Probe of a Randall-Sundrum-like model from muon pair production at high energy muon collider

We have examined inclusive ${\mu }^{+}{\mu }^{-}\to {\mu }^{+}{\mu }^{-}+E_{\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{s}}$ and annihilation ${\mu }^{+}{\mu }^{-}\to {\mu }^{+}{\mu }^{-}$ processes at future high energy muon colliders in the framework of the Randall-Sundrum-like model with a small curvature of space-time. The collision energies of 3 TeV, 14 TeV and, 100 TeV are addressed. Both differential and total cross sections are calculated, and exclusion bounds on a 5-dimensional gravity scale are obtained depending on collision energy and integrated luminosity of the muon colliders.