HTL computation of soft axion rates shows interpolation between k=0 and k≈ω, raising ΔN_eff from ~0.03 to ~0.04 for light QCD axions at fa=4×10^8 GeV.
Di Luzioet al.,Axion-pion thermalization rate in unitarized NLO chiral perturbation theory, Phys
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Energy and momentum dependence of the soft-axion interaction rate
HTL computation of soft axion rates shows interpolation between k=0 and k≈ω, raising ΔN_eff from ~0.03 to ~0.04 for light QCD axions at fa=4×10^8 GeV.