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

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 $\beta\equiv\phi_1\simeq\tfrac{\pi}{8}$.