What question did this study set out to answer?

This research aims to derive the geometric index for baryon masses using QCD Casimir operators and first principles.

May 10, 2026Open Access

QCD Casimir Structure in the Geometric Index of the 59-Dimensional Mass Framework

Key Points

This research aims to derive the geometric index for baryon masses using QCD Casimir operators and first principles.
Derived the geometric index n from first principles for nine lightest baryons: p, n, Λ, Σ, Ξ, Ω.
Utilized QCD Casimir operators, strangeness, and diquark spin in the analysis.
Compared outcomes against empirical data, showing high agreement.
Achieved over 99.7% agreement for baryons using geometric index derived from QCD.
The approach did not yield the same results for mesons due to dominance of dynamical chiral symmetry breaking.
Connected hadron masses to 59-dimensional geometry and the Riemann Hypothesis critical line.

Abstract

This paper presents the fourth installment in the 59-Dimensional Series. We solve the circularity problem of Paper I by deriving the geometric index n from first principles for the nine lightest baryons. Central Result: For p, n, Λ, Σ, Ξ, Ω baryons, n is determined by QCD Casimir operators CR, CA, TF, strangeness S, and diquark spin Jdiquark, with no free parameters beyond measured αₛ. Agreement exceeds 99. 7% for all nine baryons. Negative Result: The same approach fails for mesons due to dynamical chiral symmetry breaking dominance. We report both findings with equal clarity. The work connects particle masses to the 59 = 29+1+29 geometric partition and the Riemann Hypothesis critical line Re (s) = 1/2. This provides the first derivation of hadron masses from pure geometry and group theory.

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