Particle Masses and Riemann Zeros: An Empirical Correspondence
Abstract
We report an empirical correlation between the imaginary parts of Riemann zeta zeros and observed particle masses. The formula M = (D/163) × γₙ (GeV), where γₙ is the n-th nontrivial zero and D is a discrete scale parameter, reproduces particle masses with sub-percent accuracy across multiple sectors. For charmonium (D = 24): J/ψ and ψ(2S) masses match with errors of 0.05% and 0.10%. The mass ratio M(ψ(2S))/M(J/ψ) = γ₃/γ₂ agrees with experiment to 0.04%, with no fitted parameters. For electroweak particles (D = 32): W, Z, Higgs, and top quark masses are reproduced with errors below 0.12%. The hyperbolic invariant D·γₙ = 163·M provides a geometric interpretation. A falsifiable prediction is offered: a charmonium state at 4849 MeV. This is presented as an empirical observation — analogous to Balmer's formula for hydrogen spectral lines — requiring theoretical explanation.
Fields of Study & Subjects
Particle physics theoretical and experimental studies
Quantum Chromodynamics and Particle Interactions
Neutrino Physics Research
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 23 March 2026
- Language
- ENC
- Document type
- Preprint