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$μ$TRISTAN

The ultra-cold muon technology developed for the muon $g-2$ experiment at J-PARC provides a low emittance $μ^+$ beam which can be accelerated and used for realistic collider experiments. We consider the possibility of new collider experiments by accelerating the $μ^+$ beam up to 1 TeV. Allowing the $μ^+$ beam to collide with a high intensity $e^-$ beam at the TRISTAN energy, $E_{e^-}= 30$ GeV, in the storage ring with the same size as TRISTAN (the circumference of 3 km), one can realize a collider experiment with the center-of-mass energy $\sqrt s = 346$ GeV, which allows productions of the Higgs bosons through the vector boson fusion processes. We estimate the deliverable luminosity with existing accelerator technologies to be at the level of $5 \times 10^{33}$ cm$^{-2}$ s$^{-1}$, with which the collider can be a good Higgs boson factory. The $μ^+ μ^+$ colliders up to $\sqrt s = 2$ TeV are also possible by using the same storage ring. They have a capability of producing the superpartner of the muon up to TeV masses.