Unitarity triangle angles explained: a predictive new quark mass matrix texture

TL;DR

This paper introduces a new quark mass matrix texture with five parameters, explaining the unitarity triangle angles and fitting quark masses and mixings, with predictions testable by future experiments.

Contribution

It proposes a novel geometric ansatz for quark mass matrices with texture zeros, explaining key CP-violating angles and identifying symmetries underlying these relations.

Findings

Good fit to current quark mass ratios and CKM observables

Predicts unitarity triangle angles consistent with experimental values

Identifies symmetries explaining CP-violating phase relations

Abstract

We propose a novel quark mass matrix texture-pair with five free parameters, which fits the four quark mass ratios $m_s/m_b$, $m_d/m_b$, $m_c/m_t$, $m_u/m_t$, and the four CKM quark mixing observables. The matrices each have one texture zero, but the main innovation here is a ``geometric'' ansatz exploiting a pair of small complex expansion parameters, based on the geometry of the Unitarity Triangle. The fit to the observables is in good agreement with current experimental values renormalised to $\sim\!\!10^4$ TeV, and offers decisive tests against future high-precision measurements of the unitarity triangle angles at the weak scale. We identify two novel symmetries of these mass matrices which explain the phenomenologically-successful relations $\alpha\equiv\phi_2\simeq\tfrac{\pi}{2}$ and $\beta\equiv\phi_1\simeq\tfrac{\pi}{8}$.