Probing the CP Property of ALP-photon Interactions at Future Lepton Colliders

We investigate a charge-parity (CP) odd axion-like particle (ALP) featuring simultaneous CP-conserving ($a F_{\mu\nu}\tilde{F}^{\mu\nu}$) and CP-violating ($a F_{\mu\nu}F^{\mu\nu}$) ALP-photon interactions at future lepton colliders. The ALP signal is studied in the process $e^+e^- \to e^+e^- a \to e^+e^- \gamma\gamma$, where the CP structure of the interaction can be probed using the azimuthal angle difference between the final-state electrons, $\Delta\phi_{ee}$. We show that the projected sensitivity to the ALP-photon couplings can reach $\mathcal{O}(10^{-3})~\mathrm{TeV}^{-1}$, exceeding current constraints from the electron electric dipole moment ($e$EDM). Because purely CP-conserving, purely CP-violating, and mixed interactions generate distinct $\Delta\phi_{ee}$ distributions, a binned likelihood analysis of this observable enables an efficient discrimination of the ALP interaction structure. In particular, if the CP-conserving and CP-violating couplings are comparable--as motivated by possible symmetry considerations--the interference pattern in the $\Delta\phi_{ee}$ distribution allows future lepton colliders to identify CP violation in the ALP sector once a signal is observed. For scenarios where the two couplings differ significantly, increasing the integrated luminosity substantially improves the sensitivity to CP-violating effects.