Masses of Purely Top-Quark Bound States: Toponium and the Triply-Top Baryon

We investigate the pseudoscalar ($\eta_t$) and vector ($\psi_t$) toponium states, as well as the triply-top baryon ($\Omega_{ttt}$), using the QCD sum-rule method. This study was motivated by the recent observation of a pseudoscalar enhancement near the $t\bar{t}$ threshold, reported by the CMS and ATLAS collaborations with a statistical significance exceeding $5\sigma$. In the calculations, we consider both the perturbative and nonperturbative contributions, with the nonperturbative operators taken into account up to dimension eight. The results obtained for the pseudoscalar toponium provide a theoretical estimate that is consistent with the near-threshold events observed in recent experimental studies. The calculated negative binding energy for both the pseudoscalar and vector toponium states reflects the strong correlation within the $t\bar{t}$ system and can be interpreted as $t\bar{t}$ bound states, while the calculated central mass for the $\Omega_{ttt}$ slightly exceeds the central value of the sum of the constituent top-quark masses. The results of this study can provide a precise theoretical guide for future experimental investigations of these states, which are composed entirely of top quarks, at high-energy colliders such as the LHC and future facilities like the FCC.