Searches for axion-like particles via $\gamma \gamma$ fusion at future $\mathrm{e}^+\mathrm{e}^-$ colliders

Opportunities for searches for axion-like particles (ALPs) coupling to photons in $\mathrm{e}^+\mathrm{e}^-$ collisions at the Future Circular Collider (FCC-ee) and International Linear Collider (ILC) are investigated. We perform a study of the photon-fusion production of ALPs decaying into two photons, $\mathrm{e}^+\mathrm{e}^- \overset{\gamma \gamma}{\longrightarrow} \mathrm{e}^{+}\;a(\gamma \gamma)\;\mathrm{e}^{-}$, over the light-by-light continuum background, for the planned FCC-ee and ILC center-of-mass energies and integrated luminosities. An analysis of the feasibility measurements is presented using parametrized simulations for two types of detectors. Upper limits at 95% confidence level (CL) on the cross section for ALP production, $\sigma(\gamma \gamma \to a \to \gamma \gamma)$, and on the ALP-photon coupling are obtained over the $m_a \approx 0.1$--1000 GeV ALP mass range, and compared to current and future collider searches. Production cross sections down to $\sigma(\gamma \gamma \to a \to \gamma \gamma) \approx 1$ fb (1 ab) will be probed at $m_a\approx 1$ (300) GeV, corresponding to constraints on the axion-photon coupling as low as $g_\mathrm{a\gamma \gamma} \approx 2\cdot10^{-3}$ TeV$^{-1}$.