The QCD axion, precisely (1511.02867v2)

Abstract: We show how several properties of the QCD axion can be extracted at high precision using only first principle QCD computations. By combining NLO results obtained in chiral perturbation theory with recent Lattice QCD results the full axion potential, its mass and the coupling to photons can be reconstructed with percent precision. Axion couplings to nucleons can also be derived reliably, with uncertainties smaller than ten percent. The approach presented here allows the precision to be further improved as uncertainties on the light quark masses and the effective theory couplings are reduced. We also compute the finite temperature dependence of the axion potential and its mass up to the crossover region. For higher temperature we point out the unreliability of the conventional instanton approach and study its impact on the computation of the axion relic abundance.

• The paper refines QCD axion properties with percent-level accuracy by combining NLO chiral perturbation theory and lattice QCD.
• It computes the axion mass and its photon coupling precisely, providing tighter constraints for experimental detection.
• The study also establishes a robust method for determining nucleon couplings and temperature-dependent effects critical for axion searches.

High Precision Computations of QCD Axion Properties

The paper, "The QCD axion, precisely" by Giovanni Grilli di Cortona et al., advances our understanding of the Quantum Chromodynamics (QCD) axion through highly precise theoretical calculations. The authors aim to refine the estimates of essential properties of the QCD axion using non-perturbative QCD techniques, including Next-to-Leading Order (NLO) chiral perturbation theory and insights from Lattice QCD. Several key findings reported in this paper have implications for both theoretical axion physics and experimental searches for this elusive particle.

The QCD axion is a well-motivated extension of the Standard Model, postulated to resolve the strong-CP problem and potentially account for dark matter. Its properties, such as mass, potential, and coupling to photons, are crucial for determining both its role in cosmology and its experimental signatures.

Key Contributions

1. Axion Mass and Potential: The authors calculate the axion mass with unprecedented precision, providing a result of $$m_a = 5.70(6)(4) \, \mu\text{eV} \, (10^{12} \text{GeV}/f_a)$$, where $f_a$ is the Peccei-Quinn scale. This calculation is based on the topological susceptibility in QCD, leveraging both NLO chiral perturbation theory and lattice data. Importantly, the axion potential is derived to percent-level accuracy, revealing significant deviations from the simple cosine potential suggested by the dilute instanton gas approximation.
2. Photon Couplings: The paper refines the axion's coupling to photons, crucial for direct and indirect experimental detection, to percent-level precision. They find $$g_{a\gamma\gamma} = \frac{\alpha_{em}}{2\pi f_a} \left(\frac{E}{N} - 1.92(4)\right)$$, where $E/N$ represents the electromagnetic anomaly of the Peccei-Quinn charge.
3. Nucleon Couplings: The paper presents a strategy for determining axion-nucleon couplings based on first-principle QCD, achieving uncertainties smaller than ten percent. This advancement allows better theoretical underpinning for experimental searches that rely on axion-mediated forces.
4. Temperature-Dependent Properties: The paper explores the finite temperature dependence of the axion mass and potential. The temperature effects are calculated up to the QCD crossover using chiral Lagrangians, and beyond using lattice computations. The findings indicate significant discrepancies from the predictions of the dilute instanton gas model, suggesting the need for further non-perturbative analyses.

Implications and Future Directions

The precision in predicting the axion's properties enhances both its theoretical understanding and the feasibility of its detection. Importantly, precise mass predictions enable tighter constraints on axion models and clearer targets for ongoing experiments like ADMX, CASPEr, and future initiatives such as IAXO. The coupling constants computed in this paper are crucial for designing experiments that exploit these interactions.

Looking forward, lattice QCD calculations with physical quark masses and exploring beyond the QCD confining regimes are vital to further our understanding of axion cosmology, especially regarding its role as dark matter. Additionally, improvements in the measurements of light quark masses and lattice techniques can further tighten the precision on axion mass and couplings.

In conclusion, the paper is significant for its contribution to axion physics, particularly in its methodological advancements that harmonize inputs from chiral perturbation theory and lattice QCD. These results not only solidify the axion's theoretical framework but also guide experimental efforts seeking to unveil the nature of this hypothetical particle.