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

TL;DR

This paper investigates the masses of purely top-quark bound states, specifically the pseudoscalar $η_t$, vector $ψ_t$ toponium, and the triply-top baryon $Ω_{ttt}$, using QCD sum rules with an operator-product expansion extended to dimension eight. The authors construct two-point correlators for the interpolating currents of these states, compute the QCD side with full top-quark propagators including gluon condensates, and extract masses via Borel-transformed sum rules, matching to hadronic parameters on the physical side. They find $m_{η_t}=343.53^{+1.19}_{-1.31}$ GeV, $m_{ψ_t}=343.59^{+1.17}_{-1.28}$ GeV, and $m_{Ω_{ttt}}=517.81^{+1.82}_{-1.88}$ GeV, with negative binding energies for the two-body states and a baryon mass near the sum of constituent top-quark masses within uncertainties; nonperturbative contributions show a pattern with $D=4$ dominating in the baryon and $D=6$ dominating in the mesons. These results provide precise theoretical inputs to guide future experimental searches at the LHC and future facilities, and offer insights into quantum correlations and multi-quark dynamics at ultraheavy scales.

Abstract

We investigate the pseudoscalar ($η_t$) 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 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 $Ω_{ttt}$ 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.

Figures (1)

• Figure 1: Left panel: Dependence of the masses of the pseudoscalar toponium ($\eta_t$), vector toponium ($\psi_t$), and triply-top baryon ($\Omega_{ttt}$) on the Borel mass parameter ($M^2$) for several fixed values of the continuum threshold ($s_0$). Right panel: Dependence of the masses of the same states on the continuum threshold ($s_0$) for various fixed values of the Borel mass parameter ($M^2$).