Search for long-lived axions with far detectors at future lepton colliders

In our previous work [Phys. Rev. D 101 (2020) 075046], we have proposed to install FAr Detectors at the Electron Positron Collider (FADEPC) to enhance the discovery potential of long-lived particles (LLPs). In this study, we consider eight designs of far detectors with different locations, volumes and geometries and investigate their potential for discovering long-lived axion-like particles (ALPs) via the process $e^-e^+ \rightarrow \gamma \,\, a,~ a \to \gamma\gamma $ at future $e^{-}e^{+}$ colliders running at a center-of-mass energy of 91.2 GeV and integrated luminosities of 16, 150, and 750 ab$^{-1}$. We estimate their sensitivities on the model parameters in terms of the effective ALP-photon-photon coupling $C_{\gamma \gamma} / \Lambda $, the effective ALP-photon-$Z$ coupling $C_{\gamma Z} / \Lambda$, and ALP mass $m_a$ for three physics scenarios: $C_{\gamma Z} = 0$; $C_{\gamma Z} = C_{\gamma \gamma}$ and both $C_{\gamma Z}$ and $C_{\gamma \gamma}$ can freely change. The results provide references for the optimization of far detectors at future electron-positron colliders.