Grand Unified Yukawa Matrix Ansatz: The Standard Model Fermion Mass, Quark Mixing and CP Violation Parameters

TL;DR

This paper introduces a grand unified scale mass matrix ansatz linking fermion masses and mixings to gauge coupling constants, simplifying the parameter space and fitting observed SM fermion properties effectively.

Contribution

It proposes a novel mass matrix ansatz at the GUT scale where Yukawa elements are powers of the gauge coupling, reducing parameters and fitting fermion data.

Findings

Successfully fits fermion masses and mixings

Reduces the number of free parameters in the SM

Provides a unified framework for fermion mass hierarchy

Abstract

We propose a new mass matrix ansatz: At the grand unified (GU) scale, the standard model (SM) Yukawa coupling matrix elements are integer powers of the square root of the GU gauge coupling constant \varepsilon \equiv \sqrt{\alpha_{\text{GU}}}, multiplied by order unity random complex numbers. It relates the hierarchy of the SM ermion masses and quark mixings to the gauge coupling constants, greatly reducing the SM parameters, and can give good fitting results of the SM fermion mass, quark mixing and CP violation parameters. This is a neat but very effective ansatz.