⚛️ phenomenology

Prospects for observing the ${\eta}_{t}$ ${\to}$ $W^{+}W^{-}$ decay at the HL-LHC

Motivated by the recent observation of toponium ( $\eta_t$ ), this paper phenomenologically investigates the $\eta_t \to W^+W^-$ decay channel at the High-Luminosity LHC, predicting that tens of clean dilepton events could be observed and proposing this $b$ -jet-free signature as a sensitive probe for future studies.

Original authors: Yueling Yang, Bingbing Yang, Junfeng Sun

Published 2026-07-28

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Yueling Yang, Bingbing Yang, Junfeng Sun

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, chaotic construction site where tiny particles are the bricks. In this site, there is a super-heavy brick called the "top quark." For a long time, scientists thought this brick was so unstable and heavy that it would fall apart before it could ever stick to another brick to form a structure. It was like trying to build a house out of wet sand that evaporates the moment you touch it. However, recent experiments at the world's biggest particle collider, the Large Hadron Collider (LHC), have spotted something amazing: two of these top quarks have managed to stick together briefly to form a tiny, fleeting molecule called "toponium." It's a ghostly, short-lived structure that appears and vanishes in a flash. Now, scientists are curious: what does this ghostly molecule do right before it disappears? Does it break apart in a messy explosion, or does it take a cleaner, more elegant path? Understanding this helps us test the rules of the universe and see if our current theories about how particles behave are correct.

This paper is a detective story about one specific way this toponium molecule might vanish. The authors, a team of physicists, are investigating a process where the toponium decays into two "W bosons" (which are like heavy, force-carrying messengers), and those messengers then turn into pairs of charged particles called leptons (like electrons or muons) and invisible neutrinos. Think of the toponium as a fragile, glowing balloon. Usually, when it pops, it sprays a messy cloud of debris (quarks and other particles) that is hard to sort through in the chaotic noise of the collider. But the authors are looking for a specific, cleaner pop: one where the balloon splits into two distinct, identifiable sparks (the leptons) and two invisible ghosts (the neutrinos).

The researchers calculated how often this specific "clean pop" happens. They used two different mathematical "recipes" to guess a key property of the toponium molecule, which they call the "decay constant." This is like trying to guess how tightly the two top quarks are holding hands before they let go.

Recipe 1 (S1): Based on a classic formula, this recipe suggests the toponium is quite "tight," leading to a prediction that about 29 out of every 100,000 toponium molecules will take this clean path.
Recipe 2 (S2): Based on a different scaling rule, this recipe suggests the toponium is "looser," predicting only about 4 out of every 100,000 will take this path.

Because the top quark is so heavy, the toponium is expected to be produced in huge numbers at the future High-Luminosity LHC (HL-LHC)—potentially over 30 million of them. The authors ran simulations to see if we could actually spot these clean pops in the real world. They found that even with the messy background of the collider, if we have enough toponium events, we might be able to see anywhere from a few to over a hundred "dilepton" events (where two charged particles are detected) depending on which recipe is correct.

The paper argues that this specific decay channel is a great place to look because it avoids a major headache: "b-jets." In most toponium decays, the molecule breaks into heavy bottom quarks, which create messy sprays of particles called jets that are hard to identify. The decay into two W bosons, however, produces two fewer bottom quarks than the dominant decay mode. It's like looking for a specific type of bird in a forest; usually, you have to search through a dense thicket of confusing bushes (the b-jets), but this specific decay happens in a slightly clearer area where the signal stands out much more clearly.

However, the authors are careful not to claim this is a guaranteed discovery. They emphasize that while the signal is cleaner, there is still a lot of background noise from other processes that produce similar pairs of particles. They suggest that to actually see this, scientists will need to use very clever tricks to filter out the noise, such as checking the exact speed and direction of the particles to ensure they came from a toponium and not just random collisions. The paper concludes that while it is a very challenging task, it is feasible to hunt for this decay at the future HL-LHC. It offers a promising, complementary way to study toponium that doesn't rely on the messy bottom-quark signals, potentially giving us a clearer picture of this mysterious particle if the experiments can overcome the background noise.

Technical Summary: Prospects for observing the $\eta_t \to W^+W^-$ decay at the HL-LHC

Problem Statement
The top quark, the heaviest fundamental fermion in the Standard Model (SM), was long believed to decay too rapidly to form bound states. However, recent observations by the CMS and ATLAS collaborations of a color-singlet $S$ -wave $t\bar{t}$ bound state, identified as the pseudoscalar toponium $\eta_t$ (mass $m_{\eta_t} \approx 343$ GeV), have renewed interest in its properties. A primary challenge in characterizing $\eta_t$ is distinguishing it from the overwhelming non-resonant $t\bar{t}$ background. Both the resonant $\eta_t$ and non-resonant $t\bar{t}$ pairs predominantly decay via the weak interaction of their constituent top quarks into $W^+b W^-\bar{b}$ , resulting in complex final states with $b$ -jets that are difficult to reconstruct and prone to identification errors. The authors investigate the characteristic decay channel $\eta_t \to W^+W^-$ , which lacks $b$ -jets and offers a cleaner signature, to determine its observability at the High-Luminosity LHC (HL-LHC).

Methodology
The study performs a phenomenological investigation of the $\eta_t \to W^+W^-$ decay within the SM framework.

Theoretical Calculation: The decay proceeds via quark-exchange interaction (specifically $b$ -, $s$ -, and $d$ -quark exchange) rather than direct annihilation, which is forbidden by angular momentum and quantum number conservation. The amplitude is calculated using the matrix element of the bilinear quark operator associated with the pseudoscalar $\eta_t$ .
Decay Constant Scenarios: The calculation relies on the decay constant $f_{\eta_t}$ $f_{η_{t}}$ , an undetermined hadronic parameter. The authors evaluate two distinct scenarios to estimate $f_{\eta_t}$ $f_{η_{t}}$ :
- Scenario S1 (Royen-Weisskopf): Based on the non-relativistic wave function at the origin, assuming a Coulomb-like interquark potential. This yields $f_{\eta_t} \approx 10.711(36)$ GeV.
- Scenario S2 (Phenomenological Scaling): Based on an empirical scaling law ( $f^2_{\eta_Q}/m_{\eta_Q} \approx \text{const}$ ) derived from experimental and lattice data for charmonium ( $\eta_c$ ) and bottomonium ( $\eta_b$ ). This yields a more conservative estimate of $f_{\eta_t} \approx 4.07(93)$ GeV.
Event Yield Estimation: Using the calculated partial decay widths and branching ratios, the authors estimate the number of observable events at the HL-LHC, assuming an integrated luminosity of $4 \text{ ab}^{-1}$ and a total production of $>3 \times 10^7$ $\eta_t$ events. The analysis focuses on the cascade decay $\eta_t \to W^+W^- \to \ell^-\bar{\nu}_\ell \ell'^+\nu_{\ell'}$ (where $\ell, \ell' = e, \mu$ ), applying realistic charged lepton identification efficiencies (approx. 70% for electrons and 80% for muons).

Key Contributions and Results

Branching Ratios: The study provides updated estimates for the branching ratio $Br(\eta_t \to W^+W^-)$ . Under the S1 scenario, $Br \approx 28.8(2.4) \times 10^{-5}$ ; under the S2 scenario, $Br \approx 4.2(2.5) \times 10^{-5}$ . These results align with previous estimates from Ref. [19] and Ref. [26] respectively, but highlight significant theoretical uncertainty due to the unknown nature of the $\eta_t$ decay constant.
Observable Event Counts: The authors predict the number of observable dilepton events ( $e^+e^-$ $e^{+} e^{-}$ , $e^\pm\mu^\mp$ $e^{\pm} μ^{\mp}$ , $\mu^+\mu^-$ $μ^{+} μ^{-}$ ) after applying selection efficiencies:
- S1 Scenario: Yields approximately 49 ( $e^+e^-$ ), 110 ( $e^\pm\mu^\mp$ ), and 63 ( $\mu^+\mu^-$ ) events.
- S2 Scenario: Yields approximately 7 ( $e^+e^-$ ), 16 ( $e^\pm\mu^\mp$ ), and 9 ( $\mu^+\mu^-$ ) events.
Background Considerations: The paper acknowledges that the irreducible background from non-resonant $pp \to W^+W^-$ production is a major challenge. While kinematic cuts on the $W^+W^-$ invariant mass and the momentum of the $W$ bosons in the $\eta_t$ rest frame can suppress threshold and continuum backgrounds, residual background remains. The authors note that developing more efficient suppression methods is crucial but lies beyond the scope of the current study.

Significance and Claims
The paper claims that searching for $\eta_t$ via the $\eta_t \to W^+W^- \to \ell^-\bar{\nu}_\ell \ell'^+\nu_{\ell'}$ channel offers a complementary and potentially more sensitive probe compared to the dominant $W^+b W^-\bar{b}$ mode. The absence of $b$ -jets eliminates errors associated with $b$ -jet identification and improves signal reconstruction efficiency. The clean dilepton signatures, characterized by well-defined energies and momenta, allow for better discrimination against hadronic backgrounds.

The authors conclude that while the observation of this decay is "very challenging" due to the small branching ratios and significant backgrounds, it is "feasible" at the future HL-LHC given the anticipated high statistics ( $>3 \times 10^7$ events). The study aims to provide a useful reference for experimental searches, emphasizing that the large discrepancy between the S1 and S2 scenarios underscores the need for a more comprehensive understanding of toponium properties and the decay constant $f_{\eta_t}$ .

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