New determination of the production cross section for secondary positrons and electrons in the Galaxy

Abstract

The cosmic-ray fluxes of electrons and positrons ($e^{\pm }$) are measured with high precision by the space-borne particle spectrometer AMS-02. To infer a precise interpretation of the production processes for $e^{\pm }$ in our Galaxy, it is necessary to have an accurate description of the secondary component, produced by the interaction of cosmic-ray proton and helium with the interstellar medium atoms. We determine new analytical functions of the Lorentz invariant cross section for the production of ${\pi }^{\pm }$ and $K^{\pm }$ by fitting data from collider experiments. We also evaluate the invariant cross sections for several other channels, involving for example hyperon decays, contributing at the few \% level on the total cross section. For all these particles, the relevant 2 and 3 body decay channels are implemented, with the polarized ${\mu }^{\pm }$ decay computed with next-to-leading order corrections. The cross section for scattering of nuclei heavier than protons is modeled by fitting data on $p+C$ collisions. The total differential cross section $d\sigma /d{T}_{e^{\pm }}(p+p\to e^{\pm }+X)$ is predicted from 10 MeV up to 10 TeV of $e^{\pm }$ energy with an uncertainty of about 5-7\% in the energies relevant for AMS-02 positron flux, thus dramatically reducing the precision of the theoretical model with respect to the state of the art. Finally, we provide a prediction for the secondary Galactic $e^{\pm }$ source spectrum with an uncertainty of the same level. As a service for the scientific community, we provide numerical tables and a script to calculate energy-differential cross sections.

arXiv comment25 pages, 19 figures. Typos corrected, matches version published by PRD. The tables of the energy differential cross sections of electrons and positrons with a script to read them can be found here: https://github.com/lucaorusa/positron_electron_cross_section

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