CMS-PAS-EXO-24-038

CMS-PAS-EXO-24-038
Search for resonant production of pairs of dijet resonances through broad mediators in proton-proton collisions at $\sqrt{s} =$ 13 TeV
CMS Collaboration
23 March 2025

Abstract: A reinterpretation of a prior narrow resonance search is performed to investigate resonant production of dijet resonance pairs via broad mediators. This analysis targets events with four resolved jets, requiring dijet invariant masses $>$ 0.2 TeV and four-jet invariant masses $>$ 1.6 TeV. The search has been conducted using proton-proton collision data collected in Run 2 by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb $^{-1}$ . The benchmark model considered involves the production of heavy new resonances with widths ranging from 1.5% to 10%, decaying to a pair of vector-like quarks, which in turn each decay to a pair of jets. This signature probes resonant production in the four-jet and dijet mass distributions. Both upper limits at 95% CL and significances are reported on the production cross section of new resonances as a function of their width and masses, between 2 and 10 TeV. In particular, for the 8 TeV four-jet mass region, where there was an excess in the previous narrow resonance search, the significance of an 8-10 TeV diquark resonance is found to be relatively insensitive to the choice of width, making a broad resonance an equally valid interpretation of the excess.
Links: CDS record (PDF) ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Resonant production via a particle, $\mathrm{Y}$ , of pairs of dijet resonances, $\mathrm{X}$ .
png pdf	Figure 2: Diquark production followed by decay into a pair of vector-like quarks, each of them then decaying at one loop into a gluon and a quark.
png pdf	Figure 2-a: Diquark production followed by decay into a pair of vector-like quarks, each of them then decaying at one loop into a gluon and a quark.
png pdf	Figure 2-b: Diquark production followed by decay into a pair of vector-like quarks, each of them then decaying at one loop into a gluon and a quark.
png pdf	Figure 3: Numbers of events observed (color scale) within bins of the four-jet mass and the average mass of the two dijets (left) and within bins of the four-jet mass and the ratio $\alpha$ (right), which is the average dijet mass divided by the four-jet mass. The solid curves show the 68% probability contours from a signal simulation of a diquark with a mass of 8.4 TeV, decaying to a pair of vector-like quarks, each with a mass of 2.1 TeV. The violet, red, blue and green probability contours correspond to 0.43%, 1.5%, 5% and 10% diquark widths respectively. The right plot also shows the thirteen $\alpha$ bins used to define the four-jet mass distributions (dashed lines).
png pdf	Figure 3-a: Numbers of events observed (color scale) within bins of the four-jet mass and the average mass of the two dijets (left) and within bins of the four-jet mass and the ratio $\alpha$ (right), which is the average dijet mass divided by the four-jet mass. The solid curves show the 68% probability contours from a signal simulation of a diquark with a mass of 8.4 TeV, decaying to a pair of vector-like quarks, each with a mass of 2.1 TeV. The violet, red, blue and green probability contours correspond to 0.43%, 1.5%, 5% and 10% diquark widths respectively. The right plot also shows the thirteen $\alpha$ bins used to define the four-jet mass distributions (dashed lines).
png pdf	Figure 3-b: Numbers of events observed (color scale) within bins of the four-jet mass and the average mass of the two dijets (left) and within bins of the four-jet mass and the ratio $\alpha$ (right), which is the average dijet mass divided by the four-jet mass. The solid curves show the 68% probability contours from a signal simulation of a diquark with a mass of 8.4 TeV, decaying to a pair of vector-like quarks, each with a mass of 2.1 TeV. The violet, red, blue and green probability contours correspond to 0.43%, 1.5%, 5% and 10% diquark widths respectively. The right plot also shows the thirteen $\alpha$ bins used to define the four-jet mass distributions (dashed lines).
png pdf	Figure 4: Numbers of events (color scale) within bins of the four-jet mass and the average mass of the two dijets (left) and within bins of the four-jet mass and the ratio $\alpha$ (right), which is the average dijet mass divided by the four-jet mass, predicted by a LO QCD simulation, normalized to the luminosity of data. Superimposed with solid lines are the 68% probability contours of narrow and broad diquark resonances with mass of 8.4 TeV, $M_{\chi} / M_{ \mathrm{S}} =$ 0.25 and widths ranging from 0.43% to 10%. The right plot also shows the thirteen $\alpha$ bins used to define the four-jet mass distributions (dashed lines). The number of SM events, predicted by the LO QCD simulation, enclosed within the 68% probability contours of signals with 0.43% and 10% widths are 0.2 and 33 respectively.
png pdf	Figure 4-a: Numbers of events (color scale) within bins of the four-jet mass and the average mass of the two dijets (left) and within bins of the four-jet mass and the ratio $\alpha$ (right), which is the average dijet mass divided by the four-jet mass, predicted by a LO QCD simulation, normalized to the luminosity of data. Superimposed with solid lines are the 68% probability contours of narrow and broad diquark resonances with mass of 8.4 TeV, $M_{\chi} / M_{ \mathrm{S}} =$ 0.25 and widths ranging from 0.43% to 10%. The right plot also shows the thirteen $\alpha$ bins used to define the four-jet mass distributions (dashed lines). The number of SM events, predicted by the LO QCD simulation, enclosed within the 68% probability contours of signals with 0.43% and 10% widths are 0.2 and 33 respectively.
png pdf	Figure 4-b: Numbers of events (color scale) within bins of the four-jet mass and the average mass of the two dijets (left) and within bins of the four-jet mass and the ratio $\alpha$ (right), which is the average dijet mass divided by the four-jet mass, predicted by a LO QCD simulation, normalized to the luminosity of data. Superimposed with solid lines are the 68% probability contours of narrow and broad diquark resonances with mass of 8.4 TeV, $M_{\chi} / M_{ \mathrm{S}} =$ 0.25 and widths ranging from 0.43% to 10%. The right plot also shows the thirteen $\alpha$ bins used to define the four-jet mass distributions (dashed lines). The number of SM events, predicted by the LO QCD simulation, enclosed within the 68% probability contours of signals with 0.43% and 10% widths are 0.2 and 33 respectively.
png pdf	Figure 5: Signal differential distributions as a function of four-jet mass for $\alpha_{\mathrm{true}} =$ 0.25, diquark masses of 2, 5, 8.6 TeV and various widths, for all $\alpha$ bins inclusively. The integral of each distribution has been normalized to unity.
png pdf	Figure 6: The product of acceptance and efficiency (squared points) of a resonant signal with $\alpha_{\mathrm{true}} =$ 0.25 vs. the diquark mass for various diquark widths, and for all $\alpha$ bins inclusively. The case when the efficiency of the mass selection is unity is also shown as solid lines.
png pdf	Figure 7: The four-jet mass distributions of the data (points), within six of the thirteen $\alpha$ bins, compared with the simulated LO QCD background distribution (green histogram) and fitted with three functions: a power-law times an exponential (red dotted), the dijet function (red dashed), and the modified dijet function (red solid), each function with three free parameters. Examples of predicted narrow (0.43%) and broad (10%) diquark resonances with $\alpha_{\mathrm{true}} =$ 0.25 and $M_{ \mathrm{S}} =$ 8.6 TeV are shown, with cross sections equal to the observed upper limits at 95% confidence level. The percentage of signal across the depicted $\alpha$ bins is 90% (80%) for the narrow (broad) resonance. The lower panels show the pulls from the fit of the modified dijet function to the data, calculated using the statistical uncertainty of the data.
png pdf	Figure 8: The four-jet mass distributions of the data (points), within three of the thirteen $\alpha$ bins, compared with the simulated LO QCD background distribution (green histogram) and fitted with three functions: a power-law times an exponential (red dotted), the dijet function (red dashed), and the modified dijet function (red solid), each function with three free parameters. Examples of predicted narrow (0.4%) and broad (10%) diquark resonances with $\alpha_{\mathrm{true}} =$ 0.29 and $M_{ \mathrm{S}} =$ 3.6 TeV are shown, with cross sections equal to the observed upper limits at 95% confidence level. The percentage of signal across the depicted $\alpha$ bins is 80% (70%) for the narrow (broad) resonance. The lower panels show the pulls from the fit of the modified dijet function to the data, calculated using the statistical uncertainty of the data.
png pdf	Figure 9: The four-jet mass distribution of the data (points), for all $\alpha$ bins combined, compared with the simulated LO QCD background distribution (green histogram) and fitted with three functions: a power-law times an exponential (red dotted), the dijet function (red dashed), and the modified dijet function (red solid), each function with five free parameters. Examples of predicted narrow (0.4%) and broad (10%) diquark resonances with $\alpha_{\mathrm{true}} =$ 0.25, $M_{ \mathrm{S}} =$ 8.6 TeV and $\alpha_{\mathrm{true}} =$ 0.29, $M_{ \mathrm{S}} =$ 3.6 TeV are shown, with cross sections equal to the observed upper limits at 95% confidence level. The lower panel shows the pulls from the fit of the modified dijet function to the data, calculated using the statistical uncertainty of the data.
png pdf	Figure 10: The observed 95 $% \text{CL}$ upper limits (points) on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{ \mathrm{Y}} =$ 0.25 and width of $\mathrm{Y}$ equal to 0.43% (top left), 1.5% (top right), 5% (bottom left) and 10% (bottom right). The corresponding expected limits (dashed) and their variations at the 1 and 2 standard deviation levels (shaded bands) are also shown. Limits are compared to predictions for scalar $\mathrm{S_{uu}}$ and $\mathrm{S_{dd}}$ diquarks [3] (dot-dashed lines) with couplings to pairs of up and down quarks, $y_{\mathrm{u}\mathrm{u}}$ and $y_{\mathrm{d}\mathrm{d}}$ , and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$ , set appropriately in order to generate the corresponding widths.
png pdf	Figure 10-a: The observed 95 $% \text{CL}$ upper limits (points) on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{ \mathrm{Y}} =$ 0.25 and width of $\mathrm{Y}$ equal to 0.43% (top left), 1.5% (top right), 5% (bottom left) and 10% (bottom right). The corresponding expected limits (dashed) and their variations at the 1 and 2 standard deviation levels (shaded bands) are also shown. Limits are compared to predictions for scalar $\mathrm{S_{uu}}$ and $\mathrm{S_{dd}}$ diquarks [3] (dot-dashed lines) with couplings to pairs of up and down quarks, $y_{\mathrm{u}\mathrm{u}}$ and $y_{\mathrm{d}\mathrm{d}}$ , and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$ , set appropriately in order to generate the corresponding widths.
png pdf	Figure 10-b: The observed 95 $% \text{CL}$ upper limits (points) on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{ \mathrm{Y}} =$ 0.25 and width of $\mathrm{Y}$ equal to 0.43% (top left), 1.5% (top right), 5% (bottom left) and 10% (bottom right). The corresponding expected limits (dashed) and their variations at the 1 and 2 standard deviation levels (shaded bands) are also shown. Limits are compared to predictions for scalar $\mathrm{S_{uu}}$ and $\mathrm{S_{dd}}$ diquarks [3] (dot-dashed lines) with couplings to pairs of up and down quarks, $y_{\mathrm{u}\mathrm{u}}$ and $y_{\mathrm{d}\mathrm{d}}$ , and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$ , set appropriately in order to generate the corresponding widths.
png pdf	Figure 10-c: The observed 95 $% \text{CL}$ upper limits (points) on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{ \mathrm{Y}} =$ 0.25 and width of $\mathrm{Y}$ equal to 0.43% (top left), 1.5% (top right), 5% (bottom left) and 10% (bottom right). The corresponding expected limits (dashed) and their variations at the 1 and 2 standard deviation levels (shaded bands) are also shown. Limits are compared to predictions for scalar $\mathrm{S_{uu}}$ and $\mathrm{S_{dd}}$ diquarks [3] (dot-dashed lines) with couplings to pairs of up and down quarks, $y_{\mathrm{u}\mathrm{u}}$ and $y_{\mathrm{d}\mathrm{d}}$ , and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$ , set appropriately in order to generate the corresponding widths.
png pdf	Figure 10-d: The observed 95 $% \text{CL}$ upper limits (points) on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{ \mathrm{Y}} =$ 0.25 and width of $\mathrm{Y}$ equal to 0.43% (top left), 1.5% (top right), 5% (bottom left) and 10% (bottom right). The corresponding expected limits (dashed) and their variations at the 1 and 2 standard deviation levels (shaded bands) are also shown. Limits are compared to predictions for scalar $\mathrm{S_{uu}}$ and $\mathrm{S_{dd}}$ diquarks [3] (dot-dashed lines) with couplings to pairs of up and down quarks, $y_{\mathrm{u}\mathrm{u}}$ and $y_{\mathrm{d}\mathrm{d}}$ , and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$ , set appropriately in order to generate the corresponding widths.
png pdf	Figure 11: The observed 95 $% \text{CL}$ upper limits (points) on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with width of $\mathrm{Y}$ equal to 10%, and values of $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{ \mathrm{Y}}$ shown in each panel. The corresponding expected limits (dashed) and their variations at the 1 and 2 standard deviation levels (shaded bands) are also shown. Limits are compared to predictions for scalar $\mathrm{S_{uu}}$ and $\mathrm{S_{dd}}$ diquarks [3] (dot-dashed lines) with couplings to pairs of up and down quarks, $y_{\mathrm{u}\mathrm{u}}$ and $y_{\mathrm{d}\mathrm{d}}$ , and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$ , set appropriately in order to generate a 10% width.
png pdf	Figure 12: The observed 95% CL upper limits (points) on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with the values of $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{ \mathrm{Y}}$ shown in each panel. Different colors correspond to the various widths of the $\mathrm{Y}$ resonance. Limits are compared to predictions for scalar $\mathrm{S_{uu}}$ (solid lines) and $\mathrm{S_{dd}}$ (dashed lines) diquarks [3] with couplings to pairs of up and down quarks, $y_{\mathrm{u}\mathrm{u}}$ and $y_{\mathrm{d}\mathrm{d}}$ , and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$ , set appropriately in order to generate the corresponding widths.
png pdf	Figure 13: Observed local $p$ -value for a four-jet resonance, $\mathrm{Y}$ , decaying to a pair of dijet resonances, $\mathrm{X}$ , with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{ \mathrm{Y}} =$ 0.25 (top) and 0.29 (bottom), and various widths of $\mathrm{Y}$ superimposed. Also shown are corresponding levels of local significance (dashed lines) in units of standard deviation ( $\sigma$ ).
png pdf	Figure 13-a: Observed local $p$ -value for a four-jet resonance, $\mathrm{Y}$ , decaying to a pair of dijet resonances, $\mathrm{X}$ , with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{ \mathrm{Y}} =$ 0.25 (top) and 0.29 (bottom), and various widths of $\mathrm{Y}$ superimposed. Also shown are corresponding levels of local significance (dashed lines) in units of standard deviation ( $\sigma$ ).
png pdf	Figure 13-b: Observed local $p$ -value for a four-jet resonance, $\mathrm{Y}$ , decaying to a pair of dijet resonances, $\mathrm{X}$ , with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{ \mathrm{Y}} =$ 0.25 (top) and 0.29 (bottom), and various widths of $\mathrm{Y}$ superimposed. Also shown are corresponding levels of local significance (dashed lines) in units of standard deviation ( $\sigma$ ).
png pdf	Figure 14: Three-dimensional display of the candidate event for broad resonances with a four-jet mass of 5.8 TeV. The display shows the energy deposited in the electromagnetic (red) and hadronic (blue) calorimeters and the reconstructed tracks of charged particles (green). The grouping of the four observed jets into two dijet pairs (purple boxes) is discussed in the text.

Tables
png pdf	Table 1: Observed and expected mass limits at 95 $% \text{CL}$ for $\mathrm{S_{uu}}$ and $\mathrm{S_{dd}}$ diquark models with $\alpha_{\mathrm{true}} =$ 0.25.
png pdf	Table 2: Best fit values of $\sigma \mathcal{B} A$ and their corresponding values in terms of number of signal events, as well as local and global significance values, for a $\mathrm{Y}$ resonance mass of 8.6 TeV, $\mathrm{X}$ resonance mass of 2.15 TeV and different $\mathrm{Y}$ width scenarios.
png pdf	Table 3: Best fit values of $\sigma \mathcal{B} A$ and their corresponding values in terms of number of signal events, as well as local and global significance values, for a $\mathrm{Y}$ resonance mass of 3.6 TeV, $\mathrm{X}$ resonance mass of 1.0 TeV and different $\mathrm{Y}$ width scenarios.

Summary

A reinterpretation of a narrow resonance analysis, described in Ref. [1], has been conducted and presented, searching here for resonant production of pairs of dijet resonances with the same mass through broad mediators, in final states with at least four jets. Data from proton-proton collisions at

$\sqrt{s}=$ 13 TeV were used in this search, collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 138 fb

$^{-1}$ . The pairs of dijet resonances are produced via a massive broad mediator, leading to a four-jet resonance in the final state. Empirical functions that model the background, and simulated shapes of resonance signals with widths of 1.5%, 5% and 10%, are fit to the observed four-jet mass distributions in bins of the ratio of the dijet to the four-jet distributions. There are three events in the tails of the distributions, two with a four-jet mass of 8 TeV and one with a four-jet mass of 5.8 TeV, all of which have an average dijet mass of approximately 2 TeV, that result in an excess. Although the event with a four-jet mass of 5.8 TeV contributes minimally to a fit with narrow resonances, it is far more compatible with broad resonances of the same mass. Hence, the local significance for a diquark remains above 3.6 standard deviations even for the largest width considered, leading to the conclusion that broad resonances are an equally valid interpretation of the excess. The ATLAS event, with

$m_{\mathrm{4j}} =$ 6.6 and

$\overline{m}_{\mathrm{2j}} =$ 2.2 TeV, falls within the CMS 68% probability contour for a 5% or a 10% wide resonance with a mass of 8.4 TeV, and hence is likely compatible with those two hypotheses. A second excess with a local significance of 3.9 standard deviations is observed at four-jet and dijet resonance masses of 3.6 TeV and 1.0 TeV, respectively, for a mediator width of 10%. This excess was previously reported with a local significance of 3.6 standard deviations in Ref. [1], originating from the dijet data near a mass of 1 TeV, in the search for nonresonant production of pairs of dijet resonances. Model-independent upper limits at 95% CL are presented on the product of the cross section, branching fraction and acceptance as a function of the four-jet resonance mass between 2 and 10 TeV, for all accessible values of the ratio of the dijet to four-jet resonance masses and for widths ranging from 1.5% to 10%. Limits are compared to models [3] of diquarks, which decay to pairs of vector-like quarks, which in-turn decay to a quark and a gluon. Mass limits for all accessible values of the ratio of the vector-like quark to diquark masses, and diquark widths are presented.

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