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We investigate the possibility of secondary production as the source ofcosmic ray (CR) positrons, taking into account observed electron and antiprotonspectra and allowing that the reported steepening in the AMS-02 positronspectrum may be due to radiative losses. Using a simple argument based on theantiproton spectrum, we show that positrons cannot be purely secondary. Namely,the antiproton to positron ratio requires that positrons be uncooled up to afew hundred GeV. This requirement implies that CR protons escape from theGalaxy too quickly to reproduce the observed antiproton flux. We further showthat this result rules out also more complex secondary production scenariossuch as reacceleration and the Nested Leaky Box. Thus, we conclude that whileantiprotons can be produced exclusively in secondary interactions, a primarysource of CR positrons -- be it dark matter or pulsars -- is required toexplain their spectrum.

Nonsecondary origin of cosmic ray positrons