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The cosmic-ray fluxes of electrons and positrons ($e^{\pm}$) are measuredwith high precision by the space-borne particle spectrometer AMS-02. To infer aprecise 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 theinterstellar medium atoms. We determine new analytical functions of the Lorentzinvariant cross section for the production of $\pi^\pm$ and $K^\pm$ by fittingdata from collider experiments. We also evaluate the invariant cross sectionsfor several other channels, involving for example hyperon decays, contributingat the few \% level on the total cross section. For all these particles, therelevant 2 and 3 body decay channels are implemented, with the polarized$\mu^\pm$ decay computed with next-to-leading order corrections. The crosssection for scattering of nuclei heavier than protons is modeled by fittingdata on $p+C$ collisions. The total differential cross section$d\sigma/dT_{e^\pm}(p+p\rightarrow e^\pm+X)$ is predicted from 10 MeV up to 10TeV of $e^\pm$ energy with an uncertainty of about 5-7\% in the energiesrelevant for AMS-02 positron flux, thus dramatically reducing the precision ofthe theoretical model with respect to the state of the art. Finally, we providea prediction for the secondary Galactic $e^\pm$ source spectrum with anuncertainty of the same level. As a service for the scientific community, weprovide numerical tables and a script to calculate energy-differential crosssections.

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