What question did this study set out to answer?

The study aims to relate hadron masses to the imaginary parts of Riemann zeta zeros using a novel arithmetic operator.

March 26, 20260 citationsOpen Access

Hadron Mass Spectrum Arithmetic Operator on Primes

Key Points

The study aims to relate hadron masses to the imaginary parts of Riemann zeta zeros using a novel arithmetic operator.
Developed an arithmetic operator based on cumulative prime sums.
Applied a zero-parameter formula to the PDG 2025 database to predict hadron masses.
Performed blind regression to extract mass ratios and verify selection rules across quarkonium families.
Achieved a high R² value of 0.99998 for the mass predictions.
Confirmed three all-charm tetraquark states with >5σ significance.
Reproduced the Weinberg angle with 0.018% accuracy and verified QCD freeze-out temperature.

Abstract

A zero-parameter formula M = (D/163) × γₙ GeV relates particle masses to imaginary parts of non-trivial Riemann zeta zeros, where D ∈ 24, 32 are lattice dimensions (Leech lattice for the QCD sector, E₈ structure for the electroweak sector) and 163 is the largest Heegner number. Applied to the PDG 2025 database, the formula resolves 82 particles above spectral threshold with R² = 0. 99998 and MAPE = 0. 69%, with zero continuous free parameters. Seven parameter-free mass ratios Mᵢ/Mⱼ = γₙᵢ/γₙⱼ (mean deviation 0. 060%, p 5σ (arXiv: 2602. 02252) are mapped to consecutive zeros n = 8, 9, 10 with errors 0. 6–2. 6%. The Weinberg angle sin²θW is reproduced to 0. 018% accuracy from a zero ratio. The QCD freeze-out temperature Tfreeze = k ln 2 = 102 MeV is confirmed by ALICE data. The framework is built on a self-adjoint arithmetic operator Ĥₐrith defined from cumulative prime sums, whose spectrum converges to the Riemann zeros with exponential bounds (Theorem A) and is made exact via a Newton–Raphson map (Theorem B). A derivation of the Riemann Hypothesis is presented as a consequence of three independent spectral obstructions (convergence, spacing, completeness), formalized in Theorem 5. 17. The derivation is logically complete and awaits independent peer verification. Additional structures include: a complete effective Lagrangian with Zeta-Higgs potential and Feynman rules; electroweak consistency including the W mass from the j-invariant; a LeClair–Mussardo scattering interpretation via Bethe ansatz; an exact information conservation law verified to 10⁻¹⁴ on 29 transitions; and a thermal derivation of the QCD crossover temperature Tc = 155 MeV (lattice QCD: 156. 5 ± 1. 5 MeV). Falsifiable predictions are pre-registered for LHCb, BESIII, ALICE, KATRIN, and DUNE.

Ask AI

Helpful

Bookmark

View Full Paper