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<p>We propose a novel quark mass matrix texture-pair with five free parameters, which fits the four quark mass ratios <i>m</i><sub><i>s</i></sub>/<i>m</i><sub><i>b</i></sub>, <i>m</i><sub><i>d</i></sub>/<i>m</i><sub><i>b</i></sub>, <i>m</i><sub><i>c</i></sub>/<i>m</i><sub><i>t</i></sub>, <i>m</i><sub><i>u</i></sub>/<i>m</i><sub><i>t</i></sub>, 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 ~ 10<sup>4</sup> 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 <i>α</i> ≡ <i>ϕ</i><sub>2</sub> ≃ <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </math></EquationSource> <EquationSource Format="TEX">\( \frac{\pi }{2} \)</EquationSource> </InlineEquation> and <i>β</i> ≡ <i>ϕ</i><sub>1</sub> ≃ <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mfrac> <mi>π</mi> <mn>8</mn> </mfrac> </math></EquationSource> <EquationSource Format="TEX">\( \frac{\pi }{8} \)</EquationSource> </InlineEquation>.</p>

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

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  • 发表日期：

    2025年7月15日

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  • P. F. Harrison,
  • W. G. Scott

摘要

We propose a novel quark mass matrix texture-pair with five free parameters, which fits the four quark mass ratios ms/mb, md/mb, mc/mt, mu/mt, 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 ≃ π 2 \( \frac{\pi }{2} \) and β ≡ ϕ1 ≃ π 8 \( \frac{\pi }{8} \) .