Toponia at the HL-LHC and FCC-ee

A bstract The hint of a pseudoscalar toponium state at the Large Hadron Collider (LHC) opens a new avenue for studying a novel class of QCD (quasi-)bound states with comparable formation and decay times. Compared with charmonium and bottomonium, toponium is a quasi-bound state, resembling a hydrogen atom of the strong interaction, although it appears as a broader resonance. We compute the masses and annihilation decay widths of the lowest S -wave ( η t , ψ t ) and P -wave ( χ t 0 , χ t 1 ) toponium states, and assess their discovery prospects at the High-Luminosity LHC (HL-LHC) and future lepton colliders, such as the e + e − stage of the Future Circular Collider (FCC-ee). Detecting the vector ψ t state at the HL-LHC is hindered by the Landau-Yang theorem and the gluon-dominated production environment of the collider, whereas lepton colliders offer promising sensitivity through both constituent and two-body decays. A more precise measurement of the η t mass-approximately equal to that of ψ t -at the LHC could help determine the optimal $$ t\overline{t} $$ t t ¯ threshold center-of-mass energy for FCC-ee. The P -wave states remain challenging to observe at both the HL-LHC and future lepton colliders. We also discuss how toponium measurements can be used to probe top-quark properties and to conduct indirect searches for new physics, including light scalars that couple to the top quark.