Search for a new resonance decaying into two spin-0 bosons in a final state with two photons and two bottom quarks in proton-proton collisions at $\sqrt{s}$ = 13 TeV

The CMS collaboration Tumasyan, Armen ; Adam, Wolfgang ; Andrejkovic, Janik Walter ; et al.
CMS-HIG-21-011, 2023.
Inspire Record 2705674 DOI 10.17182/hepdata.142396

A search for a new boson X is presented using CERN LHC proton-proton collision data collected by the CMS experiment at $\sqrt{s}$ = 13 TeV in 2016-2018, and corresponding to an integrated luminosity of 138 fb$^{-1}$. The resonance X decays into either a pair of Higgs bosons HH of mass 125 GeV or an H and a new spin-0 boson Y. One H subsequently decays to a pair of photons, and the second H or Y, to a pair of bottom quarks. The explored mass ranges of X are 260-1000 GeV and 300-1000 GeV, for decays to HH and to HY, respectively, with the Y mass range being 90-800 GeV. For a spin-0 X hypothesis, the 95% confidence level upper limit on the product of its production cross section and decay branching fraction is observed to be within 0.90-0.04 fb, depending on the masses of X and Y. The largest deviation from the background-only hypothesis with a local (global) significance of 3.8 (2.8) standard deviations is observed for X and Y masses of 650 and 90 GeV, respectively. The limits are interpreted using several models of new physics.

17 data tables

Expected and observed 95% upper limits on the product of the production cross section and the branching fraction for a spin-0 resonance $X\rightarrow HH\rightarrow \gamma\gamma bb$, as a function of X mass hypothesis. The $\pm1$ and $\pm2$ $\sigma$ uncertainty bands are given in addition to the expected median value. Numerical values provided in this table correspond to Figure 6 (upper) of the publication.

Expected and observed 95% upper limits on the product of the production cross section and the branching fraction for a spin-2 resonance $X\rightarrow HH\rightarrow \gamma\gamma bb$, as a function of X mass hypothesis. The $\pm1$ and $\pm2$ $\sigma$ uncertainty bands are given in addition to the expected median value. Numerical values provided in this table correspond to Figure 6 (lower) of the publication.

Expected and observed 95% upper limits on the product of the production cross section and the branching fraction for a spin-0 resonance $X\rightarrow HY\rightarrow \gamma\gamma bb$, as a function of Y mass, for X mass = 300 GeV. The $\pm1$ and $\pm2$ $\sigma$ uncertainty bands are given in addition to the expected median value. Numerical values provided in this table correspond to Figure 7 of the publication.

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Search for high-mass exclusive diphoton production with tagged protons in proton-proton collisions at $\sqrt{s}$ = 13 TeV

The CMS & TOTEM collaborations Tumasyan, Armen ; Adam, Wolfgang ; Andrejkovic, Janik Walter ; et al.
CMS-EXO-21-007, 2023.
Inspire Record 2719536 DOI 10.17182/hepdata.142335

A search is presented for high-mass exclusive diphoton production via photon-photon fusion in proton-proton collisions at $\sqrt{s}$ = 13 TeV in events where both protons survive the interaction. The analysis utilizes data corresponding to an integrated luminosity of 103 fb$^{-1}$ collected in 2016-2018 with the central CMS detector and the CMS and TOTEM precision proton spectrometer (PPS). Events that have two photons with high transverse momenta ($p_\mathrm{T}^\gamma > $ 100 GeV), back-to-back in azimuth, and with a large diphoton invariant mass ($m_{\gamma\gamma} \gt$ 350 GeV) are selected. To remove the dominant inclusive diphoton backgrounds, the kinematic properties of the protons detected in PPS are required to match those of the central diphoton system. Only events having opposite-side forward protons detected with a fractional momentum loss between 0.035 and 0.15 (0.18) for the detectors on the negative (positive) side of CMS are considered. One exclusive diphoton candidate is observed for an expected background of 1.1 events. Limits at 95% confidence level are derived for the four-photon anomalous coupling parameters $\lvert\zeta_1\rvert \lt$ 0.073 TeV$^{-4}$ and $\lvert\zeta_2\rvert \lt$ 0.15 TeV$^{-4}$, using an effective field theory. Additionally, upper limits are placed on the production of axion-like particles with coupling strength to photons $f^{-1}$ that varies from 0.03 TeV$^{-1}$ to 1 TeV$^{-1}$ over the mass range from 500 to 2000 GeV.

3 data tables

95% expected and observed one-dimensional limits on $\zeta_1$ and $\zeta_2$ anomalous LbyL production parameters, when the other parameter is set to zero. This corresponds to a search region of $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$.

Two-dimensional limits on anomalous quartic gauge coupling parameters. The parametric elliptic form is assumed: $\sigma=a_0\zeta_1^2+a_1\zeta_1\zeta_2+a_2\zeta_2^2$.

Limits on axion-like particle production.


Version 2
Measurement and QCD analysis of double-differential inclusive jet cross sections in proton-proton collisions at $\sqrt{s}$ = 13 TeV

The CMS collaboration Tumasyan, Armen ; Adam, Wolfgang ; Andrejkovic, Janik Walter ; et al.
JHEP 02 (2022) 142, 2022.
Inspire Record 1972986 DOI 10.17182/hepdata.115022

A measurement of the inclusive jet production in proton-proton collisions at the LHC at $\sqrt{s}$ = 13 TeV is presented. The double-differential cross sections are measured as a function of the jet transverse momentum $p_\mathrm{T}$ and the absolute jet rapidity $\lvert y \rvert$. The anti-$k_\mathrm{T}$ clustering algorithm is used with distance parameter of 0.4 (0.7) in a phase space region with jet $p_\mathrm{T}$ from 97 GeV up to 3.1 TeV and $\lvert y \rvert\lt$ 2.0. Data collected with the CMS detector are used, corresponding to an integrated luminosity of 36.3 fb$^{-1}$ (33.5 fb$^{-1}$). The measurement is used in a comprehensive QCD analysis at next-to-next-to-leading order, which results in significant improvement in the accuracy of the parton distributions in the proton. Simultaneously, the value of the strong coupling constant at the Z boson mass is extracted as $\alpha_\mathrm{S}$(Z) = 0.1170 $\pm$ 0.0019. For the first time, these data are used in a standard model effective field theory analysis at next-to-leading order, where parton distributions and the QCD parameters are extracted simultaneously with imposed constraints on the Wilson coefficient $c_1$ of 4-quark contact interactions. Note added: in the Addendum to this paper, available as Appendix B in this document, an improved value of $\alpha_\mathrm{S}$(Z) = 0.1166 $\pm$ 0.0017 has been extracted. This result supersedes the number in the above abstract of the original publication.

112 data tables

The inclusive jet production cross section as a function of the jet transverse momentum~$p_\mathrm{T}$ measured in $|y| < 0.5$ for jets clustered using the anti-$k_\mathrm{t}$ algorithm with $R=0.4$.

The inclusive jet production cross section as a function of the jet transverse momentum~$p_\mathrm{T}$ measured in $|y| < 0.5$ for jets clustered using the anti-$k_\mathrm{t}$ algorithm with $R=0.4$.

The inclusive jet production cross section as a function of the jet transverse momentum~$p_\mathrm{T}$ measured in $0.5 < |y| < 1.0$ for jets clustered using the anti-$k_\mathrm{t}$ algorithm with $R=0.4$.

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Version 2
Observation of the rare decay of the $\eta$ meson to four muons

The CMS collaboration Hayrapetyan, Aram ; Tumasyan, Armen ; Adam, Wolfgang ; et al.
Phys.Rev.Lett. 131 (2023) 091903, 2023.
Inspire Record 2657654 DOI 10.17182/hepdata.140340

A search for the rare $\eta$$\to$$\mu^+\mu^-\mu^+\mu^-$ double-Dalitz decay is performed using a sample of proton-proton collisions, collected by the CMS experiment at the CERN LHC with high-rate muon triggers in 2017-2018 and corresponding to an integrated luminosity of 101 fb$^{-1}$. A signal having a statistical significance well in excess of 5 standard deviations is observed. Using the $\eta$$\to$$\mu^+ \mu^-$ decay as normalization, the branching fraction $\mathcal{B}(\eta$$\to$$\mu^+\mu^-\mu^+\mu^-)$ = [5.0 $\pm$ 0.8 (stat) $\pm$ 0.7 (syst) $\pm$ 0.7 ($\mathcal{B}_{2\mu}$)] $\times$ 10$^{-9}$ is measured, where the last term is the uncertainty in the normalization channel branching fraction. This work achieves an improved precision of over five orders of magnitude compared to previous results, leading to the first measurement of this branching fraction, which is found to agree with theoretical predictions.

6 data tables

The total efficiencies for the four-muon ($A_{4\mu}^{i,j}$, red and blue points) and two-muon ($A_{2\mu}^{i,j}$, orange and green points) decay channels, as functions of the generated meson's $p_{\mathrm{T}}$ and $y$, evaluated through MC simulation.

The total efficiencies for the four-muon ($A_{4\mu}^{i,j}$, red and blue points) and two-muon ($A_{2\mu}^{i,j}$, orange and green points) decay channels, as functions of the generated meson's $p_{\mathrm{T}}$ and $y$, evaluated through MC simulation.

Measured ratio of $\mathcal{B}_{4\mu}/\mathcal{B}_{2\mu}$

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Version 3
Search for resonant production of strongly coupled dark matter in proton-proton collisions at 13 TeV

The CMS collaboration Tumasyan, Armen ; Adam, Wolfgang ; Andrejkovic, Janik Walter ; et al.
JHEP 06 (2022) 156, 2022.
Inspire Record 1994864 DOI 10.17182/hepdata.115426

The first collider search for dark matter arising from a strongly coupled hidden sector is presented and uses a data sample corresponding to 138 fb$^{-1}$, collected with the CMS detector at the CERN LHC, at $\sqrt{s} =$ 13 TeV. The hidden sector is hypothesized to couple to the standard model (SM) via a heavy leptophobic Z' mediator produced as a resonance in proton-proton collisions. The mediator decay results in two "semivisible" jets, containing both visible matter and invisible dark matter. The final state therefore includes moderate missing energy aligned with one of the jets, a signature ignored by most dark matter searches. No structure in the dijet transverse mass spectra compatible with the signal is observed. Assuming the Z' has a universal coupling of 0.25 to the SM quarks, an inclusive search, relevant to any model that exhibits this kinematic behavior, excludes mediator masses of 1.5-4.0 TeV at 95% confidence level, depending on the other signal model parameters. To enhance the sensitivity of the search for this particular class of hidden sector models, a boosted decision tree (BDT) is trained using jet substructure variables to distinguish between semivisible jets and SM jets from background processes. When the BDT is employed to identify each jet in the dijet system as semivisible, the mediator mass exclusion increases to 5.1 TeV, for wider ranges of the other signal model parameters. These limits exclude a wide range of strongly coupled hidden sector models for the first time.

396 data tables

The normalized distribution of the characteristic variable $R_{\text{T}}$ for the simulated SM backgrounds and several signal models. The requirement on this variable is omitted, but all other preselection requirements are applied. The last bin of each histogram includes the overflow events.

The normalized distribution of the characteristic variable $R_{\text{T}}$ for the simulated SM backgrounds and several signal models. The requirement on this variable is omitted, but all other preselection requirements are applied. The last bin of each histogram includes the overflow events.

The normalized distribution of the characteristic variable $R_{\text{T}}$ for the simulated SM backgrounds and several signal models. The requirement on this variable is omitted, but all other preselection requirements are applied. The last bin of each histogram includes the overflow events.

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Version 2
Search for a massive scalar resonance decaying to a light scalar and a Higgs boson in the four b quarks final state with boosted topology

The CMS collaboration Tumasyan, Armen ; Adam, Wolfgang ; Andrejkovic, Janik Walter ; et al.
Phys.Lett.B 842 (2023) 137392, 2023.
Inspire Record 2072383 DOI 10.17182/hepdata.115995

We search for new massive scalar particles X and Y through the resonant process X $\to$ YH $\to$$\mathrm{b\bar{b}b\bar{b}}$, where H is the standard model Higgs boson. Data from CERN LHC proton-proton collisions are used, collected at a centre-of-mass energy of 13 TeV in 2016-2018 and corresponding to an integrated luminosity of 138 fb$^{-1}$. The search is performed in mass ranges of 0.9-4 TeV for X and 60-600 GeV for Y, where both Y and H are reconstructed as Lorentz-boosted single large-area jets. The results are interpreted in the context of the next-to-minimal supersymmetric standard model and also in an extension of the standard model with two additional singlet scalar fields. The 95% confidence level upper limits for the production cross section vary between 0.1 and 150 fb depending on the X and Y masses, and represent a significant improvement over results from previous searches.

7 data tables

The $M_J^Y$ distribution for the number of observed events (black markers) compared with the estimated backgrounds (filled histograms) and their uncertainties (hatched areas) in the SR1. The distributions expected from the signal under three $M_X$ and $M_Y$ hypotheses and assuming a cross section of 1 fb are also shown. The lower panels show the ''Pulls'' defined as (observed events - expected events)/$\sqrt{\smash[b]{\sigma_{obs}^{2} - \sigma_{exp}^{2}}}$, where $\sigma_{obs}$ and $\sigma_{exp}$ are the statistical and total uncertainties in the observation and the background estimation, respectively. The minus sign accounts for the correlation between data and the data-driven estimation.

The $M_J^Y$ distribution for the number of observed events (black markers) compared with the estimated backgrounds (filled histograms) and their uncertainties (hatched areas) in the SR1. The distributions expected from the signal under three $M_X$ and $M_Y$ hypotheses and assuming a cross section of 1 fb are also shown. The lower panels show the ''Pulls'' defined as (observed events - expected events)/$\sqrt{\smash[b]{\sigma_{obs}^{2} - \sigma_{exp}^{2}}}$, where $\sigma_{obs}$ and $\sigma_{exp}$ are the statistical and total uncertainties in the observation and the background estimation, respectively. The minus sign accounts for the correlation between data and the data-driven estimation.

The $M_{JJ}$ distribution for the number of observed events (black markers) compared with the estimated backgrounds (filled histograms) and their uncertainties (hatched areas) in the SR1. The distributions expected from the signal under three $M_X$ and $M_Y$ hypotheses and assuming a cross section of 1 fb are also shown. The lower panels show the ''Pulls'' defined as (observed events - expected events)/$\sqrt{\smash[b]{\sigma_{obs}^{2} - \sigma_{exp}^{2}}}$, where $\sigma_{obs}$ and $\sigma_{exp}$ are the statistical and total uncertainties in the observation and the background estimation, respectively. The minus sign accounts for the correlation between data and the data-driven estimation.

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Measurement of the Higgs boson production via vector boson fusion and its decay into bottom quarks in proton-proton collisions at $\sqrt{s}$ = 13 TeV

The CMS collaboration Hayrapetyan, Aram ; Tumasyan, Armen ; Adam, Wolfgang ; et al.
JHEP 01 (2024) 173, 2024.
Inspire Record 2684710 DOI 10.17182/hepdata.142036

A measurement of the Higgs boson (H) production via vector boson fusion (VBF) and its decay into a bottom quark-antiquark pair ($\mathrm{b\bar{b}}$) is presented using proton-proton collision data recorded by the CMS experiment at $\sqrt{s}$ = 13 TeV and corresponding to an integrated luminosity of 90.8 fb$^{-1}$. Treating the gluon-gluon fusion process as a background and constraining its rate to the value expected in the standard model (SM) within uncertainties, the signal strength of the VBF process, defined as the ratio of the observed signal rate to that predicted by the SM, is measured to be $\mu^\text{qqH}_\mathrm{Hb\bar{b}}$ = 1.01 $^{+0.55}_{-0.46}$. The VBF signal is observed with a significance of 2.4 standard deviations relative to the background prediction, while the expected significance is 2.7 standard deviations. Considering inclusive Higgs boson production and decay into bottom quarks, the signal strength is measured to be $\mu^\text{incl.}_\mathrm{Hb\bar{b}}$ = 0.99 $^{+0.48}_{-0.41}$, corresponding to an observed (expected) significance of 2.6 (2.9) standard deviations.

4 data tables

The mbb distribution after weighted combination of all categories in the analysis weighted with S/(S + B). where S is the total Hbb signal yield (both VBF and ggH) and B is the total background yield including QCD multijet and Z+jets

The best fit values of the signal strength modifier for the different processes. The uncertainties, corresponding to one standard deviation confidence intervals, include both statistical and systematic sources. The additional breakdown of the uncertainties into their separate statistical and systematic contributions is also shown.

The best fit values of the signal strength modifier for the different processes by floating the VBF and ggH production rates independently. The uncertainties, corresponding to one standard deviation confidence intervals, include both statistical and systematic sources. The additional breakdown of the uncertainties into their separate statistical and systematic contributions is also shown.

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Test of lepton flavor universality in B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$ and B$^{\pm}$$\to$ K$^{\pm}$e$^+$e$^-$ decays in proton-proton collisions at $\sqrt{s}$ = 13 TeV

The CMS collaboration Hayrapetyan, Aram ; Tumasyan, Armen ; Adam, Wolfgang ; et al.
CMS-BPH-22-005, 2024.
Inspire Record 2747130 DOI 10.17182/hepdata.146018

A test of lepton flavor universality in B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$ and B$^{\pm}$$\to$ K$^{\pm}$e$^+$e$^-$ decays, as well as a measurement of differential and integrated branching fractions of a nonresonant B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$ decay are presented. The analysis is made possible by a dedicated data set of proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded in 2018, by the CMS experiment at the LHC, using a special high-rate data stream designed for collecting about 10 billion unbiased b hadron decays. The ratio of the branching fractions $\mathcal{B}$(B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$) to $\mathcal{B}$(B$^{\pm}$$\to$ K$^{\pm}$e$^+$e$^-$) is determined from the measured double ratio $R$(K) of these decays to the respective branching fractions of the B$^\pm$$\to$ J/$\psi$K$^\pm$ with J/$\psi$$\to$$\mu^+\mu^-$ and e$^+$e$^-$ decays, which allow for significant cancellation of systematic uncertainties. The ratio $R$(K) is measured in the range 1.1 $\lt q^2 \lt$ 6.0 GeV$^2$, where $q$ is the invariant mass of the lepton pair, and is found to be $R$(K) = 0.78$^{+0.47}_{-0.23}$, in agreement with the standard model expectation $R$(K) $\approx$ 1. This measurement is limited by the statistical precision of the electron channel. The integrated branching fraction in the same $q^2$ range, $\mathcal{B}$(B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$) = (12.42 $\pm$ 0.68) $\times$ 10$^{-8}$, is consistent with the present world-average value and has a comparable precision.

9 data tables

The differential $\text{B}^+ \to \text{K}^+\mu^+\mu^-$ branching fraction measured in the individual $q^2$ bins. The uncertainties in the yields are statistical uncertainties from the fit, while the branching fraction uncertainties include both the statistical and systematic components.

Differential branching fraction $d\mathcal{B}/dq^2$, with theoretical predictions obtained with the HEPFiT, SuperIso, Flavio, and EOS packages. The HEPFiT predictions are available only for $q^2 < 8\ \mathrm{GeV}^2$.

Relative uncertainties in the differential branching fraction measurement of $\mathrm{B}^+\to\mathrm{K}^+\mu^+\mu^-$ per $q^2$ bin.

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Measurement of the double-differential inclusive jet cross section in proton-proton collisions at $\sqrt{s}$ = 5.02 TeV

The CMS collaboration Hayrapetyan, Aram ; Tumasyan, Armen ; Adam, Wolfgang ; et al.
CMS-SMP-21-009, 2024.
Inspire Record 2750408 DOI 10.17182/hepdata.146028

The inclusive jet cross section is measured as a function of jet transverse momentum $p_\mathrm{T}$ and rapidity $y$. The measurement is performed using proton-proton collision data at $\sqrt{s}$ = 5.02 TeV, recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 27.4 pb$^{-1}$. The jets are reconstructed with the anti-$k_\mathrm{T}$ algorithm using a distance parameter of $R$ = 0.4, within the rapidity interval $\lvert y\rvert$$\lt$ 2, and across the kinematic range 0.06 $\lt$$p_\mathrm{T}$$\lt$ 1 TeV. The jet cross section is unfolded from detector to particle level using the determined jet response and resolution. The results are compared to predictions of perturbative quantum chromodynamics, calculated at both next-to-leading order and next-to-next-to-leading order. The predictions are corrected for nonperturbative effects, and presented for a variety of parton distribution functions and choices of the renormalization/factorization scales and the strong coupling $\alpha_\mathrm{S}$.

32 data tables

The JEC, JER, and total systematic uncertainties in unfolded cross sections as functions of transverse momentum, for |y|<0.5. The total systematic uncertainty includes also the luminosity, jet identification and trigger efficiency uncertainties.

The JEC, JER, and total systematic uncertainties in unfolded cross sections as functions of transverse momentum, for 0.5<|y|<1. The total systematic uncertainty includes also the luminosity, jet identification and trigger efficiency uncertainties.

The JEC, JER, and total systematic uncertainties in unfolded cross sections as functions of transverse momentum, for 1<|y|<1.5. The total systematic uncertainty includes also the luminosity, jet identification and trigger efficiency uncertainties.

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Search for a vector-like quark T$'$$\to$ tH via the diphoton decay mode of the Higgs boson in proton-proton collisions at $\sqrt{s}$ = 13 TeV

The CMS collaboration Tumasyan, Armen ; Adam, Wolfgang ; Andrejkovic, Janik Walter ; et al.
JHEP 09 (2023) 057, 2023.
Inspire Record 2636335 DOI 10.17182/hepdata.134009

A search for the electroweak production of a vector-like quark T$'$, decaying to a top quark and a Higgs boson is presented. The search is based on a sample of proton-proton collision events recorded at the LHC at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. This is the first T$'$ search that exploits the Higgs boson decay to a pair of photons. For narrow isospin singlet T$'$ states with masses up to 1.1 TeV, the excellent diphoton invariant mass resolution of 1-2% results in an increased sensitivity compared to previous searches based on the same production mechanism. The electroweak production of a T$'$ quark with mass up to 960 GeV is excluded at 95% confidence level, assuming a coupling strength $\kappa_\mathrm{T}$ = 0.25 and a relative decay width $\Gamma/M_{\mathrm{T}'}$ $\lt$ 5%.

8 data tables

The combined, leptonic plus hadronic, expected (dotted black) and observed (solid black) upper limits at 95% CL on $\sigma_{T^\prime bq} \times \mathcal{B}_{T^\prime \rightarrow tH}$ displayed as a function of $\rm{M}_{T^\prime}$. The green (yellow) band represents the 68% (95%) of the limit values expected under the background-only hypothesis. The theoretical cross sections for the singlet $T^\prime$ production with representative $\kappa_T$-values fixed at 0.1, 0.15, 0.2 and 0.25 (for $\Gamma/\rm{M}_{T^\prime} < 5\%$) are shown as solid red lines. The theoretical cross sections for the singlet $T^\prime$ production with $\Gamma/\rm{M}_{T^\prime}$ = 1 and 5% are also shown in table.

The combined, leptonic plus hadronic, expected (dotted black) and observed (solid black) upper limits at 95% CL on the $T^\prime$ coupling to third-generation quarks, $\kappa_{T}$, under the narrow width approximation (NWA) displayed as a function of $\rm{M}_{T^\prime}$. The green (yellow) band represents the 68% (95%) of the limit values expected under the background-only hypothesis. The theoretical $\kappa_{T}$ values corresponding to the $\Gamma/\rm{M}_{T^\prime}$-values fixed at 1, 2, 3, 4, and 5% are shown as red dashed lines.

The expected (dotted black) and observed (solid black) upper limits at 95% CL on $\sigma_{T^\prime bq(T^\prime \rightarrow tH)}$ in the leptonic channel displayed as a function of $\rm{M}_{T^\prime}$. The green (yellow) band represents the 68% (95%) of the limit values expected under the background-only hypothesis. The theoretical cross sections for the singlet $T^\prime$ production with representative $\kappa_T$-values fixed at 0.1, 0.15, 0.2 and 0.25 (for $\Gamma/\rm{M}_{T^\prime} < 5\%$) are shown as solid red lines.

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