Quark sector CP violation of the universal seesaw model

TL;DR

This paper investigates CP violation in the quark sector of the universal seesaw model, deriving the number of CP-violating phases, constructing invariants, and analyzing mixing matrices under certain scale assumptions.

Contribution

It identifies the number of CP-violating phases and constructs invariants in the three-generation universal seesaw model, providing exact formulas for quark interactions.

Findings

Number of CP-violating phases: 19 for three generations.

Constructed nineteen CP-violating weak basis invariants.

Derived approximate expressions for mixing matrices assuming high SU(2)_R breaking scale.

Abstract

We study the CP violation of universal seesaw model, especially its quark sector. The model is based on SU(2)_L \times SU(2)_R \times U(1)_{Y^\prime}. In order to count the number of parameters in quark sector, we use the degree of freedom of weak basis transformation. For N(3)-generation model, the number of CP violating phase in quark sector is identified as 3N^2-3N+1 (19). We also construct nineteen CP violating weak basis invariants of Yukawa coupling matrices and SU(2) singlet quark mass matrices in the three-generation universal seesaw model. The quark interaction terms induced by neutral currents are given as an exact formula. Both of the charged current and the neutral current are expressed in terms of the mass basis by finding the transformations from weak basis to mass basis. Finally, we calculate the mixing matrix element approximately assuming that the SU(2)_R breaking scale v_R is much larger than the electro-weak breaking scale v_L.