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Toponium: Implementation of a toponium model in FeynRules
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abstract
Toponium -- a bound state of the top-antitop pair ($t\bar{t}$) -- emerges as the smallest and simplest hadronic system in QCD, with an ultrashort lifetime ($\tau_t \sim 2.5\times 10^{-25}$~s) and a femtometer-scale Bohr radius ($r_{\text{Bohr}} \sim 7\times 10^{-18}$~m). We present a computational framework extending the Standard Model (SM) with two S-wave toponium states: a spin-singlet $\eta_t$ ($J^{PC}=0^{-+}$) and a spin-triplet $J_t$ ($J^{PC}=1^{--}$). Using nonrelativistic QCD (NRQCD) and a Coulomb potential, we derived couplings to SM particles (gluons, electroweak bosons, Higgs boson, and fermion pairs) and implemented the Lagrangian in FeynRules, generating FeynArts, MadGraph, and WHIZARD models for collider simulations. Key results include dominant decay channels ($\eta_t \to gg/ZH$, $J_t \to W^+W^-/b\bar{b}$) and leading order (LO) cross sections for $pp \to \eta_t(nS) \to {\rm non-}t\bar{t}$ ({66 fb} at 13 TeV). The model avoids double-counting artifacts by excluding direct $t\bar{t}$ couplings, thereby ensuring consistency with perturbative QCD. This work establishes a complete pipeline for precision toponium studies, bridging NRQCD, collider phenomenology, and tests of SM validity at future lepton colliders (e.g., CEPC, FCC-ee, muon colliders) and the LHC. This provides the first publicly available UFO model for toponium, enabling direct integration with MadGraph and WHIZARD for simulations.
Forward citations
Cited by 7 Pith papers
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Topped baryons from QCD sum rules
QCD sum rules in HQET predict ground-state singly topped baryon masses near 174 GeV, some 1.1-1.5 GeV above the top quark pole mass.
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Phenomenology of Hypothetical Single-Top Hadronic States
QCD sum-rule calculations yield single-top baryon and meson masses near the top-quark mass, with a few channels slightly below the naive quark-sum threshold.
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Triple top baryon $\Omega_{ttt}$
The triple-top baryon Ωttt is predicted to have mass 513.58 GeV, binding energy 4.13 GeV, and a dominant W+W+W+bbb decay, with production cross sections too small to observe at near-future colliders.
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Probing Yoctosecond Quantum Dynamics in Toponium Formation at Colliders
The authors claim that R_b near 343 GeV can separate instantaneous from delayed toponium formation at more than 5 sigma, but the delayed scenario is parameterized by an undetermined constant A.
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The S-wave topped meson
The first four S-wave t-bar-b and t-bar-c quasi-bound states are predicted roughly 5.1/5.4/5.6/5.7 GeV and 1.9/2.2/2.5/2.6 GeV above the top-quark mass.
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Examining possible doubly topped baryon configurations
QCD sum rules give doubly topped baryon masses of 345-350 GeV, essentially the sums of the constituent quark masses, with no sign of genuine binding.
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Mass and Decay Properties of Toponium Using SUSY QM Factorization Method
SUSY QM factorization of the Cornell potential yields toponium 1S masses 344.114 and 344.141 GeV, a 2.57 MeV gg width, and radii of 0.015–0.025 fm.
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