values match experimental data closely.

Linked mixing parameters to quark mass ratios and symmetry breaking.

Abstract

The phase equivalence of the theoretical mixing matrix ${\bf V}^{th}$ derived from the breaking of the flavour permutational symmetry and the standard parametrization ${\bf V}^{PDG}$ advocated by the Particle Data Group is explicitly exhibited. From here, we derive exact explicit expressions for the three mixing angles $\theta_{12}$, $\theta_{13}$, $\theta_{23}$, and the CP violating phase $\delta_{13}$ in terms of the quark mass ratios $(m_{u}/m_{t}, m_{c}/m_{t}, m_{d}/m_{b}, m_{s}/m_{b})$ and the parameters $Z^{*1/2}$ and $\Phi^*$ characterizing the preferred symmetry breaking pattern. The computed values for the CP violating phase and the mixing angles are: $\delta^*_{13}=75^\circ$, $\sin\theta^*_{12}=0.221$, $\sin\theta^*_{13}=0.0034$, and $\sin\theta^*_{23}=0.040$, which coincide almost exactly with the central values of the experimentally determined quantities.