LAUSR

Cosmic ray energy spectra exhibit power law distributions over many orders of magnitude that are very well described by the predictions of q-generalized statistical mechanics, based on a q-generalized Hagedorn theory for transverse momentum spectra and hard QCD scattering processes. QCD at largest center of mass energies predicts the entropic index to be $$q=\frac{{\bf{13}}}{{\bf{11}}}$$q=1311. Here we show that the escort duality of the nonextensive thermodynamic formalism predicts an energy split of effective temperature given by Δ $${\boldsymbol{k}}{\boldsymbol{T}}{\boldsymbol{=}}{\boldsymbol{\pm }}\frac{{\bf{1}}}{{\bf{10}}}{\boldsymbol{k}}{{\boldsymbol{T}}}_{{\boldsymbol{H}}}{\boldsymbol{\approx }}{\boldsymbol{\pm }}{\bf{18}}$$kT=±110kTH≈±18 MeV, where TH is the Hagedorn temperature. We carefully analyse the measured data of the AMS-02 collaboration and provide evidence that the predicted temperature split is indeed observed, leading to a different energy dependence of the e+ and e− spectral indices. We also observe a distinguished energy scale E* ≈ 50 GeV where the e+ and e− spectral indices differ the most. Linear combinations of the escort and non-escort q-generalized canonical distributions yield excellent agreement with the measured AMS-02 data in the entire energy range.