Hadronic Physics · April 2026
The Pion Decay Constant Is Derived
Two companion papers closing the hadronic sector of Pentagon Physics. The pion decay constant and the neutral pion lifetime are derived from the binary icosahedral group and the McKay correspondence — zero free parameters, agreement with experiment.
Key Results
The hadronic sector is closed
The pion decay constant and the neutral pion lifetime — two of the most precisely measured quantities in hadronic physics — are derived from the character table of the binary icosahedral group 2I via the McKay correspondence. Both derivations use zero free parameters and agree with experimental measurements to within stated uncertainties.
1
The pion decay constant fπ is derived from the character table of the binary icosahedral group 2I via the McKay correspondence.
2
The neutral pion lifetime is derived from the same algebraic structure — the Adler–Bell–Jackiw anomaly emerges as a geometric consequence.
3
The Goldberger–Treiman relation is recovered as a limiting case of the 600-cell hadronic architecture.
4
Both derivations agree with experimental measurements to within stated uncertainties.
Kill Conditions
K1: Pion decay constant deviating from 92.1 MeV by more than 1% — McKay derivation falsified
K2: Neutral pion lifetime prediction outside experimental bounds — chiral anomaly geometry falsified