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REVIEW 4 major objections 6 minor 114 references

Tens of clean dilepton events from toponium decaying to W pairs could be observed at the HL-LHC.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · grok-4.5

2026-07-31 21:04 UTC pith:YPELFHLW

load-bearing objection Clean incremental pheno note: usable dilepton yields under two f_ηt brackets, but the “tens of events” headline is really an S1 story and the continuum WW background is left unquantified. the 4 major comments →

arxiv 2607.24203 v1 pith:YPELFHLW submitted 2026-07-27 hep-ph hep-ex

Prospects for observing the {η}_(t) {to} W⁺W⁻ decay at the HL-LHC

Yueling Yang , Bingbing Yang , Junfeng Sun This is my paper
classification hep-ph hep-ex
keywords toponiumeta_tHL-LHCW+W- decaydilepton signaturedecay constantpseudoscalar quarkonium
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper claims that the recently observed pseudoscalar toponium ηt can be hunted through its characteristic decay into a W+W− pair, followed by the leptonic decays of both W bosons. With more than 30 million ηt expected at the HL-LHC, two estimates of the unknown decay constant yield branching ratios that translate into roughly 7–110 observable opposite-charge electron/muon events after realistic lepton identification efficiencies. Because the final state contains no b-jets and only clean dilepton signatures, the channel avoids the reconstruction penalties and continuum top-pair backgrounds that dominate the usual WbWb modes. A confirmed excess would give a complementary, potentially cleaner window on toponium properties and help separate the bound state from ordinary top-pair production near threshold.

Core claim

Assuming more than 3×10^7 ηt at the HL-LHC and folding in realistic lepton identification efficiencies, the cascade ηt → W+W− → ℓ−ν̄ℓ ℓ′+νℓ′ (ℓ,ℓ′ = e, μ) is predicted to produce tens of experimentally observable dilepton events for either of two scenarios of the decay constant f_ηt; the absence of b-jets and the clean opposite-charge dilepton topology make this channel a complementary and potentially more sensitive probe than the dominant decays shared with non-resonant top pairs.

What carries the argument

The partial-width formula Γ(ηt → W+W−) proportional to f_ηt squared times a twist-2 wave-function integral, evaluated under two bracketing scenarios for the unknown decay constant (Royen-Weisskopf Coulomb estimate ≈10.7 GeV versus flavor-independent scaling ≈4.1 GeV), which directly sets the branching ratios and the observable event counts.

Load-bearing premise

The true toponium decay constant is assumed to lie between the two model values of roughly 4 GeV and 11 GeV; if it is substantially smaller, the predicted event yields disappear.

What would settle it

A dedicated HL-LHC analysis that either observes or firmly excludes an excess of opposite-sign dileptons with reconstructed WW mass near 343 GeV and back-to-back W kinematics after continuum WW subtraction would confirm or refute the claimed rates.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The no-b-jet dilepton channel can be added to the experimental search menu for confirming toponium.
  • An observed rate would directly constrain the still-unknown toponium decay constant f_ηt.
  • Analogous clean leptonic modes for ηt → ZZ or ZH are less promising because their branching ratios are smaller.
  • Kinematic cuts that isolate the narrow |p_W| window in the ηt rest frame can suppress continuum WW background near the top threshold.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the higher (Coulomb) yield is realized, the channel could become competitive in cleanliness with the existing tt̄-threshold excess.
  • A lattice determination of f_ηt with sufficiently fine spacing could decide which scenario is closer to reality before full HL-LHC luminosity arrives.
  • Background-rejection methods developed for this search would also improve continuum WW measurements in the same mass window.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The manuscript computes the SM branching ratio of the pseudoscalar toponium ηt → W+W− via the b/s/d-quark exchange annihilation topology (Fig. 1, Eqs. 10–18), using two ad-hoc scenarios for the unknown decay constant: S1 (Royen–Weisskopf with a pure Coulomb wave function, f_ηt ≈ 10.71 GeV, Eq. 23) and S2 (flavor-independent scaling f²/m ≈ const., f_ηt ≈ 4.07 GeV, Eq. 30). The resulting branching ratios (Br ≈ 2.9×10⁻⁴ and 4.2×10⁻⁵, Eqs. 32/35) are consistent with the earlier estimates of Refs. [19] and [26] respectively. Assuming 3×10⁷ produced ηt at the HL-LHC and realistic lepton ID efficiencies, the authors predict 49–110 observable dilepton events per channel in S1 and 7–16 in S2 (Table II), and propose the channel as a complementary, b-jet-free probe of toponium. The irreducible pp→WW continuum is acknowledged to be "comparable to, or even larger than" the signal but is not quantified.

Significance. The topic is timely: with the CMS and ATLAS observations of the ηt threshold excess, its characteristic annihilation decays are a natural next target, and the WW channel genuinely offers a b-jet-free dilepton signature. The amplitude reduction (Eqs. 10–18) is standard and correct, the phase-space and CKM factors check out, the branching-ratio estimates reproduce the authors' and independent prior results (Ref. [19] to ~20%), and Table I is a useful compilation of f_ηc/f_ηb determinations. f_ηt is an external hadronic input, so the width predictions are honest downstream statements conditional on it, not fitted to the answer. However, the paper's headline — that tens of events "could be experimentally observed" — is an observability claim, and the manuscript itself supplies the evidence that this claim is not yet supported: the continuum background is estimated only verbally, the proposed discriminating cut requires a rest-frame reconstruction that is not shown to be feasible with two neutrinos, and the event yields span a factor of ~7 between two ad-hoc scenarios whose bracketing of the true f_ηt is asserted rather than demonstrated. If the observability case were made quantitative

major comments (4)
  1. [§II, Eq. (18)] The integrand in Eq. (18), φ(x)/(1 − x x̄/z) with z = m_W²/m_ηt² ≈ 0.055, has a pole inside the physical region at x x̄ = z, i.e. x ≈ 0.06 and 0.94, corresponding to the exchanged massless b/s/d quark going on shell. The manuscript never states the iε prescription, whether a principal value is taken, or whether the resulting imaginary part (the on-shell intermediate-state cut, which is essentially the ηt → W b W b̄ sequential decay topology) is included in |A|². The quoted widths in Eqs. (31)/(34) are real numbers with no explanation of how the singularity is regulated. Since the central numerical results depend on this, the authors must state the prescription explicitly, give the real and imaginary contributions separately, and discuss whether including the cut would constitute double counting with the dominant constituent-decay channel.
  2. [§II, discussion after Table II] The paper's central claim (abstract: 'tens of dilepton events ... could be experimentally observed') is an observability statement, but the irreducible pp → W+W− background is treated only qualitatively: it 'might still reach a few fb in the ηt mass window ... comparable to, or even larger than, the signal cross section.' With σ(ηt)×Br ≈ 2.6 fb (S1) and ≈ 0.38 fb (S2), this implies S/B of order unity in S1 and ≲ 0.1 in S2 before cuts, so in the authors' own conservative scenario the 7–16 events of Table II sit under a background larger than the signal. No background cross section in the mWW window (e.g., from the ATLAS/CMS WW measurements cited as Refs. [109,110]), no S/B, and no significance estimate is given. Either a minimal quantitative background estimate with an explicit significance projection should be provided, or the abstract and §III should be reworded so that 'could be observ
  3. [§II, selection strategy (after Eq. 37)] The proposed key discriminant, |p_W| ∈ (150, 153) GeV in the ηt rest frame (Eq. 19), presupposes reconstructing that frame from a final state with two unobserved neutrinos. With two missing particles the event is underconstrained; the mWW = mηt constraint can at best yield discrete ambiguities for the neutrino momenta, and no procedure (analytic solution, MAOS/MT2-style variable, or template) is shown to work at the needed ~1% momentum resolution. As stated, the one concrete experimental handle the paper offers is not demonstrated to be implementable. A feasibility demonstration, or a clearly stated alternative selection, is needed for the search proposal to be load-bearing.
  4. [§II, Eqs. (20)–(30) and Table I] The conclusion hinges on the true f_ηt lying between the S2 (4.07 GeV) and S1 (10.71 GeV) values, but this bracketing is asserted, not argued. The paper's own Table I documents factor ~2–3 scatter among determinations of f_ηc (e.g., 231 to 618 MeV) and f_ηb across methods, and S1 relies on a pure Coulomb potential (Eq. 14) with no confining or spin-dependent terms, while the text itself notes that more complete potentials give 'large uncertainties.' Given that the rate scales as f², a factor-of-two miss in f converts the observability question from yes to no. The authors should either justify why f_ηt must fall in the stated window (e.g., via the NRQCD scaling of |ψ(0)|², which would actually favor an S1-like scaling) or present yields as a continuous function of f_ηt with the corresponding significance statement.
minor comments (6)
  1. [§II, Eqs. (20)–(23)] The numerical inputs behind Eqs. (21)–(23) are not specified: what α_s value and scale are used to obtain f_ηc = 387.83, f_ηb = 723.01, f_ηt = 10.711 MeV/GeV from f ≈ m α_s^{3/2}? Also clarify whether the O(1) coefficient from Royen–Weisskopf with a Coulomb wave function, f² = (32/9π) α_s³ m², is included or absorbed into the '≈'.
  2. [Table I] Table I lists ~60 numbers per meson with no column headers, method labels only in footnote marks, and no grouping; it is nearly unreadable in its current form. Please restructure (e.g., grouped by experiment/lattice/sum rule/model with a summary row of means and spreads).
  3. [§II, Eq. (37) and Table II] N = 3×10⁷ ηt is the produced yield at 4 ab⁻¹; Eq. (37) then applies only lepton ID efficiencies (70%/80%). Trigger efficiency, kinematic acceptance (pT, η cuts on the leptons), and dilepton trigger thresholds are not discussed; at least an estimated overall acceptance factor should be stated or the yields labeled as pre-acceptance.
  4. [Table II] Please state explicitly which Br(W→ℓν) values enter Eq. (37) (0.11 per lepton flavor is implied; e.g., 8654×0.11²×0.7² ≈ 51 vs. the quoted 49 suggests slightly different inputs).
  5. [Abstract/§III] The claim that the channel is a 'potentially more sensitive probe' (abstract, §III) is unsubstantiated given the untreatable-in-scope continuum background; 'more sensitive' than what, and under which assumptions, should be specified or the phrase removed.
  6. [References and grammar] Ref. [5] is cited as Rept. Prog. Phys. 88, 127801 (2025) for a CMS search paper; please verify the journal/volume. Several typographical issues (e.g., 'will surely eliminates', spacing artifacts) should be cleaned up.

Circularity Check

1 steps flagged

No load-bearing circularity: WW width is a genuine downstream prediction from external f_ηt scenarios; only minor non-essential self-comparison to authors' prior BR estimates.

specific steps
  1. self citation load bearing [Sec. II, after Eqs. (31)–(36)]
    "The branching ratio of the S1 (S2) scenario is comparable to the estimation of Ref. [19] (Ref. [26])."

    Refs. [19] and [26] share authors with the present paper and address the same ηt→WW branching ratio. The comparison is not used to derive Γ or f_ηt—the width is recomputed from Eqs. (10)–(18)—so it is not load-bearing; it is only a mild self-consistency check and does not force the claimed event yields.

full rationale

The central chain is: SM quark-exchange amplitude (Fig. 1, Eqs. 10–11) → twist-2 matrix element with free hadronic inputs f_ηt and φ^a_ηt (Eqs. 12, 17) → partial width Γ∝f²_ηt (Eq. 18) → Br and dilepton yields (Eq. 37, Table II). Neither S1 (Royen–Weisskopf + Coulomb wave function, Eqs. 13–23) nor S2 (empirical f²/m≈const read from external ηc/ηb lattice and experiment in Table I, Eqs. 24–30) is fitted to, or defined by, the ηt→WW rate; both are extrapolations from lighter quarkonia or a potential model. The paper does not claim a first-principles determination of f_ηt, and it explicitly flags the large S1/S2 discrepancy and the scatter in Table I. Self-citations to Refs. [19] and [26] (overlapping authors) appear only as post-hoc numerical comparisons (“comparable to”), not as premises that force the amplitude or the width formula. Event counts follow algebraically from assumed N_ηt, PDG W branching ratios, and stated lepton efficiencies. No prediction reduces to its input by construction. Score 1 only for the non-load-bearing self-comparison.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

The central event-yield claim rests on standard electroweak Feynman rules, a non-relativistic factorization of the ηt matrix element, two phenomenological ansätze for the unknown decay constant, an assumed HL-LHC ηt sample size, and constant lepton reconstruction efficiencies. No new particles or forces are introduced. The largest model dependence is the choice of f_ηt scenario.

free parameters (4)
  • f_ηt (S1 Royen-Weisskopf/Coulomb) = 10.711(36) GeV
    Set by f≈m α_s^{3/2} evaluated at the toponium scale; numerical value 10.711(36) GeV is an educated extrapolation, not a first-principles lattice number.
  • f_ηt (S2 scaling law) = 4.07(93) GeV
    Fixed by assuming f^2/m_ηQ ≈ 0.22(5) GeV^{1/2} taken from charmonium/bottomonium averages; the constant and its error bar are chosen by hand from Table I.
  • N_ηt at HL-LHC = 3e7
    Assumed >3×10^7 from σ(ηt)≈9 pb imes 4 ab^{-1}; the cross section itself carries experimental and theoretical uncertainty not propagated beyond the quoted event ranges.
  • lepton selection efficiencies ε_e, ε_μ = 0.70 / 0.80
    Taken as constant 70% (electron) and 80% (muon) from CMS/ATLAS performance papers; no pT or isolation dependence is modeled.
axioms (6)
  • domain assumption Non-relativistic factorization: ηt o W+W- amplitude is the trace of the leading-twist DA with the tree-level b/s/d-exchange weak kernel (Eqs. 10-12).
    Standard NRQCD/light-cone treatment for heavy quarkonia; higher-twist and relativistic corrections are neglected.
  • domain assumption Light-quark masses in the propagator may be set to zero and the CKM unitarity sum |Vtb|^2+|Vts|^2+|Vtd|^2=1 used.
    Justified by mb≪ mt and off-shellness of the exchanged quark; stated after Eq. 10.
  • domain assumption Only the twist-2 axial DA φ^a contributes; the distribution amplitude is the Coulomb 1S form after Fourier and transverse-momentum integration (Eq. 17).
    Follows from the Dirac structure and the pure Coulomb potential assumption of scenario S1.
  • ad hoc to paper Royen-Weisskopf formula f=√(12|ψ(0)|^2/m) together with Coulomb wave-function yields f≈m α_s^{3/2} (Eqs. 13, 20).
    Used to obtain the large S1 value; the paper notes that full potentials including confinement produce large scatter for lighter quarkonia.
  • ad hoc to paper Flavor-independent scaling f^2/m_ηQ ≈ const. extends from c,b to t (Eq. 24).
    Empirical rule calibrated on Table I; no derivation from QCD is given.
  • domain assumption Γ_ηt ≈ 2 Γ_t ≈ 2.8 GeV and m_ηt ≈ 343 GeV as measured by CMS/ATLAS.
    External experimental inputs used for branching ratios and phase space.

pith-pipeline@v1.2.0-grok45-kimik3 · 20477 in / 4273 out tokens · 75808 ms · 2026-07-31T21:04:17.924327+00:00 · methodology

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read the original abstract

Motivated by the recent observation of the pseudoscalar toponium ${\eta}_{t}$ at the LHC and by the ongoing interest in its properties, we phenomenologically investigate the ${\eta}_{t}$ ${\to}$ $W^{+}W^{-}$ process, one of the characteristic decays of toponium ${\eta}_{t}$. The branching ratio for the ${\eta}_{t}$ ${\to}$ $W^{+}W^{-}$ decay is estimated with two scenarios of the decay constant $f_{{\eta}_{t}}$. It is found that tens of dilepton events from the cascade decays, ${\eta}_{t}$ ${\to}$ $W^{+}W^{-}$ ${\to}$ ${\ell}^{-}\bar{\nu}_{\ell}{\ell}^{{\prime}+}{\nu}_{{\ell}^{\prime}}$ with ${\ell}$, ${\ell}^{\prime}$ $=$ $e$ and ${\mu}$, could be experimentally observed, when considering the realistic identification efficiency of the charged lepton and assuming more than $3{\times}10^{7}$ ${\eta}_{t}$ events available at the future HL-LHC. We propose searching for ${\eta}_{t}$ via the ${\eta}_{t}$ ${\to}$ $W^{+}W^{-}$ ${\to}$ ${\ell}^{-}\bar{\nu}_{\ell}{\ell}^{{\prime}+}{\nu}_{{\ell}^{\prime}}$ channel, which features no $b$-jets and clean dilepton signatures, thus offering a complementary and potentially more sensitive probe.

Figures

Figures reproduced from arXiv: 2607.24203 by Bingbing Yang, Junfeng Sun, Yueling Yang.

Figure 1
Figure 1. Figure 1: FIG. 1: The lowest order Feynman diagram for the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

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Reference graph

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