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Anomalous bremsstrahlung and the structure of cosmic ray electron-positron fluxes at the GeV-TeV energy range

We reveal that the energy spectra of electrons-positrons in primary cosmic rays measured at atmosphere top have double structures: an excess component $Φ^s_{e^+}(E)=Φ^s_{e^-}(E)$ around $400 GeV$, which origins from a strong $e^+e^-$-source and the distorted background $Φ^0_{e^-}(E)$. We supposed that the difference between AMS-CALET and Fermi-LAT-DAMPE data origins from the energy loss of the fluxes due to the anomalous bremsstrahlung effect at a special window. The evolution of spectra under anomalous bremsstrahlung effect satisfies an improved electromagnetic cascade equation. The above spectra are parameterized and they can be regarded as the subjects exploring new physics. We suggest to check the previous applications of the Bethe-Heitler formula in the study of the propagation of high energy electrons and photons.