[Paper Review] Thermal QCD Axions across Thresholds

Francesco D’Eramo, Fazlollah Hajkarim+1 more|arXiv (Cornell University)|Aug 11, 2021

Dark Matter and Cosmic Phenomena95 references4 citations

TL;DR

This paper presents a smooth, systematic analysis of thermal QCD axion production across key cosmological thresholds—such as the QCD phase transition, heavy fermion and Higgs boson masses—in both KSVZ and DFSZ axion models. It computes the resulting axion production rate and its impact on the effective number of neutrino species, ΔN_eff, showing robust predictions insensitive to interpolation details, with future CMB-S4 surveys expected to probe these effects with high sensitivity.

ABSTRACT

Thermal axion production in the early universe goes through several mass thresholds, and the resulting rate may change dramatically across them. Focusing on the KSVZ and DFSZ frameworks for the invisible QCD axion, we perform a systematic analysis of thermal production across thresholds and provide smooth results for the rate. The QCD phase transition is an obstacle for both classes of models. For the hadronic KSVZ axion, we also deal with production at temperatures around the mass of the heavy-colored fermion charged under the Peccei-Quinn symmetry. Within the DFSZ framework, standard model fermions are charged under this symmetry, and additional thresholds are the heavy Higgs bosons masses and the electroweak phase transition. We investigate the cosmological implications with a specific focus on axion dark radiation quantified by an effective number of neutrino species and explore the discovery reach of future CMB-S4 surveys.

Motivation & Objective

• To systematically analyze thermal axion production across critical mass thresholds in the early universe, including the QCD phase transition and heavy particle thresholds.
• To compute the axion production rate in both KSVZ and DFSZ models with smooth interpolation across the QCD crossover, avoiding discontinuities.
• To quantify the cosmological impact of thermally produced axions via the effective number of neutrino species, ΔN_eff.
• To assess the discovery potential of future CMB-S4 surveys for detecting axion-induced radiation beyond the standard model.
• To evaluate theoretical uncertainties in ΔN_eff due to interpolation methods near the QCD phase transition.

Proposed method

• Uses cubic spline interpolation to smoothly connect thermal production rates across the QCD crossover, from chiral perturbation theory (ChPT) to hadronic resonance regions.
• Solves the Boltzmann equation for axion number density evolution, tracking production from scattering and decay processes in the primordial thermal bath.
• Applies the entropy-conservation method to relate the axion comoving number density at recombination to ΔN_eff via the effective degrees of freedom in entropy.
• Derives a general formula for ΔN_eff in terms of the axion’s comoving number density at CMB formation and the SM entropy degrees of freedom.
• Evaluates the sensitivity of ΔN_eff predictions to variations in the production rate around 500 MeV, testing robustness of interpolation methods.
• Compares results across KSVZ and DFSZ models, accounting for additional thresholds such as heavy Higgs and electroweak phase transition.

Experimental results

Research questions

• RQ1 How does the thermal production rate of QCD axions change across the QCD phase transition, and what is the optimal method to interpolate across this crossover?
• RQ2 What is the resulting contribution of thermally produced axions to the effective number of neutrino species, ΔN_eff, in KSVZ and DFSZ axion models?
• RQ3 How sensitive are ΔN_eff predictions to uncertainties in the interpolation of the production rate near the QCD phase transition?
• RQ4 What is the discovery reach of future CMB-S4 surveys for detecting axion-induced radiation beyond the standard model?
• RQ5 How do additional thresholds—such as heavy fermions in KSVZ or heavy Higgs bosons in DFSZ—affect axion production and cosmological constraints?

Key findings

• The thermal production rate of QCD axions is computed with smooth interpolation across the QCD crossover using cubic splines, ensuring physical consistency without discontinuities.
• For the KSVZ model, axion production is significantly enhanced near the QCD phase transition due to the presence of heavy colored fermions, contributing to ΔN_eff.
• In the DFSZ model, additional thresholds from heavy Higgs bosons and the electroweak phase transition further modify the production rate and ΔN_eff.
• The predicted ΔN_eff is robust against variations in the interpolation method: a factor-of-two change in the production rate at 500 MeV leads to negligible changes in ΔN_eff for experimentally allowed axion decay constants.
• Future CMB-S4 surveys are expected to achieve a 1σ sensitivity of ΔN_eff ≈ 0.02–0.03, enabling the detection of axion-induced radiation if the axion decay constant is within the accessible range.
• The final formula for ΔN_eff accounts for non-instantaneous neutrino decoupling and entropy conservation, with the result expressed in terms of the axion’s comoving number density at recombination.