Toponium Production at Future Muon Colliders and in heavy ion ultraperipheral collisions

In the framework of non-relativistic quantum chromodynamics (NRQCD), we systematically investigate the inclusive and exclusive production processes of spin-singlet ${}^1{S}_0$ and spin-triplet ${}^3{S}_1$ toponium at future muon colliders and in Pb–Pb ultraperipheral collisions (Pb–Pb UPC). Using the Coulomb-plus-linear potential and solving the Schrödinger equation, we obtain the wave function at the origin as $\mathrm{\mid }{R}_{t\bar{t}}(0){\mathrm{\mid }}^2=2.507{\text{GeV}}^3$. The scattering cross sections and various kinematic distributions for two types of processes are calculated, and the corresponding event yields are estimated based on the expected integrated luminosities. Our study indicates that the detection prospects for toponium production through the aforementioned processes are unfavorable.