The CKM matrix from anti-SU(7) unification of GUT families

TL;DR

This paper estimates the CKM matrix elements within a minimal anti-SU(7) GUT model, showing that real angles can fit experimental data while the phase remains loosely constrained, and discusses possible parametrizations of the unitarity triangle.

Contribution

It introduces a novel approach to determine CKM matrix elements in an anti-SU(7) GUT framework, including phase allocation and unitarity triangle parametrizations.

Findings

Real angles fit experimental CKM data.

Phase in the right-handed matrix is loosely constrained.

Phase close to maximal for certain parametrizations.

Abstract

We estimate the CKM matrix elements in the recently proposed minimal model, anti-SU(7) GUT for the family unification, $[\,3\,]+2\,[\,2\,]+8\,[\,\bar{1}\,]$+\,(singlets). It is shown that the real angles of the right-handed unitary matrix diagonalizing the mass matrix can be determined to fit the Particle Data Group data. However, the phase in the right-handed unitary matrix is not constrained very much. We also includes an argument about allocating the Jarlskog phase in the CKM matrix. Phenomenologically, there are three classes of possible parametrizations, $\delq=\alpha,\beta,$ or $\gamma$ of the unitarity triangle. For the choice of $\delq=\alpha$, the phase is close to a maximal one.