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REVIEW 4 major objections 4 minor 46 references

Unveiling E$_6$SSM Scalar Diquarks at the HL-LHC

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims that a sub-TeV scalar diquark of the E6SSM can be discovered at the HL-LHC in the ttbb final state, with statistical significance exceeding 3 sigma for masses up to 1 TeV.

desk verdict Useful MC search projection, but the 'up to 1 TeV' claim is contradicted by the paper's own Table 5; the defensible reach is ~900 GeV. read the letter →

arxiv 2412.19445 v2 pith:YSWFYRLB submitted 2024-12-27 hep-ph

Murad Ali , Shaaban Khalil , Stefano Moretti , Shoaib Munir , Harri Waltari This is my paper · ORCID
classification hep-ph
keywords scalardiquarkE6SSMpairproductiontop-bottomdecayHL-LHCsearchfatjetsb-jettaggingbeyondStandardModel
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the lightest scalar diquark predicted by the E6SSM could be discovered at the High-Luminosity LHC. The relevant particle, of a type called S4, would be produced in pairs by QCD and would decay almost exclusively to top-bottom pairs, leaving a final state of two top quarks and two bottom quarks. The authors simulate this signal against Standard Model backgrounds and find that with 3000 inverse femtobarns the statistical significance exceeds 3 sigma for diquark masses up to about 1 TeV. They also show that present LHC data already exclude masses below roughly 600 GeV for their benchmark parameters. A reader should care because this gives the LHC a concrete, testable signature for a motivated beyond-Standard-Model particle.

What carries the argument

The central object is the S4 diquark, a color anti-triplet scalar with hypercharge $+1/3$ that couples two same-chirality quarks. In the E6SSM its couplings are naturally small and dominated by the third generation, so with the chosen parameters the branching ratio $D \to tb$ is effectively one. The mechanism carrying the argument is QCD pair production followed by the reconstruction of two top quarks and two bottom quarks: one analysis resolves individual jets, and a second, for higher masses, reconstructs each top as a single anti-$k_t$ fat jet with radius 0.8 and pairs the fat jets with the two leading $b$-jets. The statistical significance $N_S/\sqrt{N_B}$ after these cuts is what grows with integrated luminosity to cross the $3\sigma$ threshold.

What would settle it

Reconstruct the same $t\bar{t}b\bar{b}$ final state at the HL-LHC with 3000 fb$^{-1}$ and look at the diquark mass window near 900 GeV; if the event count matches the Standard Model background within statistical fluctuations, the paper's claimed $>3\sigma$ significance for a 900 GeV diquark is ruled out for that scenario.

Watch

Extended reading notes

Core claim

The central claim is that pair production of the lightest S4-type scalar diquark $D$, with mass below 1 TeV and branching fraction close to one into $tb$, is discoverable at the HL-LHC through the process $p p \to D \bar{D} \to (\bar{t} \bar{b})(t b)$. With one top decaying leptonically and the other hadronically, the signature is four $b$-jets, two light jets, one lepton and missing transverse momentum. Using a boosted analysis in which each top is reconstructed as a fat jet, the paper finds statistical significance above $3\sigma$ for a 900 GeV diquark and larger significance for 700-800 GeV at 3000 fb$^{-1}$, while the resolved-jet analysis reaches $5\sigma$ only for masses up to 600 GeV. The result depends on choosing E6SSM parameters for which the diquark has $O(10^{-3})$ couplings to third-generation quarks and negligible couplings to lighter generations.

Load-bearing premise

The result assumes the diquark decays essentially 100% of the time to a top and a bottom quark, which requires its couplings to third-generation quarks to be about $10^{-3}$ and its couplings to first- and second-generation quarks to vanish exactly; if those conditions fail, the branching fraction and the computed significance drop.

Editorial extensions

If this is right

  • At 3000 fb$^{-1}$, the HL-LHC would see a $>3\sigma$ excess for diquark masses up to about 1 TeV in the $t\bar{t}b\bar{b}$ channel.
  • Masses below about 600 GeV are already excluded by existing $tb$ resonance searches for the benchmark scenario.
  • The boosted fat-jet reconstruction is necessary for diquarks heavier than roughly 700 GeV, where resolved jets fail.
  • If the signal is absent at the HL-LHC, the E6SSM diquark interpretation with $\mathrm{BR}(D \to tb) \simeq 1$ is constrained up to 1 TeV.
  • The same event selection provides a mass reconstruction of the diquark pair, though with wide distributions that would make a precise mass measurement difficult.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If such a diquark is observed, its production rate could be used to extract the diquark Yukawa couplings to the third generation, assuming the mass is measured from the reconstructed peak.
  • The same $t\bar{t}b\bar{b}$ search strategy could be applied to color-triplet scalar diquarks in other models, such as Pati-Salam or R-parity-violating supersymmetry, where the decay to $tb$ may also dominate.
  • The quoted significance is statistical only; including systematic uncertainties in tagging and jet energy scales would lower it, so the actual discovery reach in mass is likely somewhat below 1 TeV.
  • A natural follow-up would be to search for single-diquark production through $tb$ fusion, which becomes visible if first- or second-generation couplings are not exactly zero and would complement the pair-production channel.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper studies the phenomenology of the lightest S4-type scalar diquark D predicted by the E6SSM, focusing on pair production at the LHC with D decaying to tb pairs. The authors generate signal and background events with MadGraph/Pythia/Delphes, apply a resolved analysis and a fat-jet analysis, and derive signal significances at 140, 300, and 3000 fb^-1. They also reinterpret ATLAS and CMS charged-Higgs searches to set an exclusion limit on mD. The central claim in the abstract and conclusions is that the HL-LHC can reach a statistical significance exceeding 3 sigma for diquark masses up to 1 TeV.

Significance. If the result holds, this would be a useful, detector-level study of a previously under-explored channel: pair production of E6SSM scalar diquarks in the t tbar b bbar final state with one lepton. The paper uses standard modern tools, provides cut-flow tables and mass distributions, and explicitly compares with existing LHC searches, which are all positive features. The analysis is a forward Monte Carlo simulation with free input masses and couplings, so there is no circularity. The main significance is in establishing that a 900 GeV diquark with BR(D->tb)~1 could be observable at the HL-LHC with statistical significance around 3 sigma, and in identifying the boosted fat-jet selection as the relevant strategy for the upper end of the mass range.

major comments (4)
  1. [Abstract and Sec. 5 (also Table 5 and Fig. 5)] The headline claim that the HL-LHC reach exceeds 3 sigma for masses 'up to 1 TeV' is contradicted by the paper's own cut-flow. In Table 5, for mD = 1000 GeV the final selection at 140 fb^-1 leaves 5 signal events against 117 background events (ttbb 5 + ttjj 112). Statistical significance, NS/sqrt(NB), is therefore 5/sqrt(117) = 0.46 sigma at 140 fb^-1; scaling by sqrt(3000/140) = 4.63 gives about 2.1 sigma at 3000 fb^-1, not above 3 sigma. The same table gives 7 signal events for mD = 900 GeV, corresponding to 7/sqrt(117) = 0.65 sigma at 140 fb^-1 and about 3.0 sigma at 3000 fb^-1 before K-factors. The abstract and Section 5 should be corrected to state that the 3-sigma reach applies at most to about 900 GeV, not 1 TeV, for the statistical-only significance defined in the paper.
  2. [Sec. 4.2 and Fig. 5] The K-factors used for the fat-jet significances are not specified. The only description appears in Sec. 4.1, where K-factors from Refs. [26] and [46] are mentioned, but no values are given and it is not stated whether the same K-factors are applied to the signal and to each background in the fat-jet analysis. This matters because the 900 GeV point is borderline: without K-factors it gives about 3.0 sigma at 3000 fb^-1, and the claim of 'above 3 sigma' depends on the size and treatment of the K-factors. Please tabulate the K-factors used, justify their application to this final state, and show the significance with and without them. In addition, the significance definition NS/sqrt(NB) includes no systematic uncertainties; at NS=7 and NB=117, even a modest systematic uncertainty on the background would reduce the quoted reach.
  3. [Sec. 3 and Fig. 2] The exclusion limit on mD is derived by intersecting the predicted t tbar b bbar cross section from D Dbar production with ATLAS and CMS H^+- -> tb search contours. This reinterpretation assumes that the experimental acceptance, selection efficiencies, and background composition for the charged-Higgs signal apply to the diquark pair-production signal. That assumption is not demonstrated. Since the '~600 GeV' exclusion is used to justify focusing on mD = 700 GeV and above, the authors should either validate the reinterpretation with a more detailed efficiency map or clearly label the limit as approximate and model-dependent.
  4. [Sec. 3, first paragraph] The benchmark scenario assumes BR(D -> tb) = BR(anti D -> tbar bbar) = 1, obtained by setting O(10^-3) couplings to third-generation quarks and vanishing couplings to first- and second-generation quarks. This is an input assumption, not a derived prediction. The quoted discovery reach scales with the square of this branching fraction, so the abstract and conclusions should explicitly state that the 3-sigma reach holds only under this BR=1 assumption. The paper does state the assumption in Sec. 3, but the abstract and conclusions present the reach without this caveat, which is misleading.
minor comments (4)
  1. [Sec. 4.2] In the sentence 'individual jets and leptons will can no longer be resolved', 'will can' should be corrected to 'can'. Additionally, please define P_H^T more precisely than 'total hadronic transverse energy'; specify the sum over which objects and how the 1400 GeV requirement was chosen.
  2. [Sec. 2] Equation (2) and the surrounding text refer to 'B + L1', which appears to be a typesetting issue for 'B + L'. Please clarify that the first term preserves B+L and the second violates B+L.
  3. [Fig. 5] Figure 5 does not display the numerical significance values; since the abstract claims a 1 TeV reach, the figure should explicitly mark the mD = 1000 GeV point and the 3-sigma line so the reader can see the tension with the abstract.
  4. [Sec. 5] The phrase 'fairly light (up to 1 TeV) D' is inconsistent with the paper's own analysis, which does not demonstrate sensitivity at 1 TeV; consider replacing 'up to 1 TeV' with 'up to about 900 GeV' throughout the conclusions.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the HL-LHC significance estimate is a forward MC calculation with m_D and couplings as free inputs; self-citations are not load-bearing.

full rationale

The derivation is self-contained. The signal significance is obtained by generating D Dbar -> t tbar b bbar events with MadGraph, Pythia, and Delphes, applying a fixed set of selection cuts, and comparing the surviving signal and background event counts (Tabs. 3 and 5). The diquark mass and Yukawa couplings are free inputs: m_D is scanned over representative values and the couplings are set to give BR(D -> tb) ~ 1 (Sec. 3), not fitted to reproduce the quoted significance. The K-factors are taken from external references [26] and [46], not from the authors' own previous results. The only self-citations ([28,29] for the E6SSM framework and [30] for a related leptoquark study) supply the model as an input; they are not used to justify the reach claim, and no uniqueness theorem or ansatz is imported from them to force the conclusion. One non-circular concern is that the abstract's 'up to 1 TeV' >3-sigma statement appears in tension with the 1000 GeV row of Table 5 (5 signal vs 117 background events at 140 fb^-1, corresponding to roughly 2 sigma after naive scaling to 3000 fb^-1), but that is a correctness or support issue, not a circular derivation.

Assumptions & free parameters 3 free parameters · 4 assumptions · 1 invented entities

The central projection rests on freely chosen diquark mass benchmarks and tuned couplings that enforce a 100% branching fraction to tb. These are not derived from first principles or external constraints. The model structure, D-term formulas, and reinterpretation of H± limits are carried in from prior E6SSM literature and experimental papers without re-derivation.

free parameters (3)
  • Diquark mass m_D = 700, 800, 900, 1000 GeV (plus 500, 600 GeV in the standard analysis)
    The lightest S4-type diquark mass is not predicted by the E6SSM; the authors fix m^2_Di = m^2_Dbar_i = 2e6 GeV^2 and vary A_kappa_i to obtain the benchmark masses (Sec. 3, paragraph on spectrum).
  • Diquark Yukawa couplings to third generation = O(10^-3)
    Set so that BR(D->tb) is about 1 and couplings to first and second generations vanish (Sec. 3, first paragraph); not fixed by the model or by any external constraint.
  • A_kappa_i (trilinear coupling) variation = not reported
    Chosen 'slightly' to realize the target masses; the exact values are not reported, which hampers reproducibility (Sec. 3).
assumptions (4)
  • domain assumption The E6SSM superpotential and its discrete symmetries (Z2M, Z2H, Z2L) as defined in Eqs. (6)-(7) and Table 2
    The whole analysis assumes this specific E6SSM variant where the exotic scalars are S4-type diquarks with baryon number -2/3 and +2/3.
  • domain assumption The D-term contributions to diquark masses from U(1)N are as given in Eq. (10)
    These determine the mass spectrum; taken from the model, not derived in the paper.
  • ad hoc to paper ATLAS and CMS H± -> tb search limits can be reinterpreted as limits on the D Dbar signal by comparing total cross sections
    The paper overlays the predicted D Dbar cross section on the observed exclusion contours without implementing the experimental acceptances (Fig. 2 and Sec. 3). This assumes identical acceptance and selection efficiency for the D Dbar signal.
  • ad hoc to paper K-factors from Refs [26] and [46] are applicable to the signal and backgrounds
    Used to scale LO cross sections to estimate significance; Ref [46] is for four-top production, not ttbb, so its applicability is assumed.
invented entities (1)
  • Lightest S4-type scalar diquark D with sub-TeV mass and BR(D->tb) ~ 1
    purpose: Signal candidate for LHC searches; the paper scans its mass and estimates discovery significance.
    The diquark is a standard prediction of the E6SSM, but the specific light state with mass 500-1000 GeV and O(10^-3) third-generation couplings is a benchmark choice, not a prediction with independent experimental support.

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Cite this review

Pith. "Pith review of Unveiling E$_6$SSM Scalar Diquarks at the HL-LHC." pith.science (2026). https://pith.science/paper/YSWFYRLB

@misc{pith2026241219445,
  author       = {Pith},
  title        = {Pith review of: Unveiling E$_6$SSM Scalar Diquarks at the HL-LHC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YSWFYRLB}},
  note         = {Machine review of arXiv:2412.19445}
}
abstract

We investigate the phenomenology of scalar diquarks with sub-TeV masses within the framework of the $E_6$ Supersymmetric Standard Model (E$_6$SSM) at the Large Hadron Collider (LHC). Focusing on the lightest of the six diquarks predicted by the model, we select some representative low masses for them in a parameter space region consistent with experimental constraints from direct searches for additional Higgs boson(s), Cold Dark Matter (CDM), and supersymmetry, as well as from flavor physics analyses. Using Monte Carlo ($MC$) simulations, we assess these benchmark points against the latest LHC results corresponding to an integrated luminosity of 140 fb$^{-1}$. We further evaluate the signal significance of the pair-production of these diquarks, when each of them decays into $tb$ pairs, at the $\sqrt{s}=13$ TeV LHC Run 3 with design integrated luminosity of 300 fb$^{-1}$, and also at the 3000 fb$^{-1}$ High-Luminosity LHC (HL-LHC). Our analysis yields a statistical significance exceeding $3\sigma$ at the HL-LHC for diquark masses up to 1 TeV, indicating promising prospects for their discovery.

Figures

Figures reproduced from arXiv: 2412.19445 by the authors.

Figure 1
Figure 1. LO pair-production of S4-type diquarks (DD¯) at the LHC. If we assume one of the two linear superpositions of the scalar components of D3 and D3 supermultiplets (in analogy with the SUSY sector, and for index-alignment with the only active generation of the Higgs sector) to be the lightest S4–type diquark, which we denote by D for simplification, its mass is given by m2 D = 1 2 " M2 11(3) + ∆11(3) + M2 22(3) + ∆22(3… view at source ↗
Figure 2
Figure 2. Exclusion contours in the {σ(ttb¯ ¯b), mH± } plane from the ATLAS (solid black) and CMS (dashed black) data. The blue (red) line corresponds to the (N)LO cross section predicted for ttb¯ ¯b production via DD¯ in the E6SSM. The intersection of this line with a given contour is interpreted here as the mD exclusion limit from the corresponding experiment. searches in the ATLAS [33] and CMS [34] experiments. The ATLAS a… view at source ↗
Figure 3
Figure 3. Signal and combined background event distributions (normalised to unity) for [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: DD¯ invariant mass distributions for the mD = 700 and 800 GeV signals and the combined background, using the fat–jet selection criteria [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Estimated rise in the signal significances with our fat–jet analysis with increasing lumi [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

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Reviewed August 11, 2026 · model on record in the stance chip above.