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

Abstract: We investigate the pseudoscalar ($ηt$) and vector ($ψ_t$) toponium states, as well as the triply-top baryon ($Ω{ttt}$), 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 $5σ$. 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 align with the CMS prediction within the corresponding uncertainty range. 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. 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.