Thermal axion production in the primordial quark-gluon plasma

TL;DR

This work addresses the presence of thermally produced axions in the early Universe by computing a gauge-invariant, leading-order production rate from quark–gluon plasma processes using HTL resummation and the Braaten–Yuan prescription. It provides analytic and semi-analytic expressions for the thermally produced yield $Y_a^{TP}$ in terms of the reheating temperature $T_R$ and the Peccei–Quinn scale $f_{PQ}$, and it determines the decoupling temperature $T_D$ separating thermal and nonthermal axion histories. The results show that for $f_{PQ} > 10^{11}$ GeV the thermally produced axion population can remain relativistic today and coexist with the axion CDM condensate, with $Y_a^{TP}$ bounded by the equilibrium yield when applicable. This work clarifies the cosmological impact of thermal axions, constraining reheating scenarios and PQ-scale physics, and it complements the standard misalignment mechanism for axion dark matter by delineating the parameter space where thermal production matters.

Abstract

We calculate the rate for thermal production of axions via scattering of quarks and gluons in the primordial quark-gluon plasma. To obtain a finite result in a gauge-invariant way that is consistent to leading order in the strong gauge coupling, we use systematic field theoretical methods such as hard thermal loop resummation and the Braaten-Yuan prescription. The thermally produced yield, the decoupling temperature, and the density parameter are computed for axions with a mass below 10 meV. In this regime, with a Peccei-Quinn scale above 6x10^8 GeV, the associated axion population can still be relativistic today and can coexist with the axion cold dark matter condensate.

Figures (4)

• Figure 1: The $2\to 2$ processes for axion production in the QGP. Process C also exists with antiquarks $\bar{q}_{i,j}$ replacing $q_{i,j}$.
• Figure 2: Leading contribution to the axion self-energy for soft gluon momentum transfer and hard axion energy. The blob on the gluon line denotes the HTL-resummed gluon propagator.
• Figure 3: The relic axion yield today originating from thermal processes in the primordial plasma for cosmological scenarios characterized by different $T_{\mathrm{R}}$ values covering the range from $10^4$ to $10^{12}\,\mathrm{GeV}$. The dotted, dash-dotted, dashed, and solid lines are obtained for $f_{\mathrm{PQ}}=10^9$, $10^{10}$, $10^{11}$, and $10^{12}\,\mathrm{GeV}$.
• Figure 4: The axion density parameter from thermal processes for $T_{\mathrm{R}}=10^6\,\mathrm{GeV}$ (solid), $10^7\,\mathrm{GeV}$ (dashed) and $10^8\,\mathrm{GeV}$ (dash-dotted) and the one from the misalignment mechanism for $\theta_i=1$, $0.1$, and $0.01$ (dotted). The density parameters for thermal relic axions, photons, and cold dark matter are indicated, respectively, by the gray dotted line ($\Omega_{a}^{\mathrm{eq}} h^2$), the gray thin line ($\Omega_\gamma h^2$), and the gray horizontal bar ($\Omega_{\mathrm{CDM}} h^2$).