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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 $e^-e^+ \rightarrow γ\,\, a,~ a \to γγ$ 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 $C_{γγ} / Λ$, the effective ALP-photon-$Z$ coupling $C_{γZ} / Λ$, and ALP mass $m_a$ for three physics scenarios: $C_{γZ} = 0$; $C_{γZ} = C_{γγ}$ and both $C_{γZ}$ and $C_{γγ}$ can freely change. The results provide references for the optimization of far detectors at future electron-positron colliders.