Thermal Production of Axions from Heavy Higgs Bosons

We discuss the thermal production of axions in renormalizable models involving two Higgs doublet fields and a complex singlet field with a global $U(1)$ Peccei-Quinn symmetry, i.e., DFSZ type axion models. We demonstrate that, when the reheating temperature exceeds the mass scale of heavy Higgs bosons, axions are efficiently produced through heavy Higgs boson decays and scatterings at temperatures comparable to the heavy Higgs boson mass scale. As a result, the abundance of thermally produced axions is independent of the reheating temperature, which should be contrasted with the KSVZ axion model. This is because thermal productions via renormalizable interactions are IR-dominated processes. We demonstrate that the heavy Higgs boson decays are the main channels for axion thermal productions among various processes in the DFSZ-type axion models, which were missed in the literature. Our results apply to the original DFSZ QCD axion model since the production mechanism does not depend on the axion mass. As an application of axion productions from the heavy Higgs boson decays, we calculate the contributions to $\Delta N_{\rm eff}$ for axions with a mass smaller than ${\cal O}(0.1){\rm eV}$. Future measurements of $\Delta N_{\rm eff}$ could constrain model parameters in both axion and Higgs sectors. Focusing on axions with masses from keV to sub-GeV scale, we then discuss how cosmological observations such as X-ray and cosmic microwave background constrain the produced axion. We show that a large portion of the parameter space of the models can be explored even if the amount of the axion produced from the heavy Higgs bosons is much smaller than the observed cold dark matter abundance.