Energy and momentum dependence of the soft-axion interaction rate

A bstract Axions coupled to thermal non-Abelian gauge fields may have cosmological significance. As the heat bath defines a frame, its influence depends separately on energy and momentum. A light-like momentum ( k ≈ ω ) is relevant for the axion contribution to the effective number of light neutrinos, ∆ N eff , whereas a vanishing momentum ( k = 0) plays a role for warm natural inflation or ultralight dark matter, and has been employed in lattice estimates (both classical and quantum-statistical) of the strong sphaleron rate. Focussing on soft energies ( α s T ≪ ω ≪ πT ), we carry out an HTL computation to show how the domains k = 0 and k ≈ ω interpolate to each other. We then compare with lattice data at k = 0, and connect our analysis to NLO computations at k ≈ ω ≥ πT . Assembling the current best input, we re-investigate light QCD axion decoupling dynamics at T ≥ 200 MeV, showing that efficient interactions in the ultrasoft domain increase ∆ N eff from ∼ 0.03 to ∼ 0.04 at f a = 4 × 10 8 GeV.