Comprehensive study of axion photoproduction off the nucleon in chiral effective field theory

Technical Summary: Comprehensive Study of Axion Photoproduction off the Nucleon in Chiral Effective Field Theory

Problem Statement
The search for the axion, a pseudo-Nambu-Goldstone boson proposed to solve the strong CP problem, spans particle physics, cosmology, and astrophysics. A critical process for constraining axion parameters is axion photoproduction off a nucleon target ($\gamma N \to aN$). While existing literature often relies on simple phenomenological models that include only partial leading-order contributions (typically the $a\gamma\gamma$ vertex), a systematic calculation within a rigorous theoretical framework has been lacking. This work addresses the need for a more complete calculation of the $\gamma N \to aN$ amplitudes below the $\pi N$ threshold to bridge experimental constraints with underlying theory.

Methodology
The authors perform a calculation within the framework of Chiral Effective Field Theory (EFT) with baryons, specifically employing the $SU(2)$ version for the proton and neutron degrees of freedom. The study systematically includes contributions up to next-to-leading order (NLO) in the low-energy expansion ($O(p^2)$). The calculation incorporates three distinct mechanisms:

1. Nucleon Exchanges: Contributions from $s$- and $u$-channel nucleon exchanges, derived from chiral Lagrangians up to $O(p^2)$. This includes both leading-order (LO) axial-vector couplings and NLO corrections involving the anomalous magnetic moments of nucleons.
2. Anomalous Vertices: Contributions from the $a\gamma\gamma$ vertex (Primakoff production) and the $V a\gamma$ (vector meson-axion-photon) vertices. The $a\gamma\gamma$ coupling is updated using $SU(2)$ chiral EFT results, including model-independent NLO corrections.
3. Vector-Meson Exchanges: $t$-channel exchanges of $\rho$ and $\omega$ mesons. The $V a\gamma$ couplings are estimated by combining axion-pseudoscalar mixing strengths ($\theta_{aP}$) with effective $V P\gamma$ couplings derived from Resonance Chiral Theory (R$\chi$T).

To fix unknown couplings, the authors utilize extensive hadronic inputs from the literature, including:

• Nucleon matrix elements of axial-vector quark currents ($\Delta q$) from lattice QCD.
• Parameters for $V P\gamma$ interactions and $\eta-\eta'$ mixing from R$\chi$T fits.
• QCD short-distance constraints to constrain low-energy constants (LECs).

The study evaluates both KSVZ and DFSZ axion models, varying model-dependent parameters such as $\tan\beta$ and the anomaly ratio $E/N$.

Key Contributions and Results

• Systematic Amplitude Calculation: The paper provides the first comprehensive calculation of $\gamma N \to aN$ amplitudes that simultaneously includes nucleon exchanges (up to NLO), the $a\gamma\gamma$ vertex, and vector-meson exchanges.
• Mechanism Dominance:
  • Proton Channel ($\gamma p \to ap$): The cross-section is dominated by nucleon exchanges. The NLO corrections from anomalous magnetic moments are found to be significant, comparable to the LO terms.
  • Neutron Channel ($\gamma n \to an$): In the KSVZ model (where model-independent axion-neutron coupling is suppressed), the LO nucleon exchange vanishes, making the cross-section negligible. However, when model-dependent parameters are included or for the DFSZ model, the $t$-channel vector-meson exchanges become the dominant mechanism, surpassing nucleon exchanges.
  • Photon Exchange: Pure photon exchange (Primakoff) contributions are generally 2–3 orders of magnitude smaller than nucleon exchanges in the KSVZ case, though they can be sensitive to the $E/N$ ratio in DFSZ scenarios.
• Differential Cross Sections: The study demonstrates that while total cross sections may show similar trends across different mechanisms, the differential cross sections ($d\sigma/d\cos\theta$) exhibit distinct angular distributions. These shapes are largely insensitive to model-dependent axion parameters, suggesting they can serve as useful observables to distinguish between different production mechanisms.
• Uncertainty Quantification: The authors provide theoretical uncertainty bands arising from variations in lattice QCD inputs, R$\chi$T parameters, and the difference between $SU(2)$ and $SU(3)$ chiral EFT determinations of the $a\gamma\gamma$ coupling.

Significance and Claims
The paper claims that the improved axion photoproduction amplitudes provide reliable inputs for future theoretical studies in astrophysical and cosmological environments, as well as for experimental analyses at facilities such as electron beam dumps, reactors, and electron-ion colliders. By distinguishing the distinct behaviors of total and differential cross sections for different microscopic mechanisms, the work offers a tool to discriminate between different axion models. The authors note that while approximations were made (e.g., ignoring excited baryon states like the $\Delta(1232)$ and higher-order terms beyond $O(p^2)$), the current results are expected to be robust at a qualitative level for low-energy processes away from baryon resonances.