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arXiv · 2501.18508

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

P. F. Harrison·W. G. Scott
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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 $α\equivϕ_2\simeq\tfracπ{2}$ and $β\equivϕ_1\simeq\tfracπ{8}$.

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P. F. Harrison, W. G. Scott. 2025-06-18. Unitarity triangle angles explained: a predictive new quark mass matrix texture. https://arxiv.org/abs/2501.18508

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