Quark mass matrices and observable quantities

TL;DR

This paper reviews quark mass matrix models, analyzes their structure within the Standard Model, and explores how these matrices depend on the CP-violating phase, revealing specific parameter relations consistent with experimental data.

Contribution

It provides a detailed analysis of quark mass matrices in the Standard Model using a minimal parameter basis, highlighting their dependence on the CP phase and deriving specific matrix relations.

Findings

Parameters are mostly independent of the CP phase, except for M_{d22} and M_{d23}

An approximate equality |M_{d22}|=M_{d23} occurs near the experimental CP phase

Relations M_{d12} ≈ M_{d21} and M_{d33} ≈ 2M_{d32} are observed

Abstract

A nearly historical account of quark mass matrix models is given, and the structure of quark mass matrices in the Standard Model is studied. For a minimal parameter basis suggested earlier, where $M_u$ is diagonal and $M_{d11}$, $M_{d13}$, $M_{d31}$ are zero, the dependence of mass matrices on the CP violating phase $\delta$ of $V_{CKM}$ is reported: all parameters are almost independent, except $M_{d22}$ and $M_{d23}$, and the equality $|M_{d22}|=M_{d23}$ is obtained for a value of $\delta$ very close to the value which is favoured by experiments. Moreover, on this basis, $M_{d12} \simeq M_{d21}$ and $M_{d33} \simeq 2M_{d32}$. Some comments on mass matrices in left-right symmetric models are added.