Possible mixing between elementary and bound state fields in the $t\bar{t}$ production excess at the LHC

Yoshiki Matsuoka

arxiv: 2510.16828 · v6 · submitted 2025-10-19 · ✦ hep-ph · hep-ex

Possible mixing between elementary and bound state fields in the tbar{t} production excess at the LHC

Yoshiki Matsuoka This is my paper

Pith reviewed 2026-05-18 06:15 UTC · model grok-4.3

classification ✦ hep-ph hep-ex

keywords toponiumttbar excessmixing angleCMS data2HDMinert Higgsmulticritical point principleLHC phenomenology

0 comments

The pith

Mixing between toponium and an extra scalar explains the CMS ttbar excess only for mixing angles below 13 degrees in minimal models or 1 degree in 2HDM.

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

The paper examines whether a mixture of toponium, the bound state of top and antitop quarks, and an additional elementary scalar field can account for the reported excess in top-pair production observed by CMS at the LHC. It considers a minimal scenario where the extra field resembles an inert Higgs doublet and a second scenario where the field is incorporated into two-Higgs-doublet models of Type II and Y. Couplings are fixed using the multicritical point principle to avoid extra free parameters, leading to upper bounds on the mixing angle of 13 degrees in the minimal case and 1 degree in the 2HDM cases. A sympathetic reader would care because this links composite bound states with fundamental fields in a way that interprets the excess with restricted parameters rather than ad hoc tuning.

Core claim

The mass eigenstate that contributes to the excess is defined as Ψ' = Ψ cos θ + η_t sin θ, where Ψ is the elementary field and η_t is the toponium. After imposing the multicritical point principle on the couplings, consistency with the CMS ttbar excess data restricts the mixing angle to |θ| ≤ 13° in the minimal inert-Higgs-like scenario and |θ| ≤ 1° in the 2HDM Type II and Y scenarios.

What carries the argument

The mixing angle θ that defines the physical state Ψ' from the elementary field Ψ and toponium η_t, allowing the model to reproduce the excess while satisfying multicritical point principle constraints on the relevant couplings.

If this is right

In the minimal scenario, mixing angles larger than 13 degrees are inconsistent with the CMS data.
In 2HDM Type II and Y, the mixing angle must be smaller than 1 degree to remain consistent.
The multicritical point principle removes the need for extra parameter tuning to fit the observed excess.
Different mixing limits apply when the same framework is compared to 2HDM Type I and X.

Where Pith is reading between the lines

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

Precision measurements of angular distributions in ttbar events could further narrow the allowed range of θ.
Similar mixing between bound states and elementary fields might appear in other heavy-quark production channels at higher energies.
If the excess persists in future data, the mixed state could influence rare top decays or associated Higgs production rates.
The approach suggests testable predictions for the width or lineshape of the excess feature in the invariant mass spectrum.

Load-bearing premise

The multicritical point principle fixes the coupling constants in these models without introducing additional free parameters that would need tuning to match the excess.

What would settle it

A new LHC measurement of the ttbar invariant-mass distribution or total cross section that shows either no excess or an excess magnitude incompatible with the predicted contribution from the mixed state at the allowed mixing angles.

Figures

Figures reproduced from arXiv: 2510.16828 by Yoshiki Matsuoka.

**Figure 1.** Figure 1: The x-axis and y-axis show log10( µ GeV ) and the value of each line. The blue line and orange line are Veff µ4 and 1 µ3 dVeff dµ in the case of Mt = 172.69 GeV, αs(MZ) = 0.1189, Λ = 400 GeV, yΨ(Mt) = 0.3, and κ1(Mt) = 0.29. The red line shows zero on the y-axis. It can be seen that the MPP condition is satisfied around µc = 1012.3 GeV. And the mixing angle θ between ηt and Ψ (both being pseudo-scalar comp… view at source ↗

**Figure 2.** Figure 2: The production and decay process involving the mixed mass [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

read the original abstract

Recent report by CMS Collaboration on the excess of top and anti-top pair production is studied, under the hypothesis of the coexistence of a toponium $(\eta_t)$ and an additional elementary field $(\Psi)$. We examine the scenario where toponium and an additional field are mixed, and consider the plausible scenarios in that case. Two scenarios are examined: one is the minimal model with $\Psi$ close to the inert Higgs doublet, and the other is embedded into the two Higgs doublet models (2HDM), where $\Psi$ is one of the two Higgs scalars after transforming the basis. The value of the each coupling constant is restricted by the Multicritical Point Principle (MPP). Consistency with the data gives constraints on a mixing angle $\theta\ (-45^\circ\le\theta\le45^\circ)$, with which the mass eigenstate $\Psi^\prime$ contributing to the excess is defined by $\Psi^\prime=\Psi\cos \theta + \eta_t\sin \theta$. The obtained results are $|\theta| \le 13^{\circ}$ for the minimum scenario, and $|\theta| \le 1^{\circ}$ for the second scenario of 2HDM(Type II and Y). We also briefly discuss the comparison with Type I and X.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper fits a mixing angle to the CMS ttbar excess after fixing couplings via the Multicritical Point Principle, but the reported bounds on θ may loosen if MPP conditions pick up dependence on the mixture.

read the letter

The main thing to know is that this work takes the recent CMS excess in top-pair production and attributes it to a mixed state between toponium and an elementary scalar, with the Multicritical Point Principle used to set the underlying couplings. It then extracts concrete limits: |θ| ≤ 13° in the minimal inert-Higgs-like case and |θ| ≤ 1° in 2HDM types II and Y, with a quick note on types I and X. That quantitative step tied to the 2024-2025 data is what is new here; earlier mixing ideas existed but did not carry these specific numbers under MPP. The paper does a clean job laying out the two scenarios and defining the physical state as the linear combination Ψ′ = Ψ cos θ + η_t sin θ. It stays focused on how the excess constrains θ once the couplings are fixed. The soft spot is the one the stress-test flags. Because the physical field is the mixture, the operators and beta functions that enter the multicriticality conditions at high scale receive contributions from the composite component. Nothing in the abstract shows that the authors checked whether those conditions stay independent of θ. If they shift, the fixed-point values used to compute the excess can move, which would relax or erase the quoted bounds. The approach therefore risks being a post-hoc adjustment rather than a prediction. The abstract also gives no error bars, no explicit cross-section formula, and no discussion of competing backgrounds, so the fit strength is hard to judge. This is a narrow phenomenological exercise aimed at readers who track top-sector anomalies and scalar extensions. Someone already working on toponium or 2HDM explanations for LHC excesses could find the numbers useful as a benchmark to test against. The central argument is coherent on its own terms and shows honest engagement with the literature, even if the MPP assumption is strong. I would send it to peer review so referees can verify the cross-section modification and the MPP implementation in the mixed basis.

Referee Report

1 major / 2 minor

Summary. The paper examines the CMS-reported excess in ttbar production at the LHC under the hypothesis of mixing between a toponium bound state (η_t) and an elementary scalar field (Ψ). Two scenarios are analyzed: a minimal inert-Higgs-like model and embeddings in 2HDM (Types II and Y). Couplings are fixed via the Multicritical Point Principle (MPP), and consistency with data constrains the mixing angle θ in the mass eigenstate Ψ′ = Ψ cosθ + η_t sinθ, yielding |θ| ≤ 13° for the minimal case and |θ| ≤ 1° for 2HDM II/Y (with brief comparison to Types I/X).

Significance. If the central claim holds after addressing the issues below, the work provides a concrete mechanism linking bound-state and elementary-field mixing to the ttbar excess while using MPP to restrict parameters, offering a falsifiable prediction for the allowed range of θ. This could motivate dedicated searches for mixed states in future LHC runs and further exploration of multicriticality conditions in models with composite scalars. The approach is novel in combining toponium with BSM scalars under a high-scale principle.

major comments (1)

[Model-building sections (minimal inert-Higgs-like and 2HDM scenarios)] The derivation of the θ bounds relies on MPP fixing the underlying couplings to specific values with no remaining free parameters before computing the modified ttbar cross section from the mixed state Ψ′. However, because Ψ′ = Ψ cosθ + η_t sinθ, the effective operators, beta functions, and vacuum degeneracy conditions entering the MPP (as invoked in the model-building sections for both scenarios) receive contributions from the composite η_t component. These contributions are not shown to be θ-independent; if they shift the fixed-point values, the coupling inputs used for the excess calculation can be readjusted, loosening the reported limits. An explicit check or re-derivation of the MPP conditions including the mixing is required for the bounds to be robust.

minor comments (2)

[Abstract] The abstract states the θ bounds but provides no error bars, no explicit formula for the production cross-section modification, and no discussion of alternative backgrounds or systematic uncertainties in the CMS excess; these should be added for clarity.
[Introduction or model setup] Notation for the mixed state Ψ′ and the definition of the mixing angle range (-45° ≤ θ ≤ 45°) should be introduced earlier with a clear equation to avoid ambiguity when reading the results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive major comment. We address the point below and are prepared to revise the manuscript accordingly to strengthen the robustness of our results.

read point-by-point responses

Referee: [Model-building sections (minimal inert-Higgs-like and 2HDM scenarios)] The derivation of the θ bounds relies on MPP fixing the underlying couplings to specific values with no remaining free parameters before computing the modified ttbar cross section from the mixed state Ψ′. However, because Ψ′ = Ψ cosθ + η_t sinθ, the effective operators, beta functions, and vacuum degeneracy conditions entering the MPP (as invoked in the model-building sections for both scenarios) receive contributions from the composite η_t component. These contributions are not shown to be θ-independent; if they shift the fixed-point values, the coupling inputs used for the excess calculation can be readjusted, loosening the reported limits. An explicit check or re-derivation of the MPP conditions including the mixing is required for the bounds to be robust.

Authors: We agree that this is a valid and important point that requires clarification. In the original analysis the MPP conditions were imposed on the elementary scalar sector (Ψ and associated fields) at the high scale, with the mixing to the composite toponium state η_t introduced subsequently to compute the effective ttbar production. Because the composite component is not elementary, its direct contribution to the ultraviolet beta functions and vacuum degeneracy conditions is not automatically included in the standard MPP implementation. For the small mixing angles ultimately allowed by the data (|θ| ≤ 13° in the minimal model and |θ| ≤ 1° in the 2HDM cases), we expect the back-reaction on the fixed-point values to remain perturbatively small. Nevertheless, to make the bounds fully robust we will revise the model-building sections to include an explicit estimate of the shift in the MPP-fixed couplings induced by the mixed state Ψ′. This will be done by treating the composite admixture as a small perturbation in the effective operators and re-evaluating the vacuum degeneracy conditions at leading order in sin θ. The revised manuscript will either confirm that the original θ limits are essentially unchanged or, if a modest readjustment is needed, present the updated bounds. revision: yes

Circularity Check

0 steps flagged

No significant circularity; MPP fixes couplings independently before data constrains mixing angle

full rationale

The paper applies the Multicritical Point Principle to restrict the underlying coupling constants in both the minimal inert-Higgs-like scenario and the 2HDM embeddings, then uses consistency with the CMS ttbar excess to derive upper bounds on the mixing angle θ that defines the physical mass eigenstate Ψ′. This sequence does not reduce any central result to its own inputs by construction: the MPP conditions are imposed on the model parameters prior to introducing the mixing, and the θ bounds are obtained as consistency constraints rather than as a renamed fit or self-referential prediction. No load-bearing step relies on a self-citation chain that itself assumes the target result, nor does the derivation smuggle an ansatz or rename a known empirical pattern. The derivation chain remains self-contained against the stated assumptions and external data.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim depends on the Multicritical Point Principle to eliminate free parameters in the couplings, on the existence of a toponium bound state near the 2mt threshold, and on the assumption that the observed excess is entirely due to the mixed state rather than standard-model or other new-physics contributions.

free parameters (1)

mixing angle θ
Adjusted within the stated range to reproduce the CMS excess after MPP has fixed the other couplings.

axioms (2)

domain assumption Multicritical Point Principle fixes the relevant Yukawa and quartic couplings without additional tuning
Invoked to restrict the parameter space in both the minimal and 2HDM scenarios.
ad hoc to paper The CMS-reported excess is attributable to the mixed Ψ′ state rather than unaccounted backgrounds or SM higher-order effects
Required for the consistency constraints on θ to be meaningful.

invented entities (1)

Elementary field Ψ (inert-Higgs-like or 2HDM scalar) no independent evidence
purpose: Mixes with toponium to enhance ttbar production
Postulated new scalar whose mixing with η_t produces the observed excess; no independent collider signature outside this fit is provided.

pith-pipeline@v0.9.0 · 5755 in / 1602 out tokens · 27867 ms · 2026-05-18T06:15:43.466541+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Consistency with the data gives constraints on a mixing angle θ (−45°≤θ≤45°)... |θ|≤13° for the minimum scenario, and |θ|≤1° for the second scenario of 2HDM(Type II and Y).
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We adopt the Bardeen-Hill-Lindner (BHL) framework... impose the compositeness condition Z2(μ=Λ)=0... MPP conditions at the MPP scale near μ≃μc

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Forward citations

Cited by 2 Pith papers

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Phenomenology of Hypothetical Single-Top Hadronic States
hep-ph 2026-05 unverdicted novelty 5.0

QCD sum rule calculations produce ground-state masses for single-top baryons like Lambda_t and mesons like T_t b-bar, with several central values slightly below constituent quark mass sums suggesting possible weak bin...
Masses of Purely Top-Quark Bound States: Toponium and the Triply-Top Baryon
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QCD sum-rule calculations give negative binding energies for toponium states consistent with near-threshold experimental signals and a central mass for the triply-top baryon slightly above three times the top-quark mass.

Reference graph

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