Origin of Cosmic Ray Electrons and Positrons

With experimental results of AMS on the spectra of cosmic ray (CR) $e^{-}$, $e^{+}$, $e^{-}+e^{+}$ and positron fraction, as well as new measurements of CR $e^{-}+e^{+}$ flux by HESS, one can better understand the CR lepton ($e^{-}$ and $e^{+}$) spectra and the puzzling electron-positron excess above $\sim$10 GeV. In this article, spectra of CR $e^{-}$ and $e^{+}$ are fitted with a physically motivated simple model, and their injection spectra are obtained with a one-dimensional propagation model including the diffusion and energy loss processes. Our results show that the electron-positron excess can be attributed to uniformly distributed sources that continuously inject into the galactic disk electron-positron with a power-law spectrum cutting off near 1 TeV and a triple power-law model is needed to fit the primary CR electron spectrum. The lower energy spectral break can be attributed to propagation effects giving rise to a broken power-law injection spectrum of primary CR electrons with a spectral hardening above $\sim$40 GeV.