Thermal axion production

TL;DR

This work revisits thermal axion production in the early universe, extending previous analyses by including couplings of the axion to all Standard Model particles and performing a nonperturbative resummation of thermal effects. The authors derive a unified expression for the thermal axion production rate that incorporates gluon, weak, hypercharge, and top-quark couplings, with the top Yukawa term dominating the rate when present. They show that thermal effects enhance the gluon contribution beyond the traditional HTL results and that there are no collinear enhancements requiring extra resummation. The cosmological outcome is a calculable hot axion abundance, yielding a small additional relativistic component $oxed{\Delta N_{\nu}^{\mathrm{eff}}}$, with decoupling occurring above the electroweak scale for plausible decay constants, and the framework provides a practical formula for $\gamma_a$ in terms of $c'_t$, $c'_3$, $c'_2$, and $c'_1$ along with the SM couplings and thermal masses.

Abstract

We reconsider thermal production of axions in the early universe, including axion couplings to all Standard Model (SM) particles. Concerning the axion coupling to gluons, we find that thermal effects enhance the axion production rate by a factor of few with respect to previous computations performed in the limit of small strong gauge coupling. Furthermore, we find that the top Yukawa coupling induces a much larger axion production rate, unless the axion couples to SM particles only via anomalies.

Figures (5)

• Figure 1: Our result for the axion production rate as function of the thermal mass of vectors. The functions $F_{1,2,3}(m/T)$ are defined in eq. (\ref{['defF321']}) and the thermal masses of the vectors within the SM are $m/T=g_3$ for gluons, $m/T=\sqrt{11/12} g_2$ for the $W,Z$ and $m/T = \sqrt{11/12} g_Y$ for hypercharge. For comparison, the lower dashed curve is the result of Graf:2010tv (eq. (\ref{['HTLresutl']})) computed within the HTL approximation, valid in the limit $g_3\ll1$.
• Figure 2: The leading-order $gg\to ga$ scattering rate in the thermal plasma is equivalently obtained by: a) summing the Feynman diagrams in the upper row, squaring the total amplitude, performing the thermal average; b) summing the imaginary parts of the two loop thermal diagrams in the lower row. In both cases the result is infra-red divergent, such that proper inclusion of higher order effects is needed. For simplicity, we here plotted the diagrams relative to a simplified world without quarks.
• Figure 3: The thermal diagram 'Decay', where the gluon propagator includes one-loop thermal corrections, is equivalent to the thermal diagram D (thick lines denote the propagator of the thermal gluon $g_T$) plus the resummation of higher order diagrams with corrections to the gluon propagator.
• Figure 4:
• Figure 5: The four contributions to the thermal axion production rate $\gamma_a$ induced by the SM couplings $y_t$ (upper black curve), $g_3$ (red curve), $g_2$ (blue), $g_Y$ (green) for unity values of the axion couplings $c'_t=c'_3=c'_2=c'_1=1$ in eq. (\ref{['defF321']}). The red dashed line is the previous result for the strong coupling contribution computed in Hard Thermal Loop approximation.