Pseudoscalar and vector toponia in a Dyson--Schwinger--Bethe--Salpeter framework
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2026
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| author | Zhang, H. -R. Cui, Z. -F. Segovia, J. |
| author_facet | Zhang, H. -R. Cui, Z. -F. Segovia, J. |
| contents | 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 $μ=400-800\,\text{GeV}$. 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 Poincaré-covariant nonperturbative framework, quantum chromodynamics (QCD) generates tightly correlated pseudoscalar and vector toponium systems in that extreme heavy-quark limit. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_17503 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pseudoscalar and vector toponia in a Dyson--Schwinger--Bethe--Salpeter framework Zhang, H. -R. Cui, Z. -F. Segovia, J. High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice Nuclear Experiment Nuclear Theory 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 $μ=400-800\,\text{GeV}$. 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 Poincaré-covariant nonperturbative framework, quantum chromodynamics (QCD) generates tightly correlated pseudoscalar and vector toponium systems in that extreme heavy-quark limit. |
| title | Pseudoscalar and vector toponia in a Dyson--Schwinger--Bethe--Salpeter framework |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice Nuclear Experiment Nuclear Theory |
| url | https://arxiv.org/abs/2603.17503 |