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Published February 12, 2026 | Version v6
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Derivation of Baryon Masses from Confinement Geometry and Relativistic Kinematics

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Description

The mass of any light baryon (uu, dd, ss quarks) is derived without fitting parameters from five fundamental inputs:
  1. QCD scale ΛQCD=\SI200\mega\electronvoltΛQCD=\SI200\mega\electronvolt
    Measured independently via asymptotic freedom in deep inelastic scattering (high-Q2Q2 regime where hadrons do not yet form).
  2. Geometric factor π/2=1.5708π/2=1.5708
    Arising from equilateral triangle topology of three-body confinement (90° projection angle for ground state).
  3. Quark momentum pc=ΛQCD⋅π/2=\SI314.16\mega\electronvoltpc=ΛQCDπ/2=\SI314.16\mega\electronvolt
    Direct consequence of (1) and (2) — no fitting.
  4. Current quark masses
    mu=\SI2.16\mega\electronvoltmu=\SI2.16\mega\electronvolt, md=\SI4.67\mega\electronvoltmd=\SI4.67\mega\electronvolt, ms=\SI93.0\mega\electronvoltms=\SI93.0\mega\electronvolt
    Calibrated exclusively on light meson spectra (π±π±, K±), never on baryons.
  5. Definiteness Law
    Topological constraint ΔxijΔpij≥ℏ21+ln⁡2(mi/mj)ΔxijΔpij21+ln2(mi/mj) forbidding complete localization of three fermions in a color singlet.

. The model is available under CC BY 4.0 license: \url{https://doi.org/10.5281/zenodo.18518434}.

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