The topological susceptibility in finite temperature QCD and axion cosmology (1606.03145v2)

Abstract: We study the topological susceptibility in 2+1 flavor QCD above the chiral crossover transition temperature using Highly Improved Staggered Quark action and several lattice spacings, corresponding to temporal extent of the lattice, $N_\tau=6,8,10$ and $12$. We observe very distinct temperature dependences of the topological susceptibility in the ranges above and below $250$ MeV. While for temperatures above $250$ MeV, the dependence is found to be consistent with dilute instanton gas approximation, at lower temperatures the fall-off of topological susceptibility is milder. We discuss the consequence of our results for cosmology wherein we estimate the bounds on the axion decay constant and the oscillation temperature if indeed the QCD axion is a possible dark matter candidate.

• The paper employs advanced lattice QCD simulations with HISQ action and gradient flow to accurately assess topological susceptibility across different temperatures.
• It identifies a transition around 1.5 Tc where data shifts from non-DIGA to DIGA behavior, validated by a two-loop correction scaling factor.
• Results offer essential constraints on the axion decay constant, providing vital insights for experimental axion dark matter searches.

The Topological Susceptibility in Finite Temperature QCD and Axion Cosmology

This paper examines the behavior of topological susceptibility in Quantum Chromodynamics (QCD) at finite temperature and explores its implications for axion cosmology. The authors utilize lattice gauge theory with Highly Improved Staggered Quark (HISQ) action to investigate temperature-dependent dynamics in topological structures, focusing primarily on the onset of a dilute instanton gas approximation at high temperatures.

The paper uses the topological susceptibility, a key observable sensitive to the vacuum structure of QCD, to analyze the nature of topological objects like instantons and dyons at varying temperatures. The paper employs gradient flow techniques for smoothing gauge configurations, allowing accurate measurement of topological charge and susceptibility.

Key Contributions and Findings

1. Lattice Setup and Methodology: Utilizing the HISQ discretization and operating across several lattice spacings (Nτ = 6, 8, 10, 12), the authors conduct a thorough examination of the temperature dependence of topological susceptibility. The choice of lattice parameters and gradient flow ensures reliable data for continuum extrapolation.
2. Temperature Dependence of Topological Susceptibility: The paper reveals a distinct change in the temperature dependence of topological susceptibility around 1.5 Tc, where Tc represents the chiral crossover transition temperature. Below this threshold, the behavior deviates from a dilute instanton gas approximation, whereas higher temperatures align with its predictions.
3. Numerical Continuum Extrapolation: A robust continuum extrapolation methodology is applied, showing significant cut-off effects dependent on aT = 1/Nτ rather than the lattice spacing itself. This interpolation confirms the consistency between gluonic and fermionic estimates of topological susceptibility.
4. Comparison with DIGA: The paper matches lattice-derived susceptibility with two-loop corrections in the dilute instanton gas approximation (DIGA) using a scaling factor (K = 1.90 ± 0.35). This provides insights into discrepancies observed in prior studies, emphasizing the importance of fine lattice spacing in reliable continuum results.
5. Implications for Axion Cosmology: The findings propose bounds on the axion decay constant based on topological susceptibility extrapolations, crucial for understanding QCD axions as dark matter candidates. The comparative analysis delineates future experimental constraints for axion detection.

Implications and Future Directions

The paper contributes significantly to the understanding of QCD thermodynamics at finite temperatures and posits substantial implications for axion cosmology. The robustness of lattice QCD calculations concerning topological susceptibility enhances theoretical predictions about the early universe's axion dynamics, potentially guiding future experimental designs in axion search initiatives like ADMX.

While the paper provides a thorough analysis of finite-temperature QCD, further exploration using different lattice formulations and larger configuration ensembles could elucidate the exact role of topological constituents close to chiral crossover transitions. The verification of these findings in more extensive temperature ranges and their integration with observational data will enrich both QCD phenomenology and cosmological models.