The axion-photon coupling from lattice Quantum Chromodynamics

Abstract

Quantum Chromodynamics (QCD) is the theory of the strong interactions within the Standard Model of particle physics, which explains more than 99% of the mass of the visible Universe. However, there is evidence that a substantial portion of our Universe is made up of particles beyond the Standard Model, i.e. dark matter. A popular dark matter candidate is the axion -- a hypothetical particle that also solves the so-called strong CP-problem, the unexpected symmetry of QCD under time reversal. The experimental detection of axions hinges on their conversion rate to photons, controlled by the axion-photon coupling. This coupling depends on the specific axion model, but also receives a sizable model-independent contribution from QCD. Here we present the first non-perturbative determination of the QCD contribution using continuum extrapolated lattice simulations. The calculation is based on determining the response of the QCD vacuum to time reversal-odd combinations of background electromagnetic fields. We develop two independent methods exploiting different features of this response and obtain $g_{Aγγ}^{\rm QCD} f_A/e^2=-0.0224(10)$ in units of the axion scale $f_A$ and the elementary charge $e$. Armed with this first-principles result, we present a novel update on how experimental observations can be used to constrain the landscape of axion models, useful for guiding contemporary and future observational strategies.

Figures (8)

• Figure 1: Continuum extrapolation of the QCD contribution to the axion-photon coupling using the gluonic method, involving an improved topological charge operator with rounding (left panel) and the fermionic method, employing the average light quark flavors (right panel). Each black data point represents the result of extrapolations to zero electromagnetic field, including statistical and systematic errors. The purple point in the left panel marks our final result, obtained by combining all extrapolations using the gluonic method. The faint purple point in the right panel corresponds to the continuum extrapolations using the fermionic method with the average light quark flavors. Polynomial fits with different orders and AIC weights are marked by different colors (red, yellow and blue curves are fits including terms up to $a^2$, $a^4$ and $a^6$, respectively) and line widths. The inset depicts the probability density and the cumulative density of the final result. The vertical purple line is the median of the distribution and the dashed lines mark the range corresponding to the total error.
• Figure 2: Experimental constraints on the axion parameter landscape, adapted from Ref. AxionLimits. The probability density of the magnitude of the total axion-photon coupling, given our result for the probability distribution of $g_{A\gamma\gamma}^{\text{QCD}}$ from Fig. \ref{['fig:clim']} and the preferred models of Ref. DiLuzio:2016sbl, is visualized by the orange shaded region using a logarithmic color map. The KSVZ and DFSZ models are highlighted by the dashed lines. For details on the experimental data, see Refs. AxionLimitsParticleDataGroup:2024cfk and references within.
• Figure 3: Constraints on the experimentally allowed values of the model-dependent contribution to the axion-photon coupling, adapted from Ref. AxionLimits. For details on the experimental data, see Refs. AxionLimitsParticleDataGroup:2024cfk and references within. The black lines denote the models which give the biggest and smallest values for $|g_{A\gamma\gamma}|$. The brown line marks the DFSZ model with $E/N = 8/3$ and the gray dashed line the value where the total coupling vanishes. Finally, the orange lines correspond to the rest of the models considered in Ref. DiLuzio:2016sbl. Some of the lines have been cut horizontally for visualization purposes.
• Figure 4: Comparison of the expectation value of the topological charge obtained on two different volumes (realizing slightly different low temperatures) at the same value of $\bm E\bm B$ and of the lattice spacing. We observe an agreement between the two setups within errors.
• Figure 5: Left panel: evolution of the regular and improved definitions of the topological charge with the gradient flow for two individual $48^3\times 64$ configurations and two different electromagnetic field fluxes ($n_e=2$, $n_b=3$; $n_e=3$, $n_b=4$). The maximal flow time value ($\tau_f = 1$ fm$^2$) is indicated by the dark vertical line. In this region, the topological charge has already reached a plateau. Right panel: continuum extrapolated result for $g_{A\gamma\gamma}^{\text{QCD}}$ as a function of the employed flow time $\tau_f$.