Observable windows for the QCD axion through $N_{\text{eff}}$

Abstract

We show that when the QCD axion is directly coupled to quarks with $c_q/f{\partial }_{\mu }a\bar{q}{\gamma }^{\mu }{\gamma }^{5}q$, such as in DFSZ models, the dominant production mechanism in the early universe at temperatures $1\mathrm{GeV}\lesssim T\lesssim 100\mathrm{GeV}$ is obtained via $q\bar{q}\leftrightarrow ga$ and $qg\leftrightarrow qa$, where $g$ are gluons. Different heavy quarks $q_i$ can produce a thermal axion background that decouples at a temperature $T_i$: (1) top quark at $T_t\lesssim 100\mathrm{GeV}$ for $f/c_t\lesssim 3\times 10^8\mathrm{GeV}$; (2) bottom quark at $T_b\lesssim m_b$, for $f/c_b\lesssim 8\times 10^7\mathrm{GeV}$; (3) charm quark at $T_c\lesssim m_c$ for $f/c_c\lesssim 5\times 10^7\mathrm{GeV}$. Each of these cases corresponds to a contribution to the effective number of relativistic degrees of freedom, in the windows given by $0.027\le \Delta N_{\text{eff}}\le 0.031$, $0.037\le \Delta N_{\text{eff}}\le 0.039$ and $0.039\le \Delta N_{\text{eff}}$, respectively. These contributions are larger than the one obtained when thermalization happens only above the electroweak phase transition, $\Delta N_{\mathrm{eff}}\lesssim 0.027$, and are within reach of future CMB S4 experiments, thus opening an alternative window to detect the axion and to test the early universe at such temperatures.

Comments: 6 pages, 1 figure. Numerical solution of Boltzmann equation included, 1 new plot