Three Regimes of Hadron Masses: GOR, Power Law, and the Golden Ratio (v2)

We present an empirical classification of hadron masses into three regimes: (1) Goldstone regime (π, K, η): m² ∝ m_q (GOR relation), accuracy ~7%. (2) Regge regime (light mesons ρ, f₂; quarkonia Υ, ψ): M(n) = a + b·n^c, c(m_q, L) = a_c·log10(m_q) + b_c − k·L(L+1), accuracy 0.4–1.0%. (3) Asymptotic regime (heavy quarkonia): c → x = (√5−1)/2 = 0.618 as m_q → ∞. The T8CX formula for baryons and heavy mesons (D, B) is confirmed with accuracy 0.06–0.4%. The coefficients have forms through the golden ratio. The formula is verified on Υ, ψ, ρ, and f₂. It does not work for Goldstone bosons and mixed systems (D_s). Три режима адронных масс: GOR, степенной закон и асимптотика золотого сечения. Формула T8CX для барионов и тяжёлых мезонов (D, B) подтверждена с точностью 0.06–0.4%. Редже-траектории для лёгких мезонов: α′ ≈ 1.15 ГэВ⁻². Предсказания для LHCb Run 3: η_c(3S), η_b(3S), χ_c2(2P), χ_b2(3P). New in v2: The open problem of the Ξ_{1/2} sector is solved: Ξ_{1/2} = X/4 + 1/6 = (3√5+1)/24 ≈ 0.321175, where X = 1/φ, 4 = rank(SU(5)), 6 = |W(SU(3))|. All 9 sectors of the φ-lattice are now explained.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-19
DOI
https://doi.org/10.5281/zenodo.22839446
Primary Topic
Particle physics theoretical and experimental studies
Type
preprint
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preprint

Three Regimes of Hadron Masses: GOR, Power Law, and the Golden Ratio (v2)

MOBIDUR, DEEPSEEK
Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
preprint

Three Regimes of Hadron Masses: GOR, Power Law, and the Golden Ratio (v2)

MOBIDUR, DEEPSEEK
preprint en

Abstract

We present an empirical classification of hadron masses into three regimes: (1) Goldstone regime (π, K, η): m² ∝ m_q (GOR relation), accuracy ~7%. (2) Regge regime (light mesons ρ, f₂; quarkonia Υ, ψ): M(n) = a + b·n^c, c(m_q, L) = a_c·log10(m_q) + b_c − k·L(L+1), accuracy 0.4–1.0%. (3) Asymptotic regime (heavy quarkonia): c → x = (√5−1)/2 = 0.618 as m_q → ∞. The T8CX formula for baryons and heavy mesons (D, B) is confirmed with accuracy 0.06–0.4%. The coefficients have forms through the golden ratio. The formula is verified on Υ, ψ, ρ, and f₂. It does not work for Goldstone bosons and mixed systems (D_s). Три режима адронных масс: GOR, степенной закон и асимптотика золотого сечения. Формула T8CX для барионов и тяжёлых мезонов (D, B) подтверждена с точностью 0.06–0.4%. Редже-траектории для лёгких мезонов: α′ ≈ 1.15 ГэВ⁻². Предсказания для LHCb Run 3: η_c(3S), η_b(3S), χ_c2(2P), χ_b2(3P). New in v2: The open problem of the Ξ_{1/2} sector is solved: Ξ_{1/2} = X/4 + 1/6 = (3√5+1)/24 ≈ 0.321175, where X = 1/φ, 4 = rank(SU(5)), 6 = |W(SU(3))|. All 9 sectors of the φ-lattice are now explained.

Zenodo (CERN European Organization for Nuclear Research)
Art Institute of Portland (US)
Peace, Justice and strong institutions
Particle physics theoretical and experimental studies
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Three Regimes of Hadron Masses: GOR, Power Law, and the Golden Ratio (v2) — MOBIDUR, DEEPSEEK · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS