Lattice effective-theory simulations give new SU(2)/SU(3) sphaleron rates for T = 0.6 GeV-10^15 GeV and show the soft magnetic sector contributes roughly half the thermal axion production rate at the electroweak scale and dominates below it.
Barroso Mancha and G.D
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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.
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Revisiting the sphaleron and axion production rates in QCD at high temperatures
Lattice effective-theory simulations give new SU(2)/SU(3) sphaleron rates for T = 0.6 GeV-10^15 GeV and show the soft magnetic sector contributes roughly half the thermal axion production rate at the electroweak scale and dominates below it.
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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.