Generalized statistical mechanics of cosmic rays: Application to positron-electron spectral indices

We apply generalized statistical mechanics developed for complex systems to theoretically predict energy spectra of particle and anti-particle degrees of freedom in cosmic ray fluxes, 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 $q=\frac{13}{11}$, whereas the escort duality of the nonextensive thermodynamic formalism predicts an energy split of effective temperature given by $\Delta kT =\pm \frac{1}{10} kT_H \approx \pm 18 $ MeV, where $T_H$ is the Hagedorn temperature. We carefully analyse the measured primary cosmic ray 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. Moreover, we observe that at larger energies $E$ the measured $e^+e^-$ flux starts to deviate from our QCD-based statistical mechanics theory, with a crossover scale of $E^*=(50 \pm 10)$ GeV, which could be a hint for WIMP decay or other new physics setting in at this mass scale. Fits using linear combinations of the escort and non-escort $q$-generalized canonical distributions yield excellent agreement with the measured data in the entire energy range.