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CMB bounds on dark matter annihilation: Nucleon energy-losses after recombination

We consider the propagation and energy losses of protons and anti-protons produced by dark matter annihilation at redshifts 100<z<~2000. In the case of dark matter annihilations into quarks, gluons and weak gauge bosons, protons and anti-protons carry about 20% of the energy injected into e^\pm and γ's, but their interactions are normally neglected when deriving cosmic microwave background bounds from altered recombination histories. Here, we follow numerically the energy-loss history of typical protons/antiprotons in the cosmological medium. We show that about half of their energy is channeled into photons and e^\pm, and we present a simple prescription to estimate the corresponding strengthening of the cosmic microwave background bounds on the dark matter annihilation cross section.