Galactic electrons and positrons at the Earth:new estimate of the primary and secondary fluxes

We analyse predictions of the CR lepton fluxes at the Earth of both secondary and primary origins, evaluate the theoretical uncertainties, and determine their level of consistency with respect to the available data. For propagation, we use a relativistic treatment of the energy losses for which we provide useful parameterizations. We compute the secondary components by improving on the method that we derived earlier for positrons. For primaries, we estimate the contributions from astrophysical sources (supernova remnants and pulsars) by considering all known local objects within 2 kpc and a smooth distribution beyond. We find that the electron flux in the energy range 5-30 GeV is well reproduced by a smooth distant distribution of sources with index $\gamma\sim 2.3-2.4$, while local sources dominate the flux at higher energy. For positrons, local pulsars have an important effect above 5-10 GeV. Uncertainties affecting the source modeling and propagation are degenerate and each translates into about one order of magnitude error in terms of local flux. The spectral shape at high energy is weakly correlated with the spectral indices of local sources, but more strongly with the hierarchy in their distance, age and power. Despite the large theoretical errors that we describe, our global and self-consistent analysis can explain all available data without over-tuning the parameters, and therefore without the need to consider any exotic physics. Though a \emph{standard paradigm} of Galactic CRs is well established, our results show that we can hardly talk about any \emph{standard model} of CR leptons, because of the very large theoretical uncertainties. Our analysis provides details about the impact of these uncertainties, thereby sketching a roadmap for future improvements.