The Muon Excess in Air Showers: Size of the Discrepancy and What Could Close It

Air showers contain more muons than the best hadronic interaction models predict, and the size of that statement can be made precise. In the Heitler hadronic picture the muon number grows with energy to the power beta of 0.93, and iron primaries yield 1.325e+00 times the muons of protons at fixed energy. The Auger measurements, at a representative level, exceed model predictions by a factor of 1.450e+00 near 1e19 eV. Closing that gap by adjusting the energy growth alone, between the accelerator anchor near 1e14 eV and the shower energies, requires beta to rise by 3.227e-02, to 9.623e-01, a change far outside what accelerator data permit for the multiplicity growth it represents. The discrepancy therefore points to the accumulation of many small mismodellings across the cascade's generations, or to genuinely new hadronic behaviour at the highest energies, and not to any single parameter. A density ceiling cannot supply the missing muons: shower densities sit dozens of orders of magnitude below the bound, and the muon production chain is ordinary strong-interaction physics. Simulated and computed; not a measurement.