Di-Higgs Decay of Stoponium at Future Photon-Photon Collider

We study the detectability of the stoponium in the di-Higgs decay mode at the photon-photon collider option of the International $e^+e^-$ Linear Collider (ILC), whose center-of-mass energy is planned to reach $\sim 1$ TeV. We find that $5\sigma$ detection of the di-Higgs decay mode is possible with the integrated electron-beam luminosity of $1 {\rm ab}^{-1}$ if the signal cross section, $\sigma(\gamma \gamma \rightarrow \sigma_{\tilde{t}_1} \rightarrow hh)$, of ${\cal O}(0.1)$ fb is realized for the stoponium mass smaller than $\sim$ 800 GeV at 1 TeV ILC. Such a value of the cross section can be realized in the minimal supersymmetric standard model (MSSM) with relatively large trilinear stop-stop-Higgs coupling constant. Implication of the stoponium cross section measurement for the MSSM stop sector is also discussed.