This paper reports the first non‑perturbative, first‑principles calculation of the quantum chromodynamics (QCD) contribution to the axion–photon coupling. The axion is a hypothetical particle that could explain why the strong force respects time‑reversal symmetry and might also be dark matter. Experiments that search for axions look for axions converting into photons, and that conversion rate depends on a coupling that has a model‑dependent part and a model‑independent part coming from QCD. The authors compute that QCD part directly using lattice QCD simulations, removing a longstanding uncertainty in axion predictions.

The team simulated QCD with the three light quarks (up, down and strange) on a space‑time lattice. They probed how the QCD vacuum responds to a CP‑odd combination of background electric and magnetic fields (the product E·B) and to a homogeneous background axion field. They used two independent approaches. The first measures the topological charge directly from the gluon fields (the “gluonic” method). The second is new here: it uses an identity for quark operators (an axial Ward identity) to relate the coupling to the change in a fermionic pseudoscalar observable when the background fields are switched on (the “fermionic” method). In a finite Euclidean volume their electric field must be treated as imaginary, and the coupling is obtained by numerical differentiation in the small‑field limit.

To reach a physical answer the authors performed two extrapolations. They took the background fields to zero and they removed the lattice spacing by extrapolating to the continuum. These steps were done with polynomial fits and many variants, and the variants were weighted by the Akaike Information Criterion to estimate systematic uncertainty. Statistical errors were estimated with a jackknife procedure. The two independent methods agree in the continuum limit, and the most precise number comes from the gluonic method.