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CMS-HIG-17-027 ; CERN-EP-2019-147
Search for heavy Higgs bosons decaying to a top quark pair in proton-proton collisions at $\sqrt{s} = $ 13 TeV
JHEP 04 (2020) 171
Abstract: A search is presented for additional scalar (H) or pseudoscalar (A) Higgs bosons decaying to a top quark pair in proton-proton collisions at a center-of-mass energy of 13 TeV. The data set analyzed corresponds to an integrated luminosity of 35.9 fb$^{-1}$ collected by the CMS experiment at the LHC. Final states with one or two charged leptons are considered. The invariant mass of the reconstructed top quark pair system and variables that are sensitive to the spin of the particles decaying into the top quark pair are used to search for signatures of the H or A bosons. The interference with the standard model top quark pair background is taken into account. A moderate signal-like deviation compatible with an A boson with a mass of 400 GeV is observed with a global significance of 1.9 standard deviations. New stringent constraints are reported on the strength of the coupling of the hypothetical bosons to the top quark, with the mass of the bosons ranging from 400 to 750 GeV and their total relative width from 0.5 to 25%. The results of the search are also interpreted in a minimal supersymmetric standard model scenario. Values of $m_{\mathrm{A}}$ from 400 to 700 GeV are probed, and a region with values of $\tan\beta$ below 1.0 to 1.5, depending on $m_{\mathrm{A}}$, is excluded at 95% confidence level.
Figures & Tables Summary Additional Figures & Material 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 (right).

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Figure 1-a:
The Feynman diagram for the signal process.

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Figure 1-b:
An example of Feynman diagram for the SM production of top quark.

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Figure 2:
Definition of angle $ {\theta ^*_{\mathrm{t} _\ell}}$ used in the single-lepton final state. Momenta in different coordinate systems are depicted with arrows of different colors and styles.

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Figure 3:
Observed and expected distributions of ${m_{{\mathrm{t} \mathrm{\bar{t}}}}}$ in different $ {| \cos {\theta ^*_{t_\ell}} |}$ regions in the e+jets (upper) and $\mu$+jets (lower) channels. The expected distributions have been obtained with a background-only fit to the data, and an approximate post-fit uncertainty is shown with a gray band. The impact of the best-fit signal is included in the lower panels for illustration.

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Figure 3-a:
Observed and expected distributions of ${m_{{\mathrm{t} \mathrm{\bar{t}}}}}$ in different $ {| \cos {\theta ^*_{t_\ell}} |}$ regions in the e+jets channel. The expected distributions have been obtained with a background-only fit to the data, and an approximate post-fit uncertainty is shown with a gray band. The impact of the best-fit signal is included in the lower panels for illustration.

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Figure 3-b:
Observed and expected distributions of ${m_{{\mathrm{t} \mathrm{\bar{t}}}}}$ in different $ {| \cos {\theta ^*_{t_\ell}} |}$ regions in the $\mu$+jets channel. The expected distributions have been obtained with a background-only fit to the data, and an approximate post-fit uncertainty is shown with a gray band. The impact of the best-fit signal is included in the lower panels for illustration.

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Figure 4:
Observed and expected distributions of the observables exploited in the dilepton channel. The expected distributions have been obtained with a background-only fit to the data, and an approximate post-fit uncertainty is shown with a gray band. The impact of the best-fit signal is included in the lower panel for illustration.

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Figure 5:
Model-independent constraints on the coupling strength modifier as a function of the heavy scalar boson mass, for relative widths of 0.5, 1, 2.5, 5, 10, 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 background-only hypothesis. The unphysical region of phase space in which the partial width $\Gamma _{{\mathrm{H}}\to {\mathrm{t} \mathrm{\bar{t}}}}$ becomes larger than the total width is indicated by the hatched lines.

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Figure 5-a:
Model-independent constraints on the coupling strength modifier as a function of the heavy scalar boson mass, for relative widths of 0.5%. 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 background-only hypothesis. The unphysical region of phase space in which the partial width $\Gamma _{{\mathrm{H}}\to {\mathrm{t} \mathrm{\bar{t}}}}$ becomes larger than the total width is indicated by the hatched lines.

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Figure 5-b:
Model-independent constraints on the coupling strength modifier as a function of the heavy scalar boson mass, for relative widths of 1%. 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 background-only hypothesis. The unphysical region of phase space in which the partial width $\Gamma _{{\mathrm{H}}\to {\mathrm{t} \mathrm{\bar{t}}}}$ becomes larger than the total width is indicated by the hatched lines.

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Figure 5-c:
Model-independent constraints on the coupling strength modifier as a function of the heavy scalar boson mass, for relative widths of 2.5%. 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 background-only hypothesis. The unphysical region of phase space in which the partial width $\Gamma _{{\mathrm{H}}\to {\mathrm{t} \mathrm{\bar{t}}}}$ becomes larger than the total width is indicated by the hatched lines.

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Figure 5-d:
Model-independent constraints on the coupling strength modifier as a function of the heavy scalar boson mass, for relative widths of 5%. 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 background-only hypothesis. The unphysical region of phase space in which the partial width $\Gamma _{{\mathrm{H}}\to {\mathrm{t} \mathrm{\bar{t}}}}$ becomes larger than the total width is indicated by the hatched lines.

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Figure 5-e:
Model-independent constraints on the coupling strength modifier as a function of the heavy scalar boson mass, for relative widths of 10%. 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 background-only hypothesis. The unphysical region of phase space in which the partial width $\Gamma _{{\mathrm{H}}\to {\mathrm{t} \mathrm{\bar{t}}}}$ becomes larger than the total width is indicated by the hatched lines.

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Figure 5-f:
Model-independent constraints on the coupling strength modifier as a function of the heavy scalar boson mass, for relative widths of 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 background-only hypothesis. The unphysical region of phase space in which the partial width $\Gamma _{{\mathrm{H}}\to {\mathrm{t} \mathrm{\bar{t}}}}$ becomes larger than the total width is indicated by the hatched lines.

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Figure 6:
Model-independent constraints on the coupling strength modifier as a function of the heavy pseudoscalar boson mass, for relative widths of 0.5, 1, 2.5, 5, 10, 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 background-only hypothesis. The unphysical region of phase space in which the partial width $\Gamma _{{\mathrm{A} }}\to {\mathrm{t} \mathrm{\bar{t}}}$ becomes larger than the total width is indicated by the hatched lines.

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Figure 6-a:
Model-independent constraints on the coupling strength modifier as a function of the heavy pseudoscalar boson mass, for relative widths of 0.5%. 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 background-only hypothesis. The unphysical region of phase space in which the partial width $\Gamma _{{\mathrm{A} }}\to {\mathrm{t} \mathrm{\bar{t}}}$ becomes larger than the total width is indicated by the hatched lines.

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Figure 6-b:
Model-independent constraints on the coupling strength modifier as a function of the heavy pseudoscalar boson mass, for relative widths of 1%. 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 background-only hypothesis. The unphysical region of phase space in which the partial width $\Gamma _{{\mathrm{A} }}\to {\mathrm{t} \mathrm{\bar{t}}}$ becomes larger than the total width is indicated by the hatched lines.

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Figure 6-c:
Model-independent constraints on the coupling strength modifier as a function of the heavy pseudoscalar boson mass, for relative widths of 2.5%. 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 background-only hypothesis. The unphysical region of phase space in which the partial width $\Gamma _{{\mathrm{A} }}\to {\mathrm{t} \mathrm{\bar{t}}}$ becomes larger than the total width is indicated by the hatched lines.

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Figure 6-d:
Model-independent constraints on the coupling strength modifier as a function of the heavy pseudoscalar boson mass, for relative widths of 5%. 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 background-only hypothesis. The unphysical region of phase space in which the partial width $\Gamma _{{\mathrm{A} }}\to {\mathrm{t} \mathrm{\bar{t}}}$ becomes larger than the total width is indicated by the hatched lines.

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Figure 6-e:
Model-independent constraints on the coupling strength modifier as a function of the heavy pseudoscalar boson mass, for relative widths of 10%. 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 background-only hypothesis. The unphysical region of phase space in which the partial width $\Gamma _{{\mathrm{A} }}\to {\mathrm{t} \mathrm{\bar{t}}}$ becomes larger than the total width is indicated by the hatched lines.

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Figure 6-f:
Model-independent constraints on the coupling strength modifier as a function of the heavy pseudoscalar boson mass, for relative widths of 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 background-only hypothesis. The unphysical region of phase space in which the partial width $\Gamma _{{\mathrm{A} }}\to {\mathrm{t} \mathrm{\bar{t}}}$ becomes larger than the total width is indicated by the hatched lines.

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Figure 7:
Scans of profiled likelihood for the pseudoscalar hypothesis with $m_{\mathrm{A} }= $ 400 GeV and $\Gamma _{\mathrm{A} }/ m_{\mathrm{A} } = $ 4%. The scans are shown for the single- and dilepton channels separately, as well as for the combination.

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Figure 8:
Exclusion in the $(m_{\mathrm{A} }, \tan\beta)$ plane of the hMSSM. The inner (dark gray) band and the outer (light gray) band indicate the regions containing 68 and 95%, respectively, of the distribution of constraints expected under the background-only hypothesis. The observed excluded region is indicated by the blue shaded area. Both H and A boson signals are included with masses and widths that correspond to a given point in the plane.
Tables

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Table 1:
Event yields and composition of SM background in the single-electron and single-muon channels. Expected yields are computed after the background-only fit to the data as explained in the text.

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Table 2:
Event yields and composition of SM background in the dilepton channel. Expected yields are computed in the same way as in Table 1.

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Table 3:
The systematic uncertainties considered in the analysis, indicating the number of corresponding nuisance parameters (when more than one) in the statistical model, the type (affecting shape or only normalization), the affected processes, and the correlation among the lepton channels. Uncertainties tagged in the last column with "All'' are correlated among the single-lepton and dilepton channels. In case an uncertainty is only applicable to the single-electron, the single-muon, the single-lepton, or the dilepton channel, they are indicated with e, $\mu$, $\ell $, $\ell \ell $, respectively.
Summary
Results are presented for the search for additional heavy Higgs bosons decaying to a pair of top quarks. A data sample recorded with the CMS detector at $\sqrt{s} = $ 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$, is analyzed. The final states with one or two leptons are utilized. The invariant mass of the reconstructed $\mathrm{t\bar{t}}$ system as well as angular variables sensitive to the spin of the new boson are used to search for the signal, while taking into account the interference with the standard model $\mathrm{t\bar{t}}$ production.

A moderate signal-like deviation is observed for the hypothesis of a pseudoscalar Higgs boson with the mass $m_{\mathrm{A} } \approx $ 400 GeV. After accounting for the look-elsewhere effect, its significance is 1.9 standard deviations. Further improvements of the theoretical description of the standard model $\mathrm{t\bar{t}}$ process in the vicinity of the production threshold will be needed to clarify the origin of this deviation.

Constraints on the strength of the coupling of the sought-for boson to top quarks are reported, separately for the scalar and pseudoscalar cases, for the mass ranging from 400 to 750 GeV and the total relative width from 0.5 to 25%. These are the most stringent constraints on this coupling to date. The results are also interpreted in the hMSSM scenario in the minimal supersymmetric standard model. This search probes the values of $m_{\mathrm{A}}$ from 400 to 700 GeV and excludes, at 95% confidence level, the region with values of $\tan\beta$ below 1.0 to 1.5, depending on $m_{\mathrm{A}}$. This extends the exclusion obtained in previous searches.
Additional Figures

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Additional Figure 1:
Example LO parton-level cross sections for the sum of the resonant and interference parts of the heavy Higgs boson signal corresponding to masses of 400, 600, and 800 GeV. The total decay width of the boson is assumed to be 10% of its mass, and the coupling modifier $g_{\Phi {{\mathrm {t}\overline {\mathrm {t}}}}}$ is set to unity. Cross sections are taken from Dicus, Stange, Willenbrock, PLB 333 (1994) 126 [arXiv:hep-ph/9404359].

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Additional Figure 2:
Post-fit one-dimensional projections of search variables: $m_{{{\mathrm {t}\overline {\mathrm {t}}}}}$ (left) and the angular observable (right), for the sum of the $ {\mu}$+jets and e+jets channels (upper), and for the dilepton channel (lower).

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Additional Figure 2-a:
Post-fit one-dimensional projection of $m_{{{\mathrm {t}\overline {\mathrm {t}}}}}$, for the sum of the $ {\mu}$+jets and e+jets channels.

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Additional Figure 2-b:
Post-fit one-dimensional projection of the angular observable, for the sum of the $ {\mu}$+jets and e+jets channels.

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Additional Figure 2-c:
Post-fit one-dimensional projection of $m_{{{\mathrm {t}\overline {\mathrm {t}}}}}$, for the dilepton channel.

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Additional Figure 2-d:
Post-fit one-dimensional projection of the angular observable, for the dilepton channel.

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Additional Figure 3:
Exclusion in the hMSSM obtained separately for the $\ell$+jets (a) and the dilepton channel (b).

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Additional Figure 3-a:
Exclusion in the hMSSM obtained separately for the $\ell$+jets.

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Additional Figure 3-b:
Exclusion in the hMSSM obtained separately for the dilepton channel.
Bounds for the different parity hypotheses

There are two files for the different parity hypotheses (A and H) : bounds_A.csv and bounds_H.csv.

Note that the bounds are only valid for a single parity hypothesis, i.e. for the case that the other mass is beyond the interesting range.

Each row in a file contains:
  • m_Phi: Mass of A or H boson
  • width_Phi: Relative width of A or H boson
  • obs_lower_excl_bound_0: Observed lower bound of exclusion contour
  • exp_lower_excl_bound: Expected lower bound of exclusion contour
  • obs_upper_excl_bound_0: Observed upper bound of exclusion contour (everything between obs_lower_excl_bound_0 and this value is excluded; "nan" means that there is no upper bound up to the validity limit of around 3, and therefore there is just one exclusion contour, as usually expected)
  • obs_lower_excl_bound_1: Observed lower bound of 2nd exclusion contour ("nan" indicates the regular case where there is only one excluded region)
Chi2_tt distributions

There are two files: expected.npy and observed.npy.

The $\chi^2_{\mathrm{t\bar{t}}}$ distributions are given as a function of the coupling modifiers $g_{\Phi\mathrm{t\bar{t}}}$ ($\Phi=$ H or A), for the scalar(H) and pseudoscalar (A) hypotheses for different scalar and pseudoscalar masses and relative widths.

The $\chi^2_{\mathrm{t\bar{t}}}$ distribution is defined as $ \chi^2_{\mathrm{t\bar{t}}} = -\ln [ L(g_{\Phi\mathrm{t\bar{t}}}) / L_{\text{max}} ]$, where the likelihood function $L$ is given in Eq. (2) considering either hypothesis A or H. Different from Figure 7, the distribution is not normalized by the Standard Model likelihood but by $L_{\text{max}}$ such that it vanishes for the most likely choice of mass, width, coupling strength and nuisance parameters, providing the best description of the data.

For pseudoscalar production the best description is achieved for $g_{\mathrm{At\bar{t}}}=$ 0.94, $m_{\mathrm{A}}=$ 400 GeV, and $\Gamma_{\mathrm{A}}/m_{\mathrm{A}}= $ 4.5%.

For scalar production the best description is achieved for $g_{\mathrm{Ht\bar{t}}}=$ 0.53, $m_{\mathrm{H}}=$ 750 GeV, and $\Gamma_{\mathrm{H}}/m_{\mathrm{H}}=$ 0.1%.

There are two attached files, observed.npy with the observed distributions and expected.npy with the expected ones from the Asimov dataset. The file can be read in python, e.g.

import pandas as pd
import numpy as np

infile = np.load('observed.npy')
df = pd.DataFrame(infile)
dfhypo = df[(df.parity == b'A') & (df.mass == 400) & (df.width == 4.5)]
print (dfhypo)

The second column shows the selected CP hypothesis, the third its mass, and the fourth its width. The sixth column shows the negative log likelihood, i.e. $[ L(g_{\Phi\mathrm{t\bar{t}}}) / L_{\text{max}} ]$, as as function of the coupling strength $g_{\Phi\mathrm{t\bar{t}}}$ printed in the fifth column. The first row gives the best likelihood value for the chosen values of parity, mass and width.

For questions or comments, please contact:
cms-pag-conveners-HIG@cern.ch

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