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Search for resonant production of pairs of dijet resonances through broad mediators in proton-proton collisions at $\sqrt{s}$ = 13 TeV

T0 review · 2 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The 8.6 TeV four-jet excess remains significant for resonance widths up to 10 percent, so a broad mediator is as valid as a narrow one.

desk verdict A solid, honest reinterpretation that shows the 8.6 TeV excess persists across widths, but the 'equally valid' claim overstates and the 10% result leans on an unvalidated simulated low-mass tail. read the letter →

arxiv 2507.17884 v1 pith:KOAYXCBL submitted 2025-07-23 hep-ex

CMS Collaboration This is my paper · ORCID
classification hep-ex
keywords broadmediatordijetresonancepairproductionfour-jetfinalstatewidthdiquarkmodel8.6TeVexcessLHCproton-protoncollisions13
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 reinterprets an earlier search for pairs of dijet resonances, allowing the parent four-jet resonance to be broad rather than narrow. Using the full $138~\text{fb}^{-1}$ dataset from $\sqrt{s}=13$ TeV proton-proton collisions, it shows that resonances with natural widths of 1.5, 5, and 10% of their mass all describe the observed excess near a four-jet mass of 8.6 TeV, with local significance 3.9 to 3.6 standard deviations and global significance 1.6 to 1.4 standard deviations. The key addition is that a 10% width naturally accommodates a third candidate event at 5.8 TeV that narrow-resonance fits barely use. This matters because it means the reported excess does not depend on the narrow-width assumption, and it provides model-independent limits on heavy resonances decaying to two equal-mass dijet pairs.

What carries the argument

The search is organized around the dimensionless ratio $\alpha = m_{2j}/m_{4j}$, the average dijet mass over the four-jet mass, which separates signal from the smoothly falling QCD background. Data are split into thirteen $\alpha$ bins, and in each bin the four-jet mass distribution is fitted with a three-parameter modified dijet background function, with alternative functions used as discrete nuisances. Signal templates are generated for the diquark model with widths 1.5, 5, and 10% by tuning the couplings $y_{uu}$ and $y_\chi$ in Eqs. (3)--(4); the broad templates develop a long low-mass tail that arises from incorrect jet combinations assigned by the pairing algorithm. A multibin Poisson likelihood, profiled over background and systematic nuisance parameters, yields the significances and 95% CL limits.

What would settle it

Compare the number and distribution of events with $m_{4j} \le 5.8$ TeV and $m_{2j}\approx 2$ TeV in the full Run 2 dataset against the 40% low-mass-tail prediction for the 10% width hypothesis, or rerun the analysis with a different jet-pairing algorithm and check whether the 8.6 TeV significance still stays above 3.6 standard deviations at 10% width.

Watch

Extended reading notes

Core claim

The central claim is that a broad mediator, with width up to 10% of its mass, is an equally valid interpretation of the 8.6 TeV four-jet excess previously reported under a narrow-resonance assumption. For a diquark benchmark with mass ratio $\alpha_{\text{true}} = M_X/M_Y = 0.25$, the local significance at $M_Y = 8.6$ TeV remains 3.9, 3.8, and 3.6 standard deviations for widths 1.5, 5, and 10%, while the global significance stays between 1.6 and 1.4 standard deviations. The broader signals extend to lower four-jet masses through events in which the jet-pairing algorithm combines the wrong jets; for a 10% width, 40% of the signal is expected at $m_{4j} \le 5.8$ TeV. This tail is what makes the event at $m_{4j}=5.8$ TeV, $m_{2j}=2.0$ TeV compatible with a broad resonance, supporting the interpretation. The analysis also reports a separate excess at $M_Y=3.6$ TeV, $\alpha_{\text{true}}=0.29$, whose local (global) significance rises to 3.9 (2.2) standard deviations at 10% width, and presents 95% CL upper limits on $\sigma B A$ for masses between 2 and 10 TeV.

Load-bearing premise

The weakest link is the simulation's prediction of the broad-resonance signal shape, especially the low-mass tail produced by mis-paired jets; if the rate or shape of those tail events is miscalibrated, the claimed stability of the significance with width would not hold.

Editorial extensions

If this is right

  • The 8.6 TeV excess can no longer be attributed solely to a narrow-width assumption; searches with broad mediators must be included in its interpretation.
  • The event at $m_{4j}=5.8$ TeV, which a narrow fit barely uses, becomes a signal-like member of the broad-resonance hypothesis and improves the fit.
  • The independent candidate event at $m_{4j}=6.6$ TeV and $m_{2j}=2.2$ TeV falls inside the 5% and 10% width contours, so the two experiments' observations are mutually consistent under a broad mediator.
  • For the diquark benchmark with $\alpha_{\text{true}}=0.25$ and 10% width, the $S_{uu}$ model is excluded at 95% CL above 8.8 TeV while $S_{dd}$ remains viable at 8.6 TeV, so the excess can still be a scalar diquark hypothesis.
  • The second excess at 3.6 TeV, which grows with width, provides an independent target for future searches and for model building.

Reading between the lines

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

  • If the broad-mediator interpretation is correct, the same 8.6 TeV excess should reappear in the upcoming higher-statistics Run 3 data, with the ratio of tail to peak events following the width-dependent prediction.
  • A combined fit of the CMS and the other experiment's candidate events in the two-dimensional $(m_{4j}, m_{2j})$ plane, rather than separate $\alpha$ bins, could sharpen the broad-versus-narrow discrimination.
  • The mis-pairing mechanism that creates the low-mass tail is testable with generator-level studies: if a different pairing or a boosted reconstruction removes the 5.8 TeV event from the signal region, the broad-resonance interpretation loses its main supporting event.
  • The 3.6 TeV excess's growth with width suggests it may be the same underlying component as the nonresonant dijet-pair effect seen in prior data; a dedicated search with finer $\alpha$ bins could clarify whether it is resonant at all.
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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

2 major / 4 minor

Summary. This manuscript reinterprets the CMS search for pairs of dijet resonances (Ref. [1]) by allowing the intermediate mediator Y to have a natural width up to 10% of its mass, using the same 138 fb^-1 of 13 TeV proton-proton collision data. The analysis reuses the event selection, jet pairing, and background-fitting procedure of Ref. [1], with signal templates generated for a diquark benchmark model at widths of 1.5%, 5%, and 10%, for four-jet resonance masses from 2 to 10 TeV and for several dijet-to-four-jet mass ratios. Upper limits at 95% CL on the signal cross section and local/global significances are obtained from a multibin Poisson likelihood in 13 bins of alpha = m2j/m4j. The central result is that the excess at a four-jet mass of 8.6 TeV retains a local significance of 3.9 to 3.6 s.d. as the width increases from 1.5% to 10%, leading the authors to conclude that a broad resonance is an equally valid interpretation of the excess. A second excess at 3.6 TeV is also reported, with local (global) significance up to 3.9 (2.2) s.d. at 10% width.

Significance. If the results are correct, this is a valuable reinterpretation: it demonstrates that the previously reported 8.6 TeV excess is not an artifact of the narrow-width assumption and that broad mediators remain a viable explanation. The analysis uses the established CMS statistical framework, including a multibin Poisson likelihood, background-only fits with reported p-values, discrete profiling for background functional-form uncertainty, and pseudo-experiment cross-checks for small event counts. Results are provided in the HEPData record, which is commendable for reproducibility. The paper extends the scope of the original search by scanning over widths and providing model-independent limits in the plane of four-jet mass and dijet mass ratio. The main scientific interest is the claimed width-insensitivity of the excess, which rests on a simulated low-mass signal tail; this is also the main technical risk, as discussed below.

major comments (2)
  1. [Section 4, Fig. 3; Section 3, Fig. 2] The central claim that the 8.6 TeV excess is equally compatible with broad resonances relies on the 10%-width signal template placing about 40% of its yield at m4j <= 5.8 TeV (Section 4), a region that contains the third candidate event. The text attributes this low-mass tail to incorrect jet combinations assigned by the pairing algorithm (Section 3, Fig. 2), but no closure test, control-sample validation, or generator-level comparison is presented to establish the rate and shape of this tail, and the list of systematic uncertainties in Section 5 does not include a dedicated uncertainty for this mispairing component. Because the tail dominates the broad-signal likelihood and is what allows the 5.8 TeV event to support the broad hypothesis, the reported width-insensitivity of the significance (3.9 to 3.6 s.d.) is not established without quantifying this component. The authors should validate the mispairing tail with, for example, a data control region or an alternate jet-pairing algorithm, or assign and propagate a corresponding systematic uncertainty.
  2. [Section 5; Table 1] The mass limits in Table 1 and the model comparisons in Figs. 8-10 use a cross-section prediction corrected by an 'efficiency factor that isolates the m4j range where the expected significance exceeds 99% of that obtained without the correction.' This definition is self-referential because the theoretical prediction used for the exclusion is corrected using the significance of the signal being tested, and the exact m4j range and the significance computation are not specified. As a result, the reported exclusion limits (for example, 8.8 TeV for Suu at 10% width) depend on a criterion that is not fully reproducible. The authors should provide a precise mathematical definition of this factor and demonstrate that the excluded mass regions are stable under reasonable variations of the efficiency threshold.
minor comments (4)
  1. [Section 5] The global significance is quoted separately for each width (1.6, 1.5, and 1.4 s.d. in Table 2), but it is not stated whether the trials factor includes the discrete scan over the three width hypotheses. If not, the reported global p-values are conditional on the width and should be interpreted with that caveat.
  2. [Section 3, Fig. 2] The figure labels and caption use 'SM 68% contours' for the simulated signal contours; this is ambiguous because 'SM' usually denotes the standard model. Consider renaming them to 'signal 68% contours' for clarity.
  3. [Section 4] The statement that 'diquark signals with a width larger than 10% do not exhibit a peak at the resonance mass' is presented without a reference or illustration. A supporting figure or quantitative criterion would make this modeling choice easier to assess.
  4. [Section 2] The vector-like quark width is reported to reach up to 3.7% at a mass of 4.2 TeV, but the analysis assumes that X is a narrow dijet resonance. Since the search targets narrow X, it would be useful to state explicitly that a 3.7% width is negligible compared to the experimental resolution or to restrict the affected mass range.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the width hypotheses are scanned inputs, the background is data-driven, and the observed significances are computed from a likelihood with no input equivalent to the claimed conclusion.

full rationale

The paper's central claim, that the 8.6 TeV excess remains significant for widths from 1.5% to 10%, is a genuine reinterpretation rather than a circular derivation. The resonance widths are fixed generator inputs (1.5, 5, 10%), the signal shapes are produced by a standard MadGraph/PYTHIA/GEANT chain for fixed benchmark masses and couplings, and the background is fitted to observed data with empirical functions profiled as nuisance parameters. The observed local and global significances are outputs of a Poisson likelihood fit; no fitted parameter is renamed as a prediction, and the conclusion that a broad resonance is 'equally valid' follows from the computed stability of the p-value, not from an equation that builds that conclusion into the inputs. The much-discussed 40% low-mass tail for the 10% width is a simulation prediction used to explain compatibility with the 5.8 TeV event; it is not constructed from that event, and the absence of a dedicated systematic for it is a robustness concern, not circularity. The one self-referential element, the efficiency correction that restricts the theoretical cross section to regions where expected significance exceeds 99% of the uncorrected value, is clearly disclosed and applies only to model-exclusion mass limits; it does not enter the significance extraction and is not the paper's headline result. Dependence on the previous CMS analysis (Ref. [1]) is a reuse of a published, externally reviewed event selection and background methodology, appropriate for a reinterpretation; it is not an unverified load-bearing self-citation. Overall the derivation chain is self-contained against the data and does not reduce to its own inputs.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The paper does not introduce a new particle, force, or dimension. The broad mediator and diquark benchmark are taken from prior literature [3]. All free parameters and assumptions are tied to the standard CMS fitting framework and the benchmark signal model.

free parameters (4)
  • Background function parameters per alpha bin = 3 or 5 per bin (not tabulated)
    The modified dijet, dijet, and power-law exponential functions each have 3 or 5 free parameters fitted to the m4j data in each of 13 alpha bins (Section 4). These are nuisance parameters profiled in the likelihood and are part of the significance computation.
  • Jet energy scale and mass resolution nuisance parameters = JES +/- 2%, resolution +/- 10%
    Implemented as Gaussian-constrained nuisance parameters as in Ref. [1] (Section 5). They affect the signal shapes and the fit.
  • Efficiency correction factor for model cross sections = Not tabulated as a single number
    Used in Section 5 to adjust the theoretical sigma times B prediction for mass limits: it keeps only the m4j range where the expected significance exceeds 99% of its uncorrected value. It is defined by a self-referential optimization, but does not affect the central significance versus width claim.
  • Benchmark diquark couplings (beta = yuu/ychi = 2/3) = yuu and ychi set to give widths of 1.5, 5, and 10%
    Chosen by hand as in Ref. [1] (Section 3, Eqs. 3 and 4). They define the benchmark signal model used for limits, but are not fit to the observed data.
assumptions (4)
  • domain assumption The QCD multijet background in each alpha bin is smooth and can be described by one of three empirical three-parameter functions.
    Used in Section 4. Validated by fit p-values between 0.14 and 0.91 and a combined p-value of 0.18, so it is a reasonable assumption.
  • domain assumption The signal efficiency and shapes from the MadGraph + PYTHIA + GEANT simulation, including the rate of incorrect jet pairings, accurately model the detector response for broad resonances.
    The low-mass tail of the 10% width signal, which captures the 5.8 TeV event, is attributed to incorrect jet combinations (Section 3, Fig. 2). The analysis assumes this simulation is correct.
  • standard math The modified frequentist CLs method with asymptotic approximations is valid for the multibin likelihood.
    Used in Section 5 with pseudo-experiments where event counts are small; this is an established high energy physics statistical method.
  • domain assumption The diquark model of Ref. [3] with B(chi to ug) = 1 and beta = 2/3 is a representative benchmark for the considered final state.
    Eq. (2) and Section 3. It is used to compare limits to a concrete model, not to define the search itself.

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Cite this review

Pith. "Pith review of Search for resonant production of pairs of dijet resonances through broad mediators in proton-proton collisions at $\sqrt{s}$ = 13 TeV." pith.science (2026). https://pith.science/paper/KOAYXCBL

@misc{pith2026250717884,
  author       = {Pith},
  title        = {Pith review of: Search for resonant production of pairs of dijet resonances through broad mediators in proton-proton collisions at $\sqrts$ = 13 TeV},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KOAYXCBL}},
  note         = {Machine review of arXiv:2507.17884}
}
abstract

A reinterpretation of a prior narrow-resonance search is performed to investigate the resonant production of pairs of dijet resonances via broad mediators. This analysis targets events with four resolved jets, requiring dijet invariant masses greater than 0.2 TeV and four-jet invariant masses greater than 1.6 TeV. The search uses a data sample corresponding to an integrated luminosity of 138 fb$^{-1}$ collected by the CMS experiment in proton-proton collisions at $\sqrt{s}$ = 13 TeV. The reinterpretation considers the production of new heavy four-jet resonances, with widths ranging from 1.5 to 10% of their mass, which decay to a pair of dijet resonances. This analysis probes resonant production in the four-jet and dijet mass distributions. Upper limits at 95% confidence level and significances are reported on the production cross section of new resonances as functions of their widths and masses, between 2 and 10 TeV. In particular, at a four-jet resonance mass of 8.6 TeV, the local (global) significance ranges from 3.9 (1.6) to 3.6 (1.4) standard deviations (s.d.) as the resonance width is increased from 1.5 to 10%. This relative insensitivity to the choice of width indicates that a broad resonance is an equally valid interpretation of this excess. The broad resonance hypothesis at a resonance mass of 8.6 TeV is supported by the presence of an event with a four-jet mass of 5.8 TeV and an average dijet mass of 2.0 TeV. Also, we report the reinterpretation of a second effect, at a four-jet resonance mass of 3.6 TeV, which has a local (global) significance of up to 3.9 (2.2) s.d.

Figures

Figures reproduced from arXiv: 2507.17884 by the authors.

Figure 1
Figure 1. Resonant production via a particle, Y, of pairs of dijet resonances, X. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Observed number of events (upper) and predictions of a leading order (LO) QCD [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Signal differential distributions as a function of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: The product of the acceptance (A) and efficiency of the mass selection (ε) for a resonant signal with αtrue = 0.25, shown with filled squares as a function of the diquark mass and for various diquark widths, for all α bins inclusively. The case when ε = 1 is also shown…
Figure 5
Figure 5. Figure 5: The m4j distribution in data (points), within six of the thirteen α bins, fitted with the background-only function, ModDijet-3p (red solid), and two alternative background functions, PowExp-3p and Dijet-3p (red dotted and dashed), with three free parameters. Examples o…
Figure 6
Figure 6. Figure 6: The m4j distributions of the data (points), within three of the thirteen α bins, fitted with the background-only function, ModDijet-3p (red solid), and two alternative background functions, PowExp-3p and Dijet-3p (red dotted and dashed), with three free parameters. Ex￾…
Figure 7
Figure 7. Figure 7: The m4j distribution in data (points), for all α bins combined, fitted with the background-only function, ModDijet-5p (red solid), and two alternative background functions, PowExp-5p and Dijet-5p (red dotted and dashed), with five free parameters. Examples of pre￾dicte…
Figure 8
Figure 8. Figure 8: The observed 95% CL upper limits (points) on the product of the cross section, [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: The observed 95% CL upper limits (points) on the product of the cross section, branch [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: The observed 95% CL upper limits (points) on the product of the cross section, [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 11
Figure 11. Figure 11: Observed local p-value for a four-jet resonance, Y, decaying to a pair of dijet reso￾nances, X, with αtrue = MX/MY = 0.25 (left) and 0.29 (right), and various widths of Y super￾imposed. Also shown are corresponding levels of local significance (dashed lines) in units …
Figure 12
Figure 12. Figure 12: The 3D display of the candidate event for broad resonances with a four-jet mass [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]

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Reviewed August 15, 2026 · model on record in the stance chip above.