= Relic cooling across muon annihilation
{title2=$T_H/T_\gamma=(43/57)^{1/3}$}
A relativistic relic that decouples between pion and muon annihilation keeps $aT_H$ constant. The coupled bath initially contains <photons>, electron-positron pairs, muon-antimuon pairs and three neutrino-antineutrino species, with <entropy> degrees of freedom $57/4$. After muon annihilation this is $43/4$, giving the displayed <temperature> ratio. After <neutrino decoupling>, electron-positron annihilation heats <photons> by $(11/4)^{1/3}$, so the final relic-to-photon ratio becomes $(172/627)^{1/3}$. This counting assumes the species are relativistic when counted and treats annihilations and decoupling as sharp equilibrium transitions.
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