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

We propose a novel quark mass matrix texture-pair with five free parameters, which fits the four quark mass ratios $m_s\mathrm{/}{m}_b$, $m_d\mathrm{/}{m}_b$, $m_c\mathrm{/}{m}_t$, $m_u\mathrm{/}{m}_t$, 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 $\sim \text{\hspace{0.17em}⁣}\text{\hspace{0.17em}⁣}{10}^4$ 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 $\alpha \equiv {\phi }_2\simeq \frac{\pi }{2}$ and $\beta \equiv {\phi }_1\simeq \frac{\pi }{8}$.