Searching for the toponium $η_{t}$ with the $η_{t}$ ${ o}$ $W^{+}W^{-}$ decay

Inspired by the observation of the $η_{t}$ meson at the LHC and the promising prospect of the $η_{t}$ meson available at the approaching HL-LHC, branching ratios for the $η_{t}$ ${\to}$ $f\bar{f}$, $gg$, $γγ$, $W^{+}W^{-}$, $Z^{0}Z^{0}$, $Z^{0}γ$ and $Z^{0}H$ decays are roughly estimated. It is found that tens of opposite-charge dilepton events from the $η_{t}$ ${\to}$ $W^{+}W^{-}$ decay and hundreds of events from the $η_{t}$ ${\to}$ $Z^{0}H$ ${\to}$ ${\ell}^{+}{\ell}^{-}H$ decay using the single $Z^{0}$ boson tagging method are expected to be accessible. This estimation provides a reference for future experimental study on the $η_{t}$ meson.

💡 Research Summary

The paper addresses the recent observation of an excess of events near the t t̄ production threshold at the LHC, which both CMS and ATLAS have reported with significances exceeding 5 σ. The authors interpret this excess as the manifestation of a color‑singlet CP‑odd pseudoscalar toponium state, denoted ηₜ (the ground‑state 1 ¹S₀ quarkonium composed of t t̄). They note that ηₜ is expected to have a mass m_{ηₜ}≈2 m_t≈343 GeV and a total decay width Γ_{ηₜ}≈3 GeV, roughly twice the width of a single top quark. Because the top quark decays before it can hadronize, the dominant decay mode of ηₜ is the “intrinsic” decay of its constituents: ηₜ → W⁺b W⁻\bar b, i.e. the same final state as non‑resonant t t̄ production.

Beyond this dominant channel, the authors systematically compute the leading‑order partial widths for a variety of two‑body final states: gluon‑gluon, photon‑photon, fermion‑antifermion, W⁺W⁻, Z Z, Z γ, and Z H. The formulas (Eqs. 2‑8) are standard tree‑level expressions involving the strong coupling α_s, the electromagnetic coupling α_em, the electroweak mixing angle, and the radial wave function at the origin, |R_S(0)|². The wave function is obtained from a Coulomb‑like potential V(r)=−C_Fα_s/r, yielding |R_S(0)|²∝(C_Fα_s μ_Q)³ with μ_Q=m_t/2. Input parameters are taken from the 2022 PDG (m_t=172.57 GeV, α_s(m_Z)=0.118, etc.).

Using these inputs, the authors present Table II, which lists the estimated partial widths, branching ratios, and expected event counts for an integrated luminosity of 3 ab⁻¹ at the HL‑LHC (σ(ηₜ)≈7 pb, corresponding to ≈2×10⁷ ηₜ mesons). The dominant decay is ηₜ → gg (BR≈6.3×10⁻⁴), followed by ηₜ → W⁺W⁻ (BR≈3.25×10⁻⁵) and ηₜ → Z H (BR≈1.79×10⁻⁴). The γγ channel, though much smaller (BR≈3.1×10⁻⁶), benefits from excellent photon identification, while fermionic decays are negligible due to the m_f² scaling.

The phenomenological focus is on two experimentally accessible signatures:

1. ηₜ → W⁺W⁻ → ℓ⁺ℓ⁻ + νν̄ (ℓ=e, μ). The dilepton branching fraction of the W pair is ≈5 %, yielding of order tens of clean opposite‑sign lepton events after realistic selection and efficiency factors. The authors argue that the back‑to‑back kinematics of the W bosons in the ηₜ rest frame, together with the absence of b‑jets (since the top decay products are “hidden” inside the bound state), could help discriminate signal from the overwhelming t t̄ background.

2. ηₜ → Z H → ℓ⁺ℓ⁻ H (ℓ=e, μ). By tagging a single Z boson through its leptonic decay (BR≈3.4 % per lepton flavor) and exploiting the Higgs decay to μ⁺μ⁻ (BR≈2.6×10⁻⁴) or other clean channels, the authors estimate >200 observable events. They suggest a “single‑Z tagging” strategy to suppress backgrounds.

The paper acknowledges several sources of uncertainty: higher‑order QCD corrections (potentially ~10 % for gg and γγ), the choice of α_s at the relevant scale, the modeling of the wave function, threshold effects, and the unknown exact mass and width of ηₜ. Moreover, the large natural width of ηₜ smears the resonance, making it difficult to separate from the continuum t t̄ production.

In conclusion, while the dominant gg decay will be buried under QCD background, the electroweak channels ηₜ → W⁺W⁻ and ηₜ → Z H offer realistic discovery prospects at the HL‑LHC, provided that high‑precision lepton identification, efficient trigger strategies, and sophisticated background suppression techniques are employed. The study serves as a quantitative benchmark for future experimental searches for toponium.