Quark CP-phase and Froggatt–Nielsen mechanism

Chuichiro Hattori,Masahisa Matsuda,Mamoru Matsunaga,Takeo Matsuoka

doi:10.1016/j.physletb.2016.05.054

Chuichiro Hattori, Masahisa Matsuda + Show 2 more

Open Access

https://doi.org/10.1016/j.physletb.2016.05.054

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Abstract

On the basis of the Froggatt-Nielsen mechanism, we study quark flavor mixings in the $SU(6) \times SU(2)_R$ model. The characteristic structure of the CKM matrix is attributed to the hierarchical effective Yukawa couplings due to the Froggatt-Nielsen mechanism and also to the state-mixings beyond the MSSM. We elucidate the detailed form of the CKM matrix elements and find interesting relations between the \textit{CP} violating phase and three mixing angles. Taking the existing data of three mixing angles, we estimate the quark \textit{CP}-phase at $\delta = (75 \pm 3)^{\circ}$. This result is in accord with observations.

Highlights

One of theoretically challenging issues is to understand characteristic features of quark mass patterns and the CKM-mixing matrix[1]
It seems that the important key to this issue is the state-mixing between quarks and extra particles beyond the minimal supersymmetric standard model(MSSM)
It was shown in the context of SU(6)×SU(2)R string-inspired model, which contains massless particles beyond the MSSM, that we were able to explain characteristic patterns of the observed mass spectra and mixing matrices of quarks and leptons[2, 3, 4, 5, 6]

Summary

Introduction

One of theoretically challenging issues is to understand characteristic features of quark mass patterns and the CKM-mixing matrix[1]. It seems that the important key to this issue is the state-mixing between quarks and extra particles beyond the minimal supersymmetric standard model(MSSM). We need to accomplish more accurate calculation in order to discuss the quark CP-phase For this reason, in this paper we carry out the analysis up to the next-to-leading approximation in the F-N scheme, which allows us to find more accurate relations among the CKM-matrix elements. |Vcd|2 ≃ |Vus|2 × 1 − |Vcb|2 , which yields an attractive relation between the CP-phase and three mixing angles. Using these relations, we are able to estimate the quark CP-phase without relying on a specific flavor symmetry.

Yukawa couplings and F-N mechanism

The CKM matrix

The Quark CP-phase

Summary