Motivated by the ATLAS and CMS announcements of the excesses of di-photon events, we discuss the production and decay processes of di-photon resonance at future $e^+e^-$ colliders. We assume that the excess of the di-photon events at the LHC is explained by a scalar resonance decaying into a pair of photons. In such a case, the scalar interacts with standard model gauge bosons and, consequently, the production of such a scalar is possible at the $e^+e^-$ colliders. We study the production of the scalar resonance via the associated production with photon or $Z$, as well as via the vector-boson fusion, and calculate the cross sections of these processes. We also study the backgrounds, and discuss the detectability of the signals of scalar production with various decay processes of the scalar resonance. We also consider the case where the scalar resonance has an invisible decay mode, and study how the invisible decay can be observed at the $e^+e^-$ colliders.
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