Common origin of the diffuse high energy backgrounds of gamma rays, neutrinos and cosmic ray positrons?

We show that the observed fluxes, spectra and sky distributions of the high energy diffuse backgrounds of astronomical neutrinos, gamma rays and cosmic ray positrons satisfy simple relations expected from their common production in hadronic collisions of high energy cosmic rays (CRs) with diffuse matter. This provides compelling evidence that the high energy neutrino, gamma ray, and positron backgrounds have a common origin - hadronic meson production by cosmic rays in our Galaxy and in external galaxies rather than through the decay/annihilation of dark matter particles.