CMS-TOP-24-007

CMS-TOP-24-007 ; CERN-EP-2025-061
Observation of a pseudoscalar excess at the top quark pair production threshold
CMS Collaboration
28 March 2025
Submitted to Reports on Progress in Physics
Abstract: A search for resonances in top quark pair ( $\mathrm{t} \overline{\mathrm{t}}$ ) production in final states with two charged leptons and multiple jets is presented, based on proton-proton collision data collected by the CMS experiment at the CERN LHC at $\sqrt{s}=$ 13 TeV, corresponding to 138 fb $^{-1}$ . The analysis explores the invariant mass of the $\mathrm{t} \overline{\mathrm{t}}$ system and two angular observables that provide direct access to the correlation of top quark and antiquark spins. A significant excess of events is observed near the kinematic $\mathrm{t} \overline{\mathrm{t}}$ threshold compared to the nonresonant production predicted by fixed-order perturbative quantum chromodynamics (pQCD). The observed enhancement is consistent with the production of a color-singlet pseudoscalar ( $^1\mathrm{S}_0^{[1]}$ ) quasi-bound toponium state, as predicted by nonrelativistic quantum chromodynamics. Using a simplified model for $^1\mathrm{S}_0^{[1]}$ toponium, the cross section of the excess above the pQCD prediction is measured to be 8.8 $^{+1.2}_{-1.4}$ pb.
Links: e-print arXiv:2503.22382 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; Physics Briefing ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Observed (points with statistical error bars) and predicted (stacked colored histograms) $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ distribution in three out of nine ( $c_\text{hel}$ , $c_\text{han}$ ) bins. In the upper panels, the $\mathrm{t} \overline{\mathrm{t}}$ histogram shows the FO pQCD prediction after the fit to the data that includes the $\eta_{\mathrm{t}}$ signal model (whose contribution is not drawn), and the shown event rates are divided by the bin width. The lower panels display the ratio of the data to the FO pQCD $+$ background prediction, with $\eta_{\mathrm{t}}$ signal overlaid at its best fit $\eta_{\mathrm{t}}$ cross section (red line). The gray band indicates the postfit uncertainty. The first and last $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ bins include all events with reconstructed $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ below 360 and above 1300 GeV, respectively, and the drawn bin width is used for the normalization in these bins.
png pdf	Figure 1-a: Observed (points with statistical error bars) and predicted (stacked colored histograms) $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ distribution in one out of nine bins ( $c_\text{hel} \in [-1, -1/3]$ , $c_\text{han} \in [-1, -1/3]$ ). In the upper panel, the $\mathrm{t} \overline{\mathrm{t}}$ histogram shows the FO pQCD prediction after the fit to the data that includes the $\eta_{\mathrm{t}}$ signal model (whose contribution is not drawn), and the shown event rates are divided by the bin width. The lower panel displays the ratio of the data to the FO pQCD $+$ background prediction, with $\eta_{\mathrm{t}}$ signal overlaid at its best fit $\eta_{\mathrm{t}}$ cross section (red line). The gray band indicates the postfit uncertainty. The first and last $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ bins include all events with reconstructed $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ below 360 and above 1300 GeV, respectively, and the drawn bin width is used for the normalization in these bins.
png pdf	Figure 1-b: Observed (points with statistical error bars) and predicted (stacked colored histograms) $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ distribution in one out of nine bins ( $c_\text{hel} \in [-1/3,1/3]$ , $c_\text{han} \in [-1/3,1/3]$ ). In the upper panel, the $\mathrm{t} \overline{\mathrm{t}}$ histogram shows the FO pQCD prediction after the fit to the data that includes the $\eta_{\mathrm{t}}$ signal model (whose contribution is not drawn), and the shown event rates are divided by the bin width. The lower panel displays the ratio of the data to the FO pQCD $+$ background prediction, with $\eta_{\mathrm{t}}$ signal overlaid at its best fit $\eta_{\mathrm{t}}$ cross section (red line). The gray band indicates the postfit uncertainty. The first and last $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ bins include all events with reconstructed $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ below 360 and above 1300 GeV, respectively, and the drawn bin width is used for the normalization in these bins.
png pdf	Figure 1-c: Observed (points with statistical error bars) and predicted (stacked colored histograms) $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ distribution in one out of nine bins ( $c_\text{hel} \in [1/3,1]$ , $c_\text{han} \in [1/3,1]$ ). In the upper panel, the $\mathrm{t} \overline{\mathrm{t}}$ histogram shows the FO pQCD prediction after the fit to the data that includes the $\eta_{\mathrm{t}}$ signal model (whose contribution is not drawn), and the shown event rates are divided by the bin width. The lower panel displays the ratio of the data to the FO pQCD $+$ background prediction, with $\eta_{\mathrm{t}}$ signal overlaid at its best fit $\eta_{\mathrm{t}}$ cross section (red line). The gray band indicates the postfit uncertainty. The first and last $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ bins include all events with reconstructed $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ below 360 and above 1300 GeV, respectively, and the drawn bin width is used for the normalization in these bins.
png pdf	Figure 2: Observed (points with statistical error bars) and predicted (stacked colored histograms) distributions. Left: $c_\text{hel}$ for $m_{{\mathrm{t}\overline{\mathrm{t}}} } <$ 360 GeV and integrated over $c_\text{han}$ , from the nominal fit using $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ . Right: $\smash{m_{\mathrm{b}\mathrm{b}\ell\ell}}$ integrated over $c_\text{hel}$ and $c_\text{han}$ , from the alternative fit using $\smash{m_{\mathrm{b}\mathrm{b}\ell\ell}}$ instead of $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ , which is discussed in Section 4.1. In the upper panels, the $\mathrm{t} \overline{\mathrm{t}}$ histogram shows the FO pQCD prediction after the fit to the data that includes the $\eta_{\mathrm{t}}$ signal model (whose contribution is not drawn). On the right, the shown event rates are divided by the bin width. The lower panels display the ratio of the data to the FO pQCD $+$ background prediction, with $\eta_{\mathrm{t}}$ signal overlaid at its best fit $\eta_{\mathrm{t}}$ cross section (red line). The gray band indicates the postfit uncertainty. The first and last $\smash{m_{\mathrm{b}\mathrm{b}\ell\ell}}$ bins include all events with reconstructed $\smash{m_{\mathrm{b}\mathrm{b}\ell\ell}}$ below 100 and above 750 GeV, respectively, and the drawn bin width is used for the normalization in these bins.
png pdf	Figure 2-a: Observed (points with statistical error bars) and predicted (stacked colored histograms) $c_\text{hel}$ distribution for $m_{{\mathrm{t}\overline{\mathrm{t}}} } <$ 360 GeV and integrated over $c_\text{han}$ , from the nominal fit using $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ . In the upper panel, the $\mathrm{t} \overline{\mathrm{t}}$ histogram shows the FO pQCD prediction after the fit to the data that includes the $\eta_{\mathrm{t}}$ signal model (whose contribution is not drawn). The lower panel displays the ratio of the data to the FO pQCD $+$ background prediction, with $\eta_{\mathrm{t}}$ signal overlaid at its best fit $\eta_{\mathrm{t}}$ cross section (red line). The gray band indicates the postfit uncertainty.
png pdf	Figure 2-b: Observed (points with statistical error bars) and predicted (stacked colored histograms) $\smash{m_{\mathrm{b}\mathrm{b}\ell\ell}}$ distribution integrated over $c_\text{hel}$ and $c_\text{han}$ , from the alternative fit using $\smash{m_{\mathrm{b}\mathrm{b}\ell\ell}}$ instead of $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ , which is discussed in Section 4.1. In the upper panel, the $\mathrm{t} \overline{\mathrm{t}}$ histogram shows the FO pQCD prediction after the fit to the data that includes the $\eta_{\mathrm{t}}$ signal model (whose contribution is not drawn). The shown event rates are divided by the bin width. The lower panel displays the ratio of the data to the FO pQCD $+$ background prediction, with $\eta_{\mathrm{t}}$ signal overlaid at its best fit $\eta_{\mathrm{t}}$ cross section (red line). The gray band indicates the postfit uncertainty. The first and last $\smash{m_{\mathrm{b}\mathrm{b}\ell\ell}}$ bins include all events with reconstructed $\smash{m_{\mathrm{b}\mathrm{b}\ell\ell}}$ below 100 and above 750 GeV, respectively, and the drawn bin width is used for the normalization in these bins.
png pdf	Figure 3: Best fit value (cross) and allowed regions at one (solid line), three (dashed line), and five (dotted-dashed line) SDs for the cross section of $\eta_{\mathrm{t}}$ and $\chi \mathrm{t}$ production, as observed in data (black). The FO pQCD $+$ background expectation of zero $\eta_{\mathrm{t}}$ and $\chi \mathrm{t}$ contributions is denoted by a pink star. Negative cross section values refer to a reduction of the $\mathrm{t} \overline{\mathrm{t}}$ production cross sections with respect to the FO pQCD $+$ background prediction around the threshold.
png pdf	Figure 4: Observed (points with statistical error bars) and predicted (stacked colored histograms) $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ distribution in the ( $c_\text{hel}$ , $c_\text{han}$ ) bin with the highest expected $\eta_{\mathrm{t}}$ contribution (left) and $c_\text{hel}$ distribution for $m_{{\mathrm{t}\overline{\mathrm{t}}} } <$ 360 GeV and integrated over $c_\text{han}$ (right). In the upper panels, the histograms account only for the FO pQCD $+$ background prediction, and are shown after the background-only fit to the data. On the left, the shown event rates are divided by the bin width. The lower panels display the ratio of the data to the FO pQCD $+$ background prediction. The gray band indicates the postfit uncertainty. The binning is the same as in Figs. 1 and 2 (left).
png pdf	Figure 4-a: Observed (points with statistical error bars) and predicted (stacked colored histograms) $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ distribution in the ( $c_\text{hel}$ , $c_\text{han}$ ) bin with the highest expected $\eta_{\mathrm{t}}$ contribution. In the upper panel, the histograms account only for the FO pQCD $+$ background prediction, and are shown after the background-only fit to the data. The shown event rates are divided by the bin width. The lower panel displays the ratio of the data to the FO pQCD $+$ background prediction. The gray band indicates the postfit uncertainty. The binning is the same as in Figs. 1.
png pdf	Figure 4-b: Observed (points with statistical error bars) and predicted (stacked colored histograms) $c_\text{hel}$ distribution for $m_{{\mathrm{t}\overline{\mathrm{t}}} } <$ 360 GeV and integrated over $c_\text{han}$ . In the upper panel, the histograms account only for the FO pQCD $+$ background prediction, and are shown after the background-only fit to the data. The lower panel displays the ratio of the data to the FO pQCD $+$ background prediction. The gray band indicates the postfit uncertainty. The binning is the same as in Fig. 2-a.
png pdf	Figure 5: For the nuisance parameters listed in the left column, the pulls $(\hat{\theta}-\theta_0)/\Delta\theta$ (middle column), where $\hat{\theta}$ and $\theta_0$ are the postfit and prefit values of the nuisance parameters and $\Delta\theta$ is the prefit uncertainty, are shown for the FO pQCD $+$ background ${+}\eta_{\mathrm{t}}$ (black filled circles) and FO pQCD $+$ background (gray empty circles) fit, as well as the impacts $\Delta\hat{\sigma}({{\eta}_{\mathrm{t}}} )$ (right column) for the FO pQCD $+$ background ${+}\eta_{\mathrm{t}}$ fit. The impact $\Delta\hat{\sigma}({{\eta}_{\mathrm{t}}} )$ for a nuisance parameter $\theta$ is calculated by varying $\theta$ by $\pm$ 1 SD and evaluating the shift in $\sigma({{\eta}_{\mathrm{t}}} )$ . The nuisance parameters are ordered by the maximum of their $\pm$ 1 SD impacts in the FO pQCD $+$ background ${+}\eta_{\mathrm{t}}$ fit.
png pdf	Figure 6: Ratios of the predictions for POWHEG v2 hvq $+$ HERWIG (gray) as well as POWHEG vRES bb4l $+$ PYTHIA (orange) to POWHEG v2 hvq $+$ PYTHIA (black) for $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ (left), $c_\text{hel}$ at the $\mathrm{t} \overline{\mathrm{t}}$ threshold ( $m_{{\mathrm{t}\overline{\mathrm{t}}} } <$ 360 GeV, center), and $c_\text{hel}$ in the $\mathrm{t} \overline{\mathrm{t}}$ continuum (600 $< m_{{\mathrm{t}\overline{\mathrm{t}}} } <$ 800 GeV, right), both integrated over $c_\text{han}$ . The effect of adding $\eta_{\mathrm{t}}$ to POWHEG v2 hvq $+$ PYTHIA is shown in red for comparison. The binning is the same as in Figs. 1 and 2 (left).
png pdf	Figure 6-a: Ratios of the predictions for POWHEG v2 hvq $+$ HERWIG (gray) as well as POWHEG vRES bb4l $+$ PYTHIA (orange) to POWHEG v2 hvq $+$ PYTHIA (black) for $m_{{\mathrm{t}\overline{\mathrm{t}}} }$ The effect of adding $\eta_{\mathrm{t}}$ to POWHEG v2 hvq $+$ PYTHIA is shown in red for comparison. The binning is the same as in Figs. 1.
png pdf	Figure 6-b: Ratios of the predictions for POWHEG v2 hvq $+$ HERWIG (gray) as well as POWHEG vRES bb4l $+$ PYTHIA (orange) to POWHEG v2 hvq $+$ PYTHIA (black) for $c_\text{hel}$ at the $\mathrm{t} \overline{\mathrm{t}}$ threshold ( $m_{{\mathrm{t}\overline{\mathrm{t}}} } <$ 360 GeV), integrated over $c_\text{han}$ . The effect of adding $\eta_{\mathrm{t}}$ to POWHEG v2 hvq $+$ PYTHIA is shown in red for comparison. The binning is the same as in Fig 2-a.
png pdf	Figure 6-c: Ratios of the predictions for POWHEG v2 hvq $+$ HERWIG (gray) as well as POWHEG vRES bb4l $+$ PYTHIA (orange) to POWHEG v2 hvq $+$ PYTHIA (black) for $c_\text{hel}$ in the $\mathrm{t} \overline{\mathrm{t}}$ continuum (600 $< m_{{\mathrm{t}\overline{\mathrm{t}}} } <$ 800 GeV), integrated over $c_\text{han}$ . The effect of adding $\eta_{\mathrm{t}}$ to POWHEG v2 hvq $+$ PYTHIA is shown in red for comparison. The binning is the same as in Fig 2-a.

Tables

png pdf

Table 1:
Results for

$\sigma({{\eta}_{\mathrm{t}}} )$ obtained with different simulated event samples for the FO pQCD

$\mathrm{t} \overline{\mathrm{t}}$ (+

$\mathrm{t}\mathrm{W}$ ) prediction. Nuisance parameters encoding the difference between different generators are not included in these results. The nominal result, i.e.,, POWHEG v2 hvq

$+$ PYTHIA including these nuisance parameters, is shown for comparison.

Summary

We report the observation of resonant top quark-antiquark (

$\mathrm{t} \overline{\mathrm{t}}$ ) production near the kinematic production threshold, with spin properties consistent with contributions from a pseudoscalar state, using proton-proton collision data recorded by the CMS experiment at

$\sqrt{s}=$ 13 TeV in 2016-2018 and corresponding to an integrated luminosity of 138 fb

$^{-1}$ . The data is compared to the standard model prediction including only nonresonant

$\mathrm{t} \overline{\mathrm{t}}$ production obtained with fixed-order calculations in perturbative quantum chromodynamics. An excess is observed with respect to this model, with a statistical significance exceeding five standard deviations. We emphasize, however, that the modeling of the

$\mathrm{t} \overline{\mathrm{t}}$ threshold region is challenging and requires further theoretical investigation. It is worth noting that alternative explanations of the excess are also plausible, given the current experimental resolution of the

$\mathrm{t} \overline{\mathrm{t}}$ invariant mass; we explore this direction further in Ref. [20]. The result is compatible with the formation of a

$^1\mathrm{S}_0^{[1]}$ toponium quasi-bound state

$\eta_{\mathrm{t}}$ with a measured cross section of

$\sigma({{\eta}{\mathrm{t}}} )=$ 8.8

$^{+1.2}_{-1.4}$ pb, based on a simplified model inspired by nonrelativistic quantum chromodynamics.

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107	CMS Collaboration	Measurement of the production cross section for single top quarks in association with W bosons in proton-proton collisions at $\sqrt{s}=$ 13 TeV	JHEP 10 (2018) 117	CMS-TOP-17-018 1805.07399
108	CMS Collaboration	Measurement of the cross section for top quark pair production in association with a W or Z boson in proton-proton collisions at $\sqrt{s}=$ 13 TeV	JHEP 08 (2018) 011	CMS-TOP-17-005 1711.02547
109	ATLAS Collaboration	Measurement of the ${{\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z}}$ and ${{\mathrm{t}\overline{\mathrm{t}}} \mathrm{W}}$ cross sections in proton-proton collisions at $\sqrt{s}=$ 13 TeV with the ATLAS detector	PRD 99 (2019) 072009	1901.03584
110	ATLAS Collaboration	Measurements of top-quark pair to Z-boson cross-section ratios at $\sqrt{s}=$ 13, 8, 7 TeV with the ATLAS detector	JHEP 02 (2017) 117	1612.03636