Pseudoscalar and vector toponia in a Dyson--Schwinger--Bethe--Salpeter framework

TL;DR

This study models toponium systems using Dyson--Schwinger--Bethe--Salpeter equations, predicting their masses and decay constants, and demonstrating QCD's role in forming tightly bound heavy quarkonia.

Contribution

It extends a nonperturbative QCD framework to the top quark sector, providing predictions for toponium properties and analyzing their dependence on renormalisation scale and flavor number.

Findings

Toponium masses around 344-346 GeV with small hyperfine splittings.

Large decay constants of 6-7 GeV showing heavy-quark scaling.

Mild sensitivity of results to renormalisation point and flavor number.

Abstract

We study the pseudoscalar ($J^{PC}=0^{-+}$) and vector ($1^{--}$) top--antitop (toponium) systems within the rainbow--ladder truncation of the Dyson--Schwinger and Bethe--Salpeter equations, employing the Qin--Chang effective interaction. After validating the framework in the charmonium and bottomonium sectors, we extend it consistently to the top sector, incorporating renormalisation-group running of the current quark mass and a careful treatment of the number of active flavours. We compute masses and leptonic decay constants for $N_f=5$ and $6$, then analyse their dependence on the renormalisation scale in the range $\mu=400-800\,\text{GeV}$. The resulting toponium masses lie near $344-346\,\text{GeV}$ with hyperfine splittings below $0.14-0.17\,\text{GeV}$, while the decay constants are large, $6-7\,\text{GeV}$, and exhibit the expected heavy-quark scaling behaviour. We find only mild sensitivity to the renormalisation point and a systematic reduction of binding when increasing $N_f$. Although the physical top quark decays weakly before hadronisation, our results demonstrate that, within a Poincar\'e-covariant nonperturbative framework, quantum chromodynamics (QCD) generates tightly correlated pseudoscalar and vector toponium systems in that extreme heavy-quark limit.