Energy and momentum dependence of the soft-axion interaction rate

Abstract

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 ($k\approx \omega$) is relevant for the axion contribution to the effective number of light neutrinos, $\Delta N_{\mathrm{eff}}^{}$, 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 (${\alpha }_{\mathrm{s}}^{}T\ll \omega \ll \pi T$), we carry out an HTL computation to show how the domains $k=0$ and $k\approx \omega$ interpolate to each other. We then compare with lattice data at $k=0$, and connect our analysis to NLO computations at $k\approx \omega \ge \pi T$. Assembling the current best input, we re-investigate light QCD axion decoupling dynamics at $T\ge 200$ MeV, showing that efficient interactions in the ultrasoft domain increase $\Delta N_{\mathrm{eff}}^{}$ from $\sim 0.03$ to $\sim 0.04$ at $f_a^{}=4\times 10_{}^8$ GeV.

45 pages. v2: minor clarifications

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Cited by in corpus (2)

• Revisiting the sphaleron and axion production rates in QCD at high temperatures
• Beyond thermal approximations: Precise cosmological bounds on Axion-Like Particles