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

2025/01/30 by P. F. Harrison, Harrison, P. F., W. G. Scott +1 · 2 citations
Earth and Planetary Sciences · Physics and Astronomy · #FOS: Physical sciences #Geophysics and Gravity Measurements #High Energy Physics - Phenomenology (hep-ph) #Particle physics theoretical and experimental studies #Pulsars and Gravitational Waves Research

paper · pdf · doi:10.48550/arxiv.2501.18508

openalex publication_date 2025/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ∼ 10⁴ 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≡ϕ₂≃\tfracπ2 and β≡ϕ₁≃\tfracπ8.

Cited by

• The Very Nearly Right Theory of Flavor
• The CKM sector of the exceptional-Jordan programme: finite-Dirac mass moduli, two conditional angle estimates, and the weak-to-mass bridge

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