Work

An S₃-Circulant Parametrization of Fermion Masses and Mixing and a Simplicial Vacuum-Energy Ansatz

Year: 2026

Type: preprint

Abstract: A phenomenological study of an S₃-circulant parametrization of charged-fermion masses, mixing relations and a simplicial vacuum-energy ansatz. Every relation is classified as an identity, a known relation (Koide, the Gatto–Sartori–Tonin relation for the Cabibbo angle), an ansatz or a fit. The parameter count is explicit: 9 continuous inputs (4 free) and at least 8 discrete choices, against 12 observables. That leaves 6 genuine tests: - the two that pass (m_τ and |V_us|) are known relations; - the one new sharp relation, for the reactor angle θ₁₃, is disfavoured by more than 4σ. Two structural limitations are stated: - if both quark sectors are circulant, the CKM matrix is trivial; - the vacuum-energy formula works only as a finely tuned one-parameter fit. All numbers use PDG 2024 inputs and are reproducible with the accompanying script.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.22373916

Author: Silva-Filho, Reinaldo M.

Institution: Universidade Federal de Lavras

Language: English

Topic: Particle physics theoretical and experimental studies

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

OpenAlex ID: W7208830634

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