CMSPASHIG22013  
Search for heavy pseudoscalar and scalar bosons decaying to top quark pairs in protonproton collisions at $ \sqrt{s}= $ 13 TeV  
CMS Collaboration  
1 October 2024  
Abstract: A search for heavy pseudoscalar or scalar bosons decaying to a top quark pair ($ \mathrm{t\bar{t}} $) in final states with one or two charged leptons is presented, using 138 fb$ ^{1} $ of protonproton collisions at $ \sqrt{s}= $ 13 TeV recorded by the CMS experiment at the CERN LHC. The invariant mass of the reconstructed $ \mathrm{t\bar{t}} $ system and variables sensitive to its spin state are used to discriminate against the standard model $ \mathrm{t\bar{t}} $ background. An excess of the data above the background prediction, as modeled using perturbative quantum chromodynamics (QCD) only, is observed. The excess is located close to the $ \mathrm{t\bar{t}} $ production threshold and it significantly favors the pseudoscalar signal hypothesis over the scalar hypothesis. It is compatible with the production of a $ ^1S_0^{[1]}$ $\mathrm{t\bar{t}} $ bound state ($ \eta_{\mathrm{t}} $), as predicted by a simplified model of nonrelativistic QCD, with a cross section of 7.1 pb and an uncertainty of 11%. The excess has a significance of above five standard deviations. Including the $ \eta_{\mathrm{t}} $ contribution in the background modeling, exclusion limits at 95% confidence level are set on the coupling of further pseudoscalar or scalar bosons to top quarks in a mass range of 3651000 GeV and relative widths of 0.525%.  
Links: CDS record (PDF) ; CADI line (restricted) ; 
Figures & Tables  Summary  Additional Figures  References  CMS Publications 

Figures  
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Figure 1:
The Feynman diagram for the signal process (left) and an example diagram for the SM production of top quark pairs (right). 
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Figure 1a:
The Feynman diagram for the signal process (left) and an example diagram for the SM production of top quark pairs (right). 
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Figure 1b:
The Feynman diagram for the signal process (left) and an example diagram for the SM production of top quark pairs (right). 
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Figure 2:
Normalized differential cross sections in the spin correlation observables $ c_\text{hel} $ (left) and $ c_\text{han} $ (right) at the parton level in the $ \ell \bar{\ell} $ channel, with no requirements on acceptance, for SM $ \mathrm{t} \overline{\mathrm{t}} $ (black), resonant $ \mathrm{A} $ (red), resonant H (blue), $ \eta_{\mathrm{t}} $ (green) production. 
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Figure 2a:
Normalized differential cross sections in the spin correlation observables $ c_\text{hel} $ (left) and $ c_\text{han} $ (right) at the parton level in the $ \ell \bar{\ell} $ channel, with no requirements on acceptance, for SM $ \mathrm{t} \overline{\mathrm{t}} $ (black), resonant $ \mathrm{A} $ (red), resonant H (blue), $ \eta_{\mathrm{t}} $ (green) production. 
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Figure 2b:
Normalized differential cross sections in the spin correlation observables $ c_\text{hel} $ (left) and $ c_\text{han} $ (right) at the parton level in the $ \ell \bar{\ell} $ channel, with no requirements on acceptance, for SM $ \mathrm{t} \overline{\mathrm{t}} $ (black), resonant $ \mathrm{A} $ (red), resonant H (blue), $ \eta_{\mathrm{t}} $ (green) production. 
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Figure 3:
Observed and expected $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution in $ \lvert\cos\theta^\ast_{\mathrm{t}_{\ell}}\rvert $ bins, shown for the $ \ell,\,3{\mathrm{j}} $ channel summed over lepton flavors and analysis eras. In the first panel, the data (points with statistical error bars) and predicted pQCDonly background (colored histograms) are compared before the fit to the data, and the corresponding prefit uncertainty is shown with a gray band. In the second panel, the ratio of the data to the sum of the pQCDonly background is shown, and three signal hypotheses ($\mathrm{A(365,2\%)}$, $\mathrm{H(365,2\%)}$, and $ \eta_{\mathrm{t}} $) are overlaid for illustration. In the third and fourth panels, the ratio is shown with the best fit normalization applied for two different interpretations: either fitting only the $ {\mathrm{A}}\text{/}{\mathrm{H}} $ signal with no $ \eta_{\mathrm{t}} $ considered in the background (third panel), or fitting only $ \eta_{\mathrm{t}} $ (fourth panel). In both cases, the gray band shows the postfit uncertainty, and the respective signals are overlaid with their best fit model parameters. 
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Figure 4:
Observed and expected $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution in $ \lvert\cos\theta^\ast_{\mathrm{t}_{\ell}}\rvert $ bins, shown for the $ \ell,\,\geq4{\mathrm{j}} $ channel summed over lepton flavors and analysis eras. Notations as in Fig. 3. 
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Figure 5:
Observed and expected $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution in $ c_\text{hel} $ and $ c_\text{han} $ bins, shown for the $ \ell \bar{\ell} $ channel summed over lepton flavors and analysis eras. Notations as in Fig. 3. 
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Figure 6:
Modelindependent constraints on $ c $ as a function of the $ \mathrm{A} $ mass for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{A} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the $ \mathrm{A} $ total width is indicated by the hatched line. 
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Figure 6a:
Modelindependent constraints on $ c $ as a function of the $ \mathrm{A} $ mass for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{A} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the $ \mathrm{A} $ total width is indicated by the hatched line. 
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Figure 6b:
Modelindependent constraints on $ c $ as a function of the $ \mathrm{A} $ mass for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{A} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the $ \mathrm{A} $ total width is indicated by the hatched line. 
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Figure 6c:
Modelindependent constraints on $ c $ as a function of the $ \mathrm{A} $ mass for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{A} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the $ \mathrm{A} $ total width is indicated by the hatched line. 
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Figure 6d:
Modelindependent constraints on $ c $ as a function of the $ \mathrm{A} $ mass for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{A} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the $ \mathrm{A} $ total width is indicated by the hatched line. 
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Figure 6e:
Modelindependent constraints on $ c $ as a function of the $ \mathrm{A} $ mass for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{A} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the $ \mathrm{A} $ total width is indicated by the hatched line. 
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Figure 6f:
Modelindependent constraints on $ c $ as a function of the $ \mathrm{A} $ mass for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{A} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the $ \mathrm{A} $ total width is indicated by the hatched line. 
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Figure 7:
Modelindependent constraints on $ g_{\mathrm{H t\bar{t}}} $ as a function of the H mass, for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{H} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the H total width is indicated by the hatched line. 
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Figure 7a:
Modelindependent constraints on $ g_{\mathrm{H t\bar{t}}} $ as a function of the H mass, for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{H} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the H total width is indicated by the hatched line. 
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Figure 7b:
Modelindependent constraints on $ g_{\mathrm{H t\bar{t}}} $ as a function of the H mass, for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{H} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the H total width is indicated by the hatched line. 
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Figure 7c:
Modelindependent constraints on $ g_{\mathrm{H t\bar{t}}} $ as a function of the H mass, for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{H} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the H total width is indicated by the hatched line. 
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Figure 7d:
Modelindependent constraints on $ g_{\mathrm{H t\bar{t}}} $ as a function of the H mass, for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{H} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the H total width is indicated by the hatched line. 
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Figure 7e:
Modelindependent constraints on $ g_{\mathrm{H t\bar{t}}} $ as a function of the H mass, for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{H} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the H total width is indicated by the hatched line. 
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Figure 7f:
Modelindependent constraints on $ g_{\mathrm{H t\bar{t}}} $ as a function of the H mass, for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{H} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the H total width is indicated by the hatched line. 
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Figure 8:
Pulls and impacts of the nuisance parameters with the largest impact in the $ \eta_{\mathrm{t}} $ interpretation. A detailed description of the nuisance parameters relating to the jet $ p_{\mathrm{T}} $ scale is provided in Ref. [35]. 
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Figure 9:
Correlation matrix between the $ \eta_{\mathrm{t}} $ signal strength and nuisance parameters with the largest impact in the $ \eta_{\mathrm{t}} $ interpretation. A detailed description of the nuisance parameters relating to the jet $ p_{\mathrm{T}} $ scale is provided in Ref. [35]. 
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Figure 10:
Modelindependent constraints on $ g_{\mathrm{A t\bar{t}}} $ as a function of the $ \mathrm{A} $ mass for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{A} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the $ \mathrm{A} $ total width is indicated by the hatched line. 
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Figure 10a:
Modelindependent constraints on $ g_{\mathrm{A t\bar{t}}} $ as a function of the $ \mathrm{A} $ mass for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{A} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the $ \mathrm{A} $ total width is indicated by the hatched line. 
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Figure 10b:
Modelindependent constraints on $ g_{\mathrm{A t\bar{t}}} $ as a function of the $ \mathrm{A} $ mass for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{A} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the $ \mathrm{A} $ total width is indicated by the hatched line. 
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Figure 10c:
Modelindependent constraints on $ g_{\mathrm{A t\bar{t}}} $ as a function of the $ \mathrm{A} $ mass for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{A} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the $ \mathrm{A} $ total width is indicated by the hatched line. 
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Figure 10d:
Modelindependent constraints on $ g_{\mathrm{A t\bar{t}}} $ as a function of the $ \mathrm{A} $ mass for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{A} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the $ \mathrm{A} $ total width is indicated by the hatched line. 
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Figure 10e:
Modelindependent constraints on $ g_{\mathrm{A t\bar{t}}} $ as a function of the $ \mathrm{A} $ mass for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{A} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the $ \mathrm{A} $ total width is indicated by the hatched line. 
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Figure 10f:
Modelindependent constraints on $ g_{\mathrm{A t\bar{t}}} $ as a function of the $ \mathrm{A} $ mass for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{A} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the $ \mathrm{A} $ total width is indicated by the hatched line. 
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Figure 11:
Modelindependent constraints on $ g_{\mathrm{H t\bar{t}}} $ as a function of the H mass, for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{H} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the H total width is indicated by the hatched line. 
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Figure 11a:
Modelindependent constraints on $ g_{\mathrm{H t\bar{t}}} $ as a function of the H mass, for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{H} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the H total width is indicated by the hatched line. 
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Figure 11b:
Modelindependent constraints on $ g_{\mathrm{H t\bar{t}}} $ as a function of the H mass, for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{H} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the H total width is indicated by the hatched line. 
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Figure 11c:
Modelindependent constraints on $ g_{\mathrm{H t\bar{t}}} $ as a function of the H mass, for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{H} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the H total width is indicated by the hatched line. 
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Figure 11d:
Modelindependent constraints on $ g_{\mathrm{H t\bar{t}}} $ as a function of the H mass, for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{H} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the H total width is indicated by the hatched line. 
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Figure 11e:
Modelindependent constraints on $ g_{\mathrm{H t\bar{t}}} $ as a function of the H mass, for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{H} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the H total width is indicated by the hatched line. 
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Figure 11f:
Modelindependent constraints on $ g_{\mathrm{H t\bar{t}}} $ as a function of the H mass, for relative widths of 1, 2, 5, 10, 18, and 25%. The observed constraints are indicated by the blue shaded area. The inner green band and the outer yellow band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the backgroundonly hypothesis. The unphysical region of phase space in which the partial width $ \Gamma_{\mathrm{H} \to {\mathrm{t}\overline{\mathrm{t}}} } $ becomes larger than the H total width is indicated by the hatched line. 
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Figure 12:
Frequentist 2D exclusion contours for $ g_{\mathrm{A t\bar{t}}} $ and $ g_{\mathrm{H t\bar{t}}} $ in the $ {\mathrm{A}}\text{+}{\mathrm{H}} $ interpretation for four different signal hypotheses: $ g_{\mathrm{A(365,2\%)}} $ + $ g_{\mathrm{H(365,2\%)}} $ (upper left), $ g_{\mathrm{A(365,2\%)}} $ + $ g_{\mathrm{H(1000,5\%)}} $ (upper right), $ g_{\mathrm{A(1000,5\%)}} $ + $ g_{\mathrm{H(365,2\%)}} $ (lower left), and $ g_{\mathrm{A(1000,5\%)}} $+ $ g_{\mathrm{H(1000,5\%)}} $ (lower right). The expected and observed contours, evaluated with the FeldmanCousins prescription [108], are shown in black and red, respectively, with the solid and dashed lines corresponding to exclusions at 68 and 95% CL, and the respective bestfit points for $ g_{\mathrm{A t\bar{t}}} $ and $ g_{\mathrm{H t\bar{t}}} $ are shown as the colored crosses. In all cases, the $ \eta_{\mathrm{t}} $ contribution is considered as part of the background. 
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Figure 12a:
Frequentist 2D exclusion contours for $ g_{\mathrm{A t\bar{t}}} $ and $ g_{\mathrm{H t\bar{t}}} $ in the $ {\mathrm{A}}\text{+}{\mathrm{H}} $ interpretation for four different signal hypotheses: $ g_{\mathrm{A(365,2\%)}} $ + $ g_{\mathrm{H(365,2\%)}} $ (upper left), $ g_{\mathrm{A(365,2\%)}} $ + $ g_{\mathrm{H(1000,5\%)}} $ (upper right), $ g_{\mathrm{A(1000,5\%)}} $ + $ g_{\mathrm{H(365,2\%)}} $ (lower left), and $ g_{\mathrm{A(1000,5\%)}} $+ $ g_{\mathrm{H(1000,5\%)}} $ (lower right). The expected and observed contours, evaluated with the FeldmanCousins prescription [108], are shown in black and red, respectively, with the solid and dashed lines corresponding to exclusions at 68 and 95% CL, and the respective bestfit points for $ g_{\mathrm{A t\bar{t}}} $ and $ g_{\mathrm{H t\bar{t}}} $ are shown as the colored crosses. In all cases, the $ \eta_{\mathrm{t}} $ contribution is considered as part of the background. 
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Figure 12b:
Frequentist 2D exclusion contours for $ g_{\mathrm{A t\bar{t}}} $ and $ g_{\mathrm{H t\bar{t}}} $ in the $ {\mathrm{A}}\text{+}{\mathrm{H}} $ interpretation for four different signal hypotheses: $ g_{\mathrm{A(365,2\%)}} $ + $ g_{\mathrm{H(365,2\%)}} $ (upper left), $ g_{\mathrm{A(365,2\%)}} $ + $ g_{\mathrm{H(1000,5\%)}} $ (upper right), $ g_{\mathrm{A(1000,5\%)}} $ + $ g_{\mathrm{H(365,2\%)}} $ (lower left), and $ g_{\mathrm{A(1000,5\%)}} $+ $ g_{\mathrm{H(1000,5\%)}} $ (lower right). The expected and observed contours, evaluated with the FeldmanCousins prescription [108], are shown in black and red, respectively, with the solid and dashed lines corresponding to exclusions at 68 and 95% CL, and the respective bestfit points for $ g_{\mathrm{A t\bar{t}}} $ and $ g_{\mathrm{H t\bar{t}}} $ are shown as the colored crosses. In all cases, the $ \eta_{\mathrm{t}} $ contribution is considered as part of the background. 
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Figure 12c:
Frequentist 2D exclusion contours for $ g_{\mathrm{A t\bar{t}}} $ and $ g_{\mathrm{H t\bar{t}}} $ in the $ {\mathrm{A}}\text{+}{\mathrm{H}} $ interpretation for four different signal hypotheses: $ g_{\mathrm{A(365,2\%)}} $ + $ g_{\mathrm{H(365,2\%)}} $ (upper left), $ g_{\mathrm{A(365,2\%)}} $ + $ g_{\mathrm{H(1000,5\%)}} $ (upper right), $ g_{\mathrm{A(1000,5\%)}} $ + $ g_{\mathrm{H(365,2\%)}} $ (lower left), and $ g_{\mathrm{A(1000,5\%)}} $+ $ g_{\mathrm{H(1000,5\%)}} $ (lower right). The expected and observed contours, evaluated with the FeldmanCousins prescription [108], are shown in black and red, respectively, with the solid and dashed lines corresponding to exclusions at 68 and 95% CL, and the respective bestfit points for $ g_{\mathrm{A t\bar{t}}} $ and $ g_{\mathrm{H t\bar{t}}} $ are shown as the colored crosses. In all cases, the $ \eta_{\mathrm{t}} $ contribution is considered as part of the background. 
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Figure 12d:
Frequentist 2D exclusion contours for $ g_{\mathrm{A t\bar{t}}} $ and $ g_{\mathrm{H t\bar{t}}} $ in the $ {\mathrm{A}}\text{+}{\mathrm{H}} $ interpretation for four different signal hypotheses: $ g_{\mathrm{A(365,2\%)}} $ + $ g_{\mathrm{H(365,2\%)}} $ (upper left), $ g_{\mathrm{A(365,2\%)}} $ + $ g_{\mathrm{H(1000,5\%)}} $ (upper right), $ g_{\mathrm{A(1000,5\%)}} $ + $ g_{\mathrm{H(365,2\%)}} $ (lower left), and $ g_{\mathrm{A(1000,5\%)}} $+ $ g_{\mathrm{H(1000,5\%)}} $ (lower right). The expected and observed contours, evaluated with the FeldmanCousins prescription [108], are shown in black and red, respectively, with the solid and dashed lines corresponding to exclusions at 68 and 95% CL, and the respective bestfit points for $ g_{\mathrm{A t\bar{t}}} $ and $ g_{\mathrm{H t\bar{t}}} $ are shown as the colored crosses. In all cases, the $ \eta_{\mathrm{t}} $ contribution is considered as part of the background. 
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Figure A1:
Local significance contours for the pair of $\mathrm{A/H(365,2\%}$, considering only the resonant signal components. Different line styles are used to indicate the regions compatible with the data at progressive confidence levels. 
Tables  
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Table 1:
Derived scale factors for the $ \mathrm{Z}\text{/}\gamma^\ast $ event yield in the different lepton flavor final states, and their statistical uncertainties. 
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Table 2:
The systematic uncertainties considered in the analysis, indicating the number of corresponding nuisance parameters (if not one) in the statistical model, the type (affecting only normalization or also the shape of the search templates), and the affected processes and analysis channels they are applicable to. 
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Table B1:
Results on the $ \eta_{\mathrm{t}} $ cross section, using only the $ \ell \bar{\ell} $ channels, for the $g_{\mathrm{A{365,{2\%}}}}$ background prediction and for the default setup. The quoted uncertainty for bb4$\ell$ assumes the same uncertainty as for the nominal result. 
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Table C1:
Bestfit values of the signal strengths or coupling modifiers as well as differences in $ 2 \ln L $ between the bestfit point and the backgroundonly hypothesis for the $ \eta_{\mathrm{t}} $, single $ \mathrm{A} $ boson, and single H boson interpretations. 
Summary 
A search for the production of heavy pseudoscalar or scalar bosons produced in protonproton collisions at $ \sqrt{s}= $ 13 TeV and decaying to a top quark pair ($ \mathrm{t} \overline{\mathrm{t}} $) in the final states with one or two charged leptons is presented, using data corresponding to an integrated luminosity of 138 fb$ ^{1} $ recorded with the CMS detector at the LHC. The invariant mass of the reconstructed $ \mathrm{t} \overline{\mathrm{t}} $ system and angular variables sensitive to its spin are used to discriminate the signal from the standard model $ \mathrm{t} \overline{\mathrm{t}} $ background. Both resonant production of the new boson and interference terms with the perturbative QCD (pQCD) $ \mathrm{t} \overline{\mathrm{t}} $ background are included in the signal model. A deviation from the background prediction, modeled only using pQCD, is observed. It is located close to the $ \mathrm{t} \overline{\mathrm{t}} $ production threshold, similar to the moderate deviation observed in a previous CMS search based on a data sample corresponding to an integrated luminosity of 35.9 fb$ ^{1} $ [24]. This deviation significantly favors the pseudoscalar signal hypothesis over the scalar hypothesis. It is compatible with the production of a $ ^1S_0^{[1]} $ $ \mathrm{t} \overline{\mathrm{t}} $ bound state $ \eta_{\mathrm{t}} $, as predicted by a simplified model of nonrelativistic QCD. The cross section of this contribution is found to be $ \sigma (\eta_{\mathrm{t}}) = $ 7.1 pb, with an uncertainty of 11%. The excess has a significance of above five standard deviations. Further investigations by both the experimental and theoretical communities are necessary to elucidate the nature of this excess. Including $ \eta_{\mathrm{t}} $ production with an unconstrained normalization in the background prediction leads to a good description of the observed data, with no hint for further new pseudoscalar or scalar boson production. Exclusion limits at 95% confidence level are set on the coupling strength between top quarks and new bosons, covering masses of 3651000 GeV and relative widths of 0.525%. Stringent constraints are found for the three cases of a new pseudoscalar boson, a new scalar boson, and the simultaneous presence of one new pseudoscalar and one new scalar boson, excluding coupling values as low as 0.4 (0.6) in the pseudoscalar (scalar) case. 
Additional Figures  
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Additional Figure 1:
Normalized differential cross sections in the cosine of the top quark scattering angle $ \cos\theta^\ast_{\mathrm{t}} $ at the parton level in the $ \ell \mathrm{j} $ channel, with no requirements on acceptance, for SM $ \mathrm{t} \overline{\mathrm{t}} $ (black), resonant $ \mathrm{A} $ (red), resonant H (blue), $ \eta_{\mathrm{t}} $ (green) production. 
png pdf 
Additional Figure 2:
Observed and expected $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution in $ \lvert\cos\theta^\ast_{\mathrm{t}_{\ell}}\rvert $ bins, shown for the $ \ell,\,3 \mathrm{j} $ channel summed over lepton flavors and analysis eras. In the upper panel, the data (points with statistical error bars) and predicted pQCDonly background (colored histograms) are compared before the fit to the data. In the lower panel, the ratio of the data to the sum of the pQCDonly background is shown, and the three signal hypotheses ($A(365,2\%)$, $H(365,2\%)$, and $ \eta_{\mathrm{t}} $) are overlaid for illustration. In both panels, the corresponding prefit uncertainty is shown with a gray band. The figure corresponds to the top ratio panel of Fig. 3 in the main body. 
png pdf 
Additional Figure 3:
Observed and expected $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution in $ \lvert\cos\theta^\ast_{\mathrm{t}_{\ell}}\rvert $ bins, shown for the $ \ell,\,\geq4 \mathrm{j} $ channel summed over lepton flavors and analysis eras. Notations as in Additional Fig. 2. The figure corresponds to the top ratio panel of Fig. 4 in the main body. 
png pdf 
Additional Figure 4:
Observed and expected $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution in $ c_\text{hel} $ and $ c_\text{han} $ bins, shown for the $ \ell \overline{\ell} $ channel summed over lepton flavors and analysis eras. Notations as in Additional Fig. 2. The figure corresponds to the top ratio panel of Fig. 5 in the main body. 
png pdf 
Additional Figure 5:
Observed and expected $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution in $ \lvert\cos\theta^\ast_{\mathrm{t}_{\ell}}\rvert $ bins, shown for the $ \ell,\,3 \mathrm{j} $ channel summed over lepton flavors and analysis eras. In the upper panel, the data (points with statistical error bars) and predicted pQCDonly background (colored histograms) are compared after the fit to the data using only the $ {\mathrm{A}}\text{/}{\mathrm{H}} $ signal with no $ \eta_{\mathrm{t}} $ considered in the background. In the lower panel, the ratio of the data to the sum of the pQCDonly background is shown, and the two signal hypotheses ($A(365,2\%)$ and $H(365,2\%)$) at their best fit model parameters are overlaid for illustration. In both panels, the corresponding postfit uncertainty is shown with a gray band. The figure corresponds to the middle ratio panel of Fig. 3 in the main body. 
png pdf 
Additional Figure 6:
Observed and expected $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution in $ \lvert\cos\theta^\ast_{\mathrm{t}_{\ell}}\rvert $ bins, shown for the $ \ell,\,\geq4 \mathrm{j} $ channel summed over lepton flavors and analysis eras. Notations as in Additional Fig. 5. The figure corresponds to the middle ratio panel of Fig. 4 in the main body. 
png pdf 
Additional Figure 7:
Observed and expected $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution in $ c_\text{hel} $ and $ c_\text{han} $ bins, shown for the $ \ell \overline{\ell} $ channel summed over lepton flavors and analysis eras. Notations as in Additional Fig. 5. The figure corresponds to the middle ratio panel of Fig. 5 in the main body. 
png pdf 
Additional Figure 8:
Observed and expected $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution in $ \lvert\cos\theta^\ast_{\mathrm{t}_{\ell}}\rvert $ bins, shown for the $ \ell,\,3 \mathrm{j} $ channel summed over lepton flavors and analysis eras. In the upper panel, the data (points with statistical error bars) and predicted pQCDonly background (colored histograms) are compared after the fit to the data using only $ \eta_{\mathrm{t}} $ as signal. In the lower panel, the ratio of the data to the sum of the pQCDonly background is shown, and the signal $ \eta_{\mathrm{t}} $ is overlaid with its best fit normalization for illustration. In both panels, the corresponding postfit uncertainty is shown with a gray band. The figure corresponds to the bottom ratio panel of Fig. 3 in the main body. 
png pdf 
Additional Figure 9:
Observed and expected $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution in $ \lvert\cos\theta^\ast_{\mathrm{t}_{\ell}}\rvert $ bins, shown for the $ \ell,\,\geq4 \mathrm{j} $ channel summed over lepton flavors and analysis eras. Notations as in Additional Fig. 8. The figure corresponds to the bottom ratio panel of Fig. 4 in the main body. 
png pdf 
Additional Figure 10:
Observed and expected $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution in $ c_\text{hel} $ and $ c_\text{han} $ bins, shown for the $ \ell \overline{\ell} $ channel summed over lepton flavors and analysis eras. Notations as in Additional Fig. 8. The figure corresponds to the bottom ratio panel of Fig. 5 in the main body. 
png pdf 
Additional Figure 11:
Observed and expected $ c_\text{hel} $ distributions in the $ \ell \overline{\ell} $ channel, summed over lepton flavors, analysis eras, $ c_\text{han} $ bins, and $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ ranges of $ m_{{\mathrm{t}\overline{\mathrm{t}}} } < $ 360 GeV (left) and 800 $ < m_{{\mathrm{t}\overline{\mathrm{t}}} } < $ 1050 GeV (right), before the fit to the data. $ \mathrm{A} $, H and $ \eta_{\mathrm{t}} $ signals are overlaid over the pQCD background prediction (black dashed line). The plots correspond to appropriate 1D projections of Fig. 5 in the main body. 
png pdf 
Additional Figure 11a:
Observed and expected $ c_\text{hel} $ distributions in the $ \ell \overline{\ell} $ channel, summed over lepton flavors, analysis eras, $ c_\text{han} $ bins, and $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ ranges of $ m_{{\mathrm{t}\overline{\mathrm{t}}} } < $ 360 GeV (left) and 800 $ < m_{{\mathrm{t}\overline{\mathrm{t}}} } < $ 1050 GeV (right), before the fit to the data. $ \mathrm{A} $, H and $ \eta_{\mathrm{t}} $ signals are overlaid over the pQCD background prediction (black dashed line). The plots correspond to appropriate 1D projections of Fig. 5 in the main body. 
png pdf 
Additional Figure 11b:
Observed and expected $ c_\text{hel} $ distributions in the $ \ell \overline{\ell} $ channel, summed over lepton flavors, analysis eras, $ c_\text{han} $ bins, and $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ ranges of $ m_{{\mathrm{t}\overline{\mathrm{t}}} } < $ 360 GeV (left) and 800 $ < m_{{\mathrm{t}\overline{\mathrm{t}}} } < $ 1050 GeV (right), before the fit to the data. $ \mathrm{A} $, H and $ \eta_{\mathrm{t}} $ signals are overlaid over the pQCD background prediction (black dashed line). The plots correspond to appropriate 1D projections of Fig. 5 in the main body. 
png pdf 
Additional Figure 12:
Observed and expected $ c_\text{hel} $ distributions in the $ \ell \overline{\ell} $ channel, summed over lepton flavors, analysis eras, $ c_\text{han} $ bins, and $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ ranges of $ m_{{\mathrm{t}\overline{\mathrm{t}}} } < $ 360 GeV (left) and 800 $ < m_{{\mathrm{t}\overline{\mathrm{t}}} } < $ 1050 GeV (right), after the fit to the data in the single$ \Phi $ interpretation. $ \mathrm{A} $ and H signals are overlaid over the pQCD background prediction (black dashed line), corresponding to the bestfit values of $g_{\mathrm{A t\bar{t}}}$ and $g_{\mathrm{H t\bar{t}}}$. The plots correspond to appropriate 1D projections of Fig. 5 in the main body. 
png pdf 
Additional Figure 12a:
Observed and expected $ c_\text{hel} $ distributions in the $ \ell \overline{\ell} $ channel, summed over lepton flavors, analysis eras, $ c_\text{han} $ bins, and $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ ranges of $ m_{{\mathrm{t}\overline{\mathrm{t}}} } < $ 360 GeV (left) and 800 $ < m_{{\mathrm{t}\overline{\mathrm{t}}} } < $ 1050 GeV (right), after the fit to the data in the single$ \Phi $ interpretation. $ \mathrm{A} $ and H signals are overlaid over the pQCD background prediction (black dashed line), corresponding to the bestfit values of $g_{\mathrm{A t\bar{t}}}$ and $g_{\mathrm{H t\bar{t}}}$. The plots correspond to appropriate 1D projections of Fig. 5 in the main body. 
png pdf 
Additional Figure 12b:
Observed and expected $ c_\text{hel} $ distributions in the $ \ell \overline{\ell} $ channel, summed over lepton flavors, analysis eras, $ c_\text{han} $ bins, and $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ ranges of $ m_{{\mathrm{t}\overline{\mathrm{t}}} } < $ 360 GeV (left) and 800 $ < m_{{\mathrm{t}\overline{\mathrm{t}}} } < $ 1050 GeV (right), after the fit to the data in the single$ \Phi $ interpretation. $ \mathrm{A} $ and H signals are overlaid over the pQCD background prediction (black dashed line), corresponding to the bestfit values of $g_{\mathrm{A t\bar{t}}}$ and $g_{\mathrm{H t\bar{t}}}$. The plots correspond to appropriate 1D projections of Fig. 5 in the main body. 
png pdf 
Additional Figure 13:
Observed and expected $ c_\text{hel} $ distributions in the $ \ell \overline{\ell} $ channel, summed over lepton flavors, analysis eras, $ c_\text{han} $ bins, and a $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ range of $ m_{{\mathrm{t}\overline{\mathrm{t}}} } < $ 360 GeV, after the fit to the data in the $ \eta_{\mathrm{t}} $ interpretation. The $ \eta_{\mathrm{t}} $ signal is overlaid over the pQCD background prediction (black dashed line), corresponding to the bestfit value of $ \mu(\eta_{\mathrm{t}} ) $. The plot corresponds to an appropriate 1D projection of Fig. 5 in the main body. 
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