Unique Mass Texture for Quarks and Leptons

TL;DR

This paper investigates specific quark mass matrix textures, finding that only a unique texture with four zeros can fit low energy data, while others with more zeros are incompatible.

Contribution

It identifies a unique four-zero texture structure for quark mass matrices that successfully fits experimental data, ruling out other textures with fewer or more zeros.

Findings

Texture 6 zeros matrices cannot fit data.

Texture 5 zeros matrices are incompatible with latest measurements.

A unique four-zero texture fits all low energy data.

Abstract

Texture specific quark mass matrices which are hermitian and hierarchical are examined in detail . In the case of texture 6 zeros matrices, out of sixteen possibilities examined by us, none is able to fit the low energy data (LED), for example, $V_{us} = 0.2196 \pm 0.0023$, $V_{cb} = 0.0395 \pm 0.0017$, $\frac{V_{ub}}{V_{cb}} = 0.08 \pm 0.02$, $V_{td}$ lies in the range $0.004 - 0.013$ (PDG). Similarly none of the 32 texture 5 zeros mass matrices considered is able to reproduce LED. In particular, the latest data from LEP regarding $|V_{ub}|/|V_{cb}|(=0.093\pm0.016)$ rules out all of them. In the texture 4 zeros case, we find that there is a unique texture structure for $U$ and $D$ mass matrices which is able to fit the data.