The Yukawa Spectrum Classified: Parameter Smallness with a Power-Law Organiser, Not Demonstrated Accumulation

The nine charged-fermion Yukawa couplings span 5.529 orders of magnitude, from y_e = 2.94e-6 to y_t = 0.992. A Froggatt-Nielsen style ladder with a single expansion parameter epsilon = 0.22 and minimal integer charges (8, 7, 7, 5, 5, 3, 3, 2, 0) reproduces the spectrum with an RMS residual of 0.180 dex and a worst case of a factor 2.02. A Monte Carlo comparison shows 40.4 percent of random log-uniform spectra in the same range fit the ladder at least as well, and the ladder replaces nine continuous inputs with nine discrete inputs rather than fewer inputs. The spectrum is therefore classified, extending an earlier classification of the strong CP problem, as parameter smallness with a power-law organiser, not demonstrated accumulation. AI assistance (Dave) was used in computation and drafting; the author reviewed the results.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-10
DOI
https://doi.org/10.5281/zenodo.24110419
Primary Topic
Particle physics theoretical and experimental studies
Type
article
Field-Weighted Citation Impact
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article

The Yukawa Spectrum Classified: Parameter Smallness with a Power-Law Organiser, Not Demonstrated Accumulation

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
article

The Yukawa Spectrum Classified: Parameter Smallness with a Power-Law Organiser, Not Demonstrated Accumulation

William Alexander Aldred
article en

Abstract

The nine charged-fermion Yukawa couplings span 5.529 orders of magnitude, from y_e = 2.94e-6 to y_t = 0.992. A Froggatt-Nielsen style ladder with a single expansion parameter epsilon = 0.22 and minimal integer charges (8, 7, 7, 5, 5, 3, 3, 2, 0) reproduces the spectrum with an RMS residual of 0.180 dex and a worst case of a factor 2.02. A Monte Carlo comparison shows 40.4 percent of random log-uniform spectra in the same range fit the ladder at least as well, and the ladder replaces nine continuous inputs with nine discrete inputs rather than fewer inputs. The spectrum is therefore classified, extending an earlier classification of the strong CP problem, as parameter smallness with a power-law organiser, not demonstrated accumulation. AI assistance (Dave) was used in computation and drafting; the author reviewed the results.

Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
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