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| CMS-TOP-22-009 ; CERN-EP-2023-201 | ||
| Inclusive and differential cross section measurements of $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ production in the lepton+jets channel at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 25 September 2023 | ||
| JHEP 05 (2024) 042 | ||
| Abstract: Measurements of inclusive and normalized differential cross sections of the associated production of top quark-antiquark and bottom quark-antiquark pairs, $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $, are presented. The results are based on data from proton-proton collisions collected by the CMS detector at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The cross sections are measured in the lepton+jets decay channel of the top quark pair, using events containing exactly one isolated electron or muon and at least five jets. Measurements are made in four fiducial phase space regions, targeting different aspects of the $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ process. Distributions are unfolded to the particle level through maximum likelihood fits, and compared with predictions from several event generators. The inclusive cross section measurements of this process in the fiducial phase space regions are the most precise to date. In most cases, the measured inclusive cross sections exceed the predictions with the chosen generator settings. The only exception is when using a particular choice of dynamic renormalization scale, $ {\mu_{\mathrm{R}}=\frac12 \prod_{i=\mathrm{t},\bar{\mathrm{t}},\mathrm{b},\bar{\mathrm{b}}} m_{\mathrm{T},i}^{1/4}} $, where $ {m_{\mathrm{T},i}^2=m_i^2+p_{\mathrm{T},i}^2} $ are the transverse masses of top and bottom quarks. The differential cross sections show varying degrees of compatibility with the theoretical predictions, and none of the tested generators with the chosen settings simultaneously describe all the measured distributions. | ||
| Links: e-print arXiv:2309.14442 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Jet (left) and b-tagged jet (right) multiplicity with the $ \geq $5 jets: $ \geq $3b selection prior to any fit, shown for both lepton channels and all data periods combined. For the purpose of visualisation, the contributions from simulation have been scaled by a common factor to match the yield in data. The $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{X} $ contribution includes the $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{H} $, $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{W} $, and $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{Z} $ processes. The shaded bands include all a priori uncertainties described in Section 7, including the $ {\mathrm{t}\bar{\mathrm{t}}} {\mathrm{B}} $ cross section uncertainty estimated from the nominal $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ simulation. Only effects on the shape of the distributions are considered. The last bins also contain the overflow. |
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Figure 1-a:
Jet (left) and b-tagged jet (right) multiplicity with the $ \geq $5 jets: $ \geq $3b selection prior to any fit, shown for both lepton channels and all data periods combined. For the purpose of visualisation, the contributions from simulation have been scaled by a common factor to match the yield in data. The $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{X} $ contribution includes the $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{H} $, $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{W} $, and $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{Z} $ processes. The shaded bands include all a priori uncertainties described in Section 7, including the $ {\mathrm{t}\bar{\mathrm{t}}} {\mathrm{B}} $ cross section uncertainty estimated from the nominal $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ simulation. Only effects on the shape of the distributions are considered. The last bins also contain the overflow. |
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Figure 1-b:
Jet (left) and b-tagged jet (right) multiplicity with the $ \geq $5 jets: $ \geq $3b selection prior to any fit, shown for both lepton channels and all data periods combined. For the purpose of visualisation, the contributions from simulation have been scaled by a common factor to match the yield in data. The $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{X} $ contribution includes the $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{H} $, $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{W} $, and $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{Z} $ processes. The shaded bands include all a priori uncertainties described in Section 7, including the $ {\mathrm{t}\bar{\mathrm{t}}} {\mathrm{B}} $ cross section uncertainty estimated from the nominal $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ simulation. Only effects on the shape of the distributions are considered. The last bins also contain the overflow. |
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Figure 2:
Number of jets b tagged at the tight working point with the $ \geq $5 jets: $ \geq $3b (left) and $ \geq $6 jets: $ \geq $4b selections (right) prior to any fit, shown for all lepton channels and years combined. For the purpose of visualisation, the contributions from simulation have been scaled by a common factor to match the yield in data. The shaded bands include all uncertainties described in Section 7, including the $ {\mathrm{t}\bar{\mathrm{t}}} {\mathrm{B}} $ cross section uncertainty estimated from the nominal $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ simulation. Only effects on the shape of the distributions are considered. The last bins also contain the overflow. The vertical dashed lines indicate the ancillary regions. |
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Figure 2-a:
Number of jets b tagged at the tight working point with the $ \geq $5 jets: $ \geq $3b (left) and $ \geq $6 jets: $ \geq $4b selections (right) prior to any fit, shown for all lepton channels and years combined. For the purpose of visualisation, the contributions from simulation have been scaled by a common factor to match the yield in data. The shaded bands include all uncertainties described in Section 7, including the $ {\mathrm{t}\bar{\mathrm{t}}} {\mathrm{B}} $ cross section uncertainty estimated from the nominal $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ simulation. Only effects on the shape of the distributions are considered. The last bins also contain the overflow. The vertical dashed lines indicate the ancillary regions. |
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Figure 2-b:
Number of jets b tagged at the tight working point with the $ \geq $5 jets: $ \geq $3b (left) and $ \geq $6 jets: $ \geq $4b selections (right) prior to any fit, shown for all lepton channels and years combined. For the purpose of visualisation, the contributions from simulation have been scaled by a common factor to match the yield in data. The shaded bands include all uncertainties described in Section 7, including the $ {\mathrm{t}\bar{\mathrm{t}}} {\mathrm{B}} $ cross section uncertainty estimated from the nominal $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ simulation. Only effects on the shape of the distributions are considered. The last bins also contain the overflow. The vertical dashed lines indicate the ancillary regions. |
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Figure 3:
Structural representation of the neural network used for the assignment of the additional b-jet pair. The neural network uses two sets of input variables:\ global event information is connected to three dense network layers, and jet-specific information is connected via convolutional network layers (CNN) and a long short-term memory (LSTM) cell. The input sequences are concatenated into one dense layer. The output layer consists of six nodes, each representing one of the six possible candidate jet combinations. |
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Figure 4:
Response matrix for $ \Delta R(\smash[t]{\mathrm{b}\mathrm{b}^{\text{extra}}} ) $ in the $ \geq $6 jets: $ \geq $4b phase space. The $ x $ ($ y $) axes show the generator- (detector-)level observables. The upper figure includes the ancillary variable, unrolled on the same axis as the detector-level observable, so that the binning of the detector-level observable, stacked vertically, is repeated twice. For the lower figure, the ancillary variables are projected out to more easily visualize the correspondence between true and reconstructed values. The coloured bins show the finer binning used at reconstructed level (bins split in two), while the numbers show the values one would obtain when using the same binning at the generator and detector level. |
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Figure 4-a:
Response matrix for $ \Delta R(\smash[t]{\mathrm{b}\mathrm{b}^{\text{extra}}} ) $ in the $ \geq $6 jets: $ \geq $4b phase space. The $ x $ ($ y $) axes show the generator- (detector-)level observables. The upper figure includes the ancillary variable, unrolled on the same axis as the detector-level observable, so that the binning of the detector-level observable, stacked vertically, is repeated twice. For the lower figure, the ancillary variables are projected out to more easily visualize the correspondence between true and reconstructed values. The coloured bins show the finer binning used at reconstructed level (bins split in two), while the numbers show the values one would obtain when using the same binning at the generator and detector level. |
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Figure 4-b:
Response matrix for $ \Delta R(\smash[t]{\mathrm{b}\mathrm{b}^{\text{extra}}} ) $ in the $ \geq $6 jets: $ \geq $4b phase space. The $ x $ ($ y $) axes show the generator- (detector-)level observables. The upper figure includes the ancillary variable, unrolled on the same axis as the detector-level observable, so that the binning of the detector-level observable, stacked vertically, is repeated twice. For the lower figure, the ancillary variables are projected out to more easily visualize the correspondence between true and reconstructed values. The coloured bins show the finer binning used at reconstructed level (bins split in two), while the numbers show the values one would obtain when using the same binning at the generator and detector level. |
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Figure 5:
Effect of the considered sources of uncertainties on the measurement of the normalized differential cross section of the $ H_{\mathrm{T}} $ of b jets in the $ \geq $5 jets: $ \geq $3b phase space, obtained by combining the impacts of associated nuisance parameters according to Eq. (2). The ordering of the various sources is similar for other observables and in the other phase space regions. The last bin of the distribution is not shown, since it has no associated parameter of interest but is constrained by the other bins as described in Section 6.3. The category ``other theory'' includes b quark fragmentation, top quark $ p_{\mathrm{T}} $ modelling, PDF, $ h_{\mathrm{damp}} $, colour reconnection, and underlying event uncertainties. The category ``other experimental'' includes pileup and the integrated luminosity uncertainties. |
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Figure 6:
Measured inclusive cross sections for each considered phase space, compared to predictions from different $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ simulation approaches shown as coloured symbols. The predictions include uncertainties (horizontal bars) due to the limited number of simulated events. The blue colour is reserved for models using massive b quarks and NLO QCD $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ MEs, while red is used for the inclusive $ \mathrm{t} \bar{\mathrm{t}} $ generators at NLO in QCD with massless b quarks. The right panel shows the ratios between the predicted and measured cross sections, with the black bars showing the relative uncertainties in the measurements. |
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Figure 7:
The $ |\eta| $ of the third-hardest b jet in $ p_{\mathrm{T}} $ ($ |\eta(b_{3})| $) in the $ \geq $5 jets: $ \geq $3b phase space (upper) and the $ |\eta| $ of the subleading additional b jet ($ |\eta(b_{2}^{\text{extra}})| $) in the $ \geq $6 jets: $ \geq $4b phase space (lower) after the fit to data, shown for both lepton channels and all data periods combined. The distributions are shown separately for each ancillary region, as defined in Section 6.1. In the $ \geq $5 jets: $ \geq $3b ($ \geq $6 jets: $ \geq $4b) phase space the ancillary regions are defined as $ \leq $2, 2, and $ \geq $3 ($ \leq $3 and $ \geq $3) tight b-tagged jets. The shaded bands include all uncertainties described in Section 7 after profiling the nuisance parameters in the fit, estimated by sampling the predicted yields from the fit covariance matrix. The blue line shows the sum of the predicted yields for all processes before the fit to data, using the nominal $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ samples and its corresponding cross section for the signal. In the ratio panel the expected yields before the fit to data are shown relative to the predicted yields after the fit to data. The last bins contain the overflow. |
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Figure 7-a:
The $ |\eta| $ of the third-hardest b jet in $ p_{\mathrm{T}} $ ($ |\eta(b_{3})| $) in the $ \geq $5 jets: $ \geq $3b phase space (upper) and the $ |\eta| $ of the subleading additional b jet ($ |\eta(b_{2}^{\text{extra}})| $) in the $ \geq $6 jets: $ \geq $4b phase space (lower) after the fit to data, shown for both lepton channels and all data periods combined. The distributions are shown separately for each ancillary region, as defined in Section 6.1. In the $ \geq $5 jets: $ \geq $3b ($ \geq $6 jets: $ \geq $4b) phase space the ancillary regions are defined as $ \leq $2, 2, and $ \geq $3 ($ \leq $3 and $ \geq $3) tight b-tagged jets. The shaded bands include all uncertainties described in Section 7 after profiling the nuisance parameters in the fit, estimated by sampling the predicted yields from the fit covariance matrix. The blue line shows the sum of the predicted yields for all processes before the fit to data, using the nominal $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ samples and its corresponding cross section for the signal. In the ratio panel the expected yields before the fit to data are shown relative to the predicted yields after the fit to data. The last bins contain the overflow. |
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Figure 7-b:
The $ |\eta| $ of the third-hardest b jet in $ p_{\mathrm{T}} $ ($ |\eta(b_{3})| $) in the $ \geq $5 jets: $ \geq $3b phase space (upper) and the $ |\eta| $ of the subleading additional b jet ($ |\eta(b_{2}^{\text{extra}})| $) in the $ \geq $6 jets: $ \geq $4b phase space (lower) after the fit to data, shown for both lepton channels and all data periods combined. The distributions are shown separately for each ancillary region, as defined in Section 6.1. In the $ \geq $5 jets: $ \geq $3b ($ \geq $6 jets: $ \geq $4b) phase space the ancillary regions are defined as $ \leq $2, 2, and $ \geq $3 ($ \leq $3 and $ \geq $3) tight b-tagged jets. The shaded bands include all uncertainties described in Section 7 after profiling the nuisance parameters in the fit, estimated by sampling the predicted yields from the fit covariance matrix. The blue line shows the sum of the predicted yields for all processes before the fit to data, using the nominal $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ samples and its corresponding cross section for the signal. In the ratio panel the expected yields before the fit to data are shown relative to the predicted yields after the fit to data. The last bins contain the overflow. |
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Figure 8:
The $ H_{\mathrm{T}} $ of all light jets in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light phase space (upper) and the azimuthal angle between the hardest remaining light jet and the softest b jet ($ |\Delta\phi(\mathrm{lj}_{1}^{\text{extra}},\mathrm{b}_{\text{soft}})| $) in the $ \geq $7 jets: $ \geq $4b, $ \geq $3 light phase space (lower) after the fit to data, shown for both lepton channels and all data periods combined. The distributions are shown separately for each ancillary region, as defined in Section 6.1. In the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light ($ \geq $7 jets: $ \geq $4b, $ \geq $3 light ) phase space the ancillary regions are defined as $ \leq $2, 2, and $ \geq $3 ($ \leq $3 and $ \geq $3) tight b-tagged jets. The shaded bands include all uncertainties described in Section 7 after profiling the nuisance parameters in the fit, estimated by sampling the predicted yields from the fit covariance matrix. The blue line shows the sum of the predicted yields for all processes before the fit to data, using the nominal $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ samples and its corresponding cross section for the signal. In the ratio panel the expected yields before the fit to data are shown relative to the predicted yields after the fit to data. The last bins contain the overflow. |
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Figure 8-a:
The $ H_{\mathrm{T}} $ of all light jets in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light phase space (upper) and the azimuthal angle between the hardest remaining light jet and the softest b jet ($ |\Delta\phi(\mathrm{lj}_{1}^{\text{extra}},\mathrm{b}_{\text{soft}})| $) in the $ \geq $7 jets: $ \geq $4b, $ \geq $3 light phase space (lower) after the fit to data, shown for both lepton channels and all data periods combined. The distributions are shown separately for each ancillary region, as defined in Section 6.1. In the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light ($ \geq $7 jets: $ \geq $4b, $ \geq $3 light ) phase space the ancillary regions are defined as $ \leq $2, 2, and $ \geq $3 ($ \leq $3 and $ \geq $3) tight b-tagged jets. The shaded bands include all uncertainties described in Section 7 after profiling the nuisance parameters in the fit, estimated by sampling the predicted yields from the fit covariance matrix. The blue line shows the sum of the predicted yields for all processes before the fit to data, using the nominal $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ samples and its corresponding cross section for the signal. In the ratio panel the expected yields before the fit to data are shown relative to the predicted yields after the fit to data. The last bins contain the overflow. |
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Figure 8-b:
The $ H_{\mathrm{T}} $ of all light jets in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light phase space (upper) and the azimuthal angle between the hardest remaining light jet and the softest b jet ($ |\Delta\phi(\mathrm{lj}_{1}^{\text{extra}},\mathrm{b}_{\text{soft}})| $) in the $ \geq $7 jets: $ \geq $4b, $ \geq $3 light phase space (lower) after the fit to data, shown for both lepton channels and all data periods combined. The distributions are shown separately for each ancillary region, as defined in Section 6.1. In the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light ($ \geq $7 jets: $ \geq $4b, $ \geq $3 light ) phase space the ancillary regions are defined as $ \leq $2, 2, and $ \geq $3 ($ \leq $3 and $ \geq $3) tight b-tagged jets. The shaded bands include all uncertainties described in Section 7 after profiling the nuisance parameters in the fit, estimated by sampling the predicted yields from the fit covariance matrix. The blue line shows the sum of the predicted yields for all processes before the fit to data, using the nominal $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ samples and its corresponding cross section for the signal. In the ratio panel the expected yields before the fit to data are shown relative to the predicted yields after the fit to data. The last bins contain the overflow. |
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Figure 9:
Correlations between the parameters of interest $ \vec{\mu} $ in the fit for $ |\eta(b_{3})| $ in the $ \geq $5 jets: $ \geq $3b phase space. |
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Figure 10:
Predicted and observed normalized differential cross sections in the $ \geq $5 jets: $ \geq $3b fiducial phase space, for the inclusive jet multiplicity (upper left), the b jet multiplicity (upper right), the inclusive jet $ H_{\mathrm{T}} $ (middle left, \smash $ H_{\mathrm{T}}^{{\mathrm{j}} } $), the $ H_{\mathrm{T}} $ of b jets (middle right, \smash $ H_{\mathrm{T}}^{\mathrm{b}} $), the $ |\eta| $ of the third b jet (lower left), and the $ p_{\mathrm{T}} $ of the third b jet (lower right). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section prediction obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ N_{\text{jets}} $, $ N_{\mathrm{b}} $, \smash $ H_{\mathrm{T}}^{{\mathrm{j}} } $, \smash $ H_{\mathrm{T}}^{\mathrm{b}} $, and $p_{\mathrm{T}}(\mathrm{b}_{3}) $, the last bins contain the overflow. |
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Figure 10-a:
Predicted and observed normalized differential cross sections in the $ \geq $5 jets: $ \geq $3b fiducial phase space, for the inclusive jet multiplicity (upper left), the b jet multiplicity (upper right), the inclusive jet $ H_{\mathrm{T}} $ (middle left, \smash $ H_{\mathrm{T}}^{{\mathrm{j}} } $), the $ H_{\mathrm{T}} $ of b jets (middle right, \smash $ H_{\mathrm{T}}^{\mathrm{b}} $), the $ |\eta| $ of the third b jet (lower left), and the $ p_{\mathrm{T}} $ of the third b jet (lower right). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section prediction obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ N_{\text{jets}} $, $ N_{\mathrm{b}} $, \smash $ H_{\mathrm{T}}^{{\mathrm{j}} } $, \smash $ H_{\mathrm{T}}^{\mathrm{b}} $, and $p_{\mathrm{T}}(\mathrm{b}_{3}) $, the last bins contain the overflow. |
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Figure 10-b:
Predicted and observed normalized differential cross sections in the $ \geq $5 jets: $ \geq $3b fiducial phase space, for the inclusive jet multiplicity (upper left), the b jet multiplicity (upper right), the inclusive jet $ H_{\mathrm{T}} $ (middle left, \smash $ H_{\mathrm{T}}^{{\mathrm{j}} } $), the $ H_{\mathrm{T}} $ of b jets (middle right, \smash $ H_{\mathrm{T}}^{\mathrm{b}} $), the $ |\eta| $ of the third b jet (lower left), and the $ p_{\mathrm{T}} $ of the third b jet (lower right). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section prediction obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ N_{\text{jets}} $, $ N_{\mathrm{b}} $, \smash $ H_{\mathrm{T}}^{{\mathrm{j}} } $, \smash $ H_{\mathrm{T}}^{\mathrm{b}} $, and $p_{\mathrm{T}}(\mathrm{b}_{3}) $, the last bins contain the overflow. |
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Figure 10-c:
Predicted and observed normalized differential cross sections in the $ \geq $5 jets: $ \geq $3b fiducial phase space, for the inclusive jet multiplicity (upper left), the b jet multiplicity (upper right), the inclusive jet $ H_{\mathrm{T}} $ (middle left, \smash $ H_{\mathrm{T}}^{{\mathrm{j}} } $), the $ H_{\mathrm{T}} $ of b jets (middle right, \smash $ H_{\mathrm{T}}^{\mathrm{b}} $), the $ |\eta| $ of the third b jet (lower left), and the $ p_{\mathrm{T}} $ of the third b jet (lower right). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section prediction obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ N_{\text{jets}} $, $ N_{\mathrm{b}} $, \smash $ H_{\mathrm{T}}^{{\mathrm{j}} } $, \smash $ H_{\mathrm{T}}^{\mathrm{b}} $, and $p_{\mathrm{T}}(\mathrm{b}_{3}) $, the last bins contain the overflow. |
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Figure 10-d:
Predicted and observed normalized differential cross sections in the $ \geq $5 jets: $ \geq $3b fiducial phase space, for the inclusive jet multiplicity (upper left), the b jet multiplicity (upper right), the inclusive jet $ H_{\mathrm{T}} $ (middle left, \smash $ H_{\mathrm{T}}^{{\mathrm{j}} } $), the $ H_{\mathrm{T}} $ of b jets (middle right, \smash $ H_{\mathrm{T}}^{\mathrm{b}} $), the $ |\eta| $ of the third b jet (lower left), and the $ p_{\mathrm{T}} $ of the third b jet (lower right). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section prediction obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ N_{\text{jets}} $, $ N_{\mathrm{b}} $, \smash $ H_{\mathrm{T}}^{{\mathrm{j}} } $, \smash $ H_{\mathrm{T}}^{\mathrm{b}} $, and $p_{\mathrm{T}}(\mathrm{b}_{3}) $, the last bins contain the overflow. |
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Figure 10-e:
Predicted and observed normalized differential cross sections in the $ \geq $5 jets: $ \geq $3b fiducial phase space, for the inclusive jet multiplicity (upper left), the b jet multiplicity (upper right), the inclusive jet $ H_{\mathrm{T}} $ (middle left, \smash $ H_{\mathrm{T}}^{{\mathrm{j}} } $), the $ H_{\mathrm{T}} $ of b jets (middle right, \smash $ H_{\mathrm{T}}^{\mathrm{b}} $), the $ |\eta| $ of the third b jet (lower left), and the $ p_{\mathrm{T}} $ of the third b jet (lower right). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section prediction obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ N_{\text{jets}} $, $ N_{\mathrm{b}} $, \smash $ H_{\mathrm{T}}^{{\mathrm{j}} } $, \smash $ H_{\mathrm{T}}^{\mathrm{b}} $, and $p_{\mathrm{T}}(\mathrm{b}_{3}) $, the last bins contain the overflow. |
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Figure 10-f:
Predicted and observed normalized differential cross sections in the $ \geq $5 jets: $ \geq $3b fiducial phase space, for the inclusive jet multiplicity (upper left), the b jet multiplicity (upper right), the inclusive jet $ H_{\mathrm{T}} $ (middle left, \smash $ H_{\mathrm{T}}^{{\mathrm{j}} } $), the $ H_{\mathrm{T}} $ of b jets (middle right, \smash $ H_{\mathrm{T}}^{\mathrm{b}} $), the $ |\eta| $ of the third b jet (lower left), and the $ p_{\mathrm{T}} $ of the third b jet (lower right). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section prediction obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ N_{\text{jets}} $, $ N_{\mathrm{b}} $, \smash $ H_{\mathrm{T}}^{{\mathrm{j}} } $, \smash $ H_{\mathrm{T}}^{\mathrm{b}} $, and $p_{\mathrm{T}}(\mathrm{b}_{3}) $, the last bins contain the overflow. |
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Figure 11:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the inclusive jet $ H_{\mathrm{T}} $ (upper left), the $ H_{\mathrm{T}} $ of b jets (upper right), the $ |\eta| $ of the third b jet (middle left), the $ p_{\mathrm{T}} $ of the third b jet (middle right), the $ |\eta| $ of the fourth b jet (lower left), and the $ p_{\mathrm{T}} $ of the fourth b jet (lower right). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ H_{\mathrm{T}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 11-a:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the inclusive jet $ H_{\mathrm{T}} $ (upper left), the $ H_{\mathrm{T}} $ of b jets (upper right), the $ |\eta| $ of the third b jet (middle left), the $ p_{\mathrm{T}} $ of the third b jet (middle right), the $ |\eta| $ of the fourth b jet (lower left), and the $ p_{\mathrm{T}} $ of the fourth b jet (lower right). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ H_{\mathrm{T}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 11-b:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the inclusive jet $ H_{\mathrm{T}} $ (upper left), the $ H_{\mathrm{T}} $ of b jets (upper right), the $ |\eta| $ of the third b jet (middle left), the $ p_{\mathrm{T}} $ of the third b jet (middle right), the $ |\eta| $ of the fourth b jet (lower left), and the $ p_{\mathrm{T}} $ of the fourth b jet (lower right). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ H_{\mathrm{T}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
png pdf |
Figure 11-c:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the inclusive jet $ H_{\mathrm{T}} $ (upper left), the $ H_{\mathrm{T}} $ of b jets (upper right), the $ |\eta| $ of the third b jet (middle left), the $ p_{\mathrm{T}} $ of the third b jet (middle right), the $ |\eta| $ of the fourth b jet (lower left), and the $ p_{\mathrm{T}} $ of the fourth b jet (lower right). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ H_{\mathrm{T}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 11-d:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the inclusive jet $ H_{\mathrm{T}} $ (upper left), the $ H_{\mathrm{T}} $ of b jets (upper right), the $ |\eta| $ of the third b jet (middle left), the $ p_{\mathrm{T}} $ of the third b jet (middle right), the $ |\eta| $ of the fourth b jet (lower left), and the $ p_{\mathrm{T}} $ of the fourth b jet (lower right). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ H_{\mathrm{T}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
png pdf |
Figure 11-e:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the inclusive jet $ H_{\mathrm{T}} $ (upper left), the $ H_{\mathrm{T}} $ of b jets (upper right), the $ |\eta| $ of the third b jet (middle left), the $ p_{\mathrm{T}} $ of the third b jet (middle right), the $ |\eta| $ of the fourth b jet (lower left), and the $ p_{\mathrm{T}} $ of the fourth b jet (lower right). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ H_{\mathrm{T}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
png pdf |
Figure 11-f:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the inclusive jet $ H_{\mathrm{T}} $ (upper left), the $ H_{\mathrm{T}} $ of b jets (upper right), the $ |\eta| $ of the third b jet (middle left), the $ p_{\mathrm{T}} $ of the third b jet (middle right), the $ |\eta| $ of the fourth b jet (lower left), and the $ p_{\mathrm{T}} $ of the fourth b jet (lower right). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ H_{\mathrm{T}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
png pdf |
Figure 12:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the average $ \Delta R $ of all possible $ \mathrm{b}\mathrm{b} $ pairs (upper left), the largest invariant mass of any $ \mathrm{b}\mathrm{b} $ pair (upper right), the invariant mass (middle left), $ \Delta R $ (middle right), $ p_{\mathrm{T}} $ (lower left), and $ |\eta| $ (lower right) of the extra b-jet pair. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ m_{\mathrm{b}\mathrm{b}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
png pdf |
Figure 12-a:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the average $ \Delta R $ of all possible $ \mathrm{b}\mathrm{b} $ pairs (upper left), the largest invariant mass of any $ \mathrm{b}\mathrm{b} $ pair (upper right), the invariant mass (middle left), $ \Delta R $ (middle right), $ p_{\mathrm{T}} $ (lower left), and $ |\eta| $ (lower right) of the extra b-jet pair. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ m_{\mathrm{b}\mathrm{b}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
png pdf |
Figure 12-b:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the average $ \Delta R $ of all possible $ \mathrm{b}\mathrm{b} $ pairs (upper left), the largest invariant mass of any $ \mathrm{b}\mathrm{b} $ pair (upper right), the invariant mass (middle left), $ \Delta R $ (middle right), $ p_{\mathrm{T}} $ (lower left), and $ |\eta| $ (lower right) of the extra b-jet pair. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ m_{\mathrm{b}\mathrm{b}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 12-c:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the average $ \Delta R $ of all possible $ \mathrm{b}\mathrm{b} $ pairs (upper left), the largest invariant mass of any $ \mathrm{b}\mathrm{b} $ pair (upper right), the invariant mass (middle left), $ \Delta R $ (middle right), $ p_{\mathrm{T}} $ (lower left), and $ |\eta| $ (lower right) of the extra b-jet pair. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ m_{\mathrm{b}\mathrm{b}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 12-d:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the average $ \Delta R $ of all possible $ \mathrm{b}\mathrm{b} $ pairs (upper left), the largest invariant mass of any $ \mathrm{b}\mathrm{b} $ pair (upper right), the invariant mass (middle left), $ \Delta R $ (middle right), $ p_{\mathrm{T}} $ (lower left), and $ |\eta| $ (lower right) of the extra b-jet pair. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ m_{\mathrm{b}\mathrm{b}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 12-e:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the average $ \Delta R $ of all possible $ \mathrm{b}\mathrm{b} $ pairs (upper left), the largest invariant mass of any $ \mathrm{b}\mathrm{b} $ pair (upper right), the invariant mass (middle left), $ \Delta R $ (middle right), $ p_{\mathrm{T}} $ (lower left), and $ |\eta| $ (lower right) of the extra b-jet pair. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ m_{\mathrm{b}\mathrm{b}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 12-f:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the average $ \Delta R $ of all possible $ \mathrm{b}\mathrm{b} $ pairs (upper left), the largest invariant mass of any $ \mathrm{b}\mathrm{b} $ pair (upper right), the invariant mass (middle left), $ \Delta R $ (middle right), $ p_{\mathrm{T}} $ (lower left), and $ |\eta| $ (lower right) of the extra b-jet pair. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ m_{\mathrm{b}\mathrm{b}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 13:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the $ |\eta| $ (upper left) and $ p_{\mathrm{T}} $ (upper right) of the first extra b jet, the $ |\eta| $ (middle left) and $ p_{\mathrm{T}} $ (middle right) of the second extra b jet, and the inclusive jet multiplicity (lower left). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ N_{\text{jets}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 13-a:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the $ |\eta| $ (upper left) and $ p_{\mathrm{T}} $ (upper right) of the first extra b jet, the $ |\eta| $ (middle left) and $ p_{\mathrm{T}} $ (middle right) of the second extra b jet, and the inclusive jet multiplicity (lower left). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ N_{\text{jets}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 13-b:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the $ |\eta| $ (upper left) and $ p_{\mathrm{T}} $ (upper right) of the first extra b jet, the $ |\eta| $ (middle left) and $ p_{\mathrm{T}} $ (middle right) of the second extra b jet, and the inclusive jet multiplicity (lower left). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ N_{\text{jets}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 13-c:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the $ |\eta| $ (upper left) and $ p_{\mathrm{T}} $ (upper right) of the first extra b jet, the $ |\eta| $ (middle left) and $ p_{\mathrm{T}} $ (middle right) of the second extra b jet, and the inclusive jet multiplicity (lower left). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ N_{\text{jets}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 13-d:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the $ |\eta| $ (upper left) and $ p_{\mathrm{T}} $ (upper right) of the first extra b jet, the $ |\eta| $ (middle left) and $ p_{\mathrm{T}} $ (middle right) of the second extra b jet, and the inclusive jet multiplicity (lower left). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ N_{\text{jets}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 13-e:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the $ |\eta| $ (upper left) and $ p_{\mathrm{T}} $ (upper right) of the first extra b jet, the $ |\eta| $ (middle left) and $ p_{\mathrm{T}} $ (middle right) of the second extra b jet, and the inclusive jet multiplicity (lower left). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ N_{\text{jets}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 14:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the invariant mass (upper left), $ \Delta R $ (upper right), $ p_{\mathrm{T}} $ (lower left), and $ |\eta| $ (lower right) of the additional b-jet pair not originating from decaying top quarks. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ m_{\mathrm{b}\mathrm{b}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 14-a:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the invariant mass (upper left), $ \Delta R $ (upper right), $ p_{\mathrm{T}} $ (lower left), and $ |\eta| $ (lower right) of the additional b-jet pair not originating from decaying top quarks. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ m_{\mathrm{b}\mathrm{b}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 14-b:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the invariant mass (upper left), $ \Delta R $ (upper right), $ p_{\mathrm{T}} $ (lower left), and $ |\eta| $ (lower right) of the additional b-jet pair not originating from decaying top quarks. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ m_{\mathrm{b}\mathrm{b}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 14-c:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the invariant mass (upper left), $ \Delta R $ (upper right), $ p_{\mathrm{T}} $ (lower left), and $ |\eta| $ (lower right) of the additional b-jet pair not originating from decaying top quarks. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ m_{\mathrm{b}\mathrm{b}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 14-d:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the invariant mass (upper left), $ \Delta R $ (upper right), $ p_{\mathrm{T}} $ (lower left), and $ |\eta| $ (lower right) of the additional b-jet pair not originating from decaying top quarks. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ m_{\mathrm{b}\mathrm{b}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 15:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the $ |\eta| $ (left) and $ p_{\mathrm{T}} $ (right) of the first (upper row) and second (lower row) additional b of the b-jet pair not originating from decaying top quarks. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 15-a:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the $ |\eta| $ (left) and $ p_{\mathrm{T}} $ (right) of the first (upper row) and second (lower row) additional b of the b-jet pair not originating from decaying top quarks. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 15-b:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the $ |\eta| $ (left) and $ p_{\mathrm{T}} $ (right) of the first (upper row) and second (lower row) additional b of the b-jet pair not originating from decaying top quarks. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 15-c:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the $ |\eta| $ (left) and $ p_{\mathrm{T}} $ (right) of the first (upper row) and second (lower row) additional b of the b-jet pair not originating from decaying top quarks. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 15-d:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $4b fiducial phase space, for the $ |\eta| $ (left) and $ p_{\mathrm{T}} $ (right) of the first (upper row) and second (lower row) additional b of the b-jet pair not originating from decaying top quarks. The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols. For $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 16:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light (left) and $ \geq $7 jets: $ \geq $4b, $ \geq $3 light (right) fiducial phase space regions, for the $ H_{\mathrm{T}} $ of light jets (upper row), the $ p_{\mathrm{T}} $ of the extra light jet (middle row), and the $ \Delta\phi $ between the extra light jet and the softest b jet (lower row). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ H_{\mathrm{T}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 16-a:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light (left) and $ \geq $7 jets: $ \geq $4b, $ \geq $3 light (right) fiducial phase space regions, for the $ H_{\mathrm{T}} $ of light jets (upper row), the $ p_{\mathrm{T}} $ of the extra light jet (middle row), and the $ \Delta\phi $ between the extra light jet and the softest b jet (lower row). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ H_{\mathrm{T}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 16-b:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light (left) and $ \geq $7 jets: $ \geq $4b, $ \geq $3 light (right) fiducial phase space regions, for the $ H_{\mathrm{T}} $ of light jets (upper row), the $ p_{\mathrm{T}} $ of the extra light jet (middle row), and the $ \Delta\phi $ between the extra light jet and the softest b jet (lower row). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ H_{\mathrm{T}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 16-c:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light (left) and $ \geq $7 jets: $ \geq $4b, $ \geq $3 light (right) fiducial phase space regions, for the $ H_{\mathrm{T}} $ of light jets (upper row), the $ p_{\mathrm{T}} $ of the extra light jet (middle row), and the $ \Delta\phi $ between the extra light jet and the softest b jet (lower row). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ H_{\mathrm{T}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 16-d:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light (left) and $ \geq $7 jets: $ \geq $4b, $ \geq $3 light (right) fiducial phase space regions, for the $ H_{\mathrm{T}} $ of light jets (upper row), the $ p_{\mathrm{T}} $ of the extra light jet (middle row), and the $ \Delta\phi $ between the extra light jet and the softest b jet (lower row). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ H_{\mathrm{T}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 16-e:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light (left) and $ \geq $7 jets: $ \geq $4b, $ \geq $3 light (right) fiducial phase space regions, for the $ H_{\mathrm{T}} $ of light jets (upper row), the $ p_{\mathrm{T}} $ of the extra light jet (middle row), and the $ \Delta\phi $ between the extra light jet and the softest b jet (lower row). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ H_{\mathrm{T}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 16-f:
Predicted and observed normalized differential cross sections in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light (left) and $ \geq $7 jets: $ \geq $4b, $ \geq $3 light (right) fiducial phase space regions, for the $ H_{\mathrm{T}} $ of light jets (upper row), the $ p_{\mathrm{T}} $ of the extra light jet (middle row), and the $ \Delta\phi $ between the extra light jet and the softest b jet (lower row). The data are represented by points, with inner (outer) vertical bars indicating the systematic (total) uncertainties, also represented as blue (grey) bands. Cross section predictions obtained at the particle level from different simulation approaches are shown, including their statistical uncertainties, as coloured symbols with different shapes. For $ H_{\mathrm{T}} $ and $ p_{\mathrm{T}} $, the last bins contain the overflow. |
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Figure 17:
Observed $ z $ score for each of the theoretical predictions, given the unfolded normalized differential cross sections and their covariances. A lower value indicates a better agreement between prediction and measurement. The dashed line at $ z= $ 2 indicates a $ p $-value of 5%. Predictions for which the $ z $ score exceeds the visible range of the figure are marked with arrows ($ \to $). |
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Figure A1:
Post-fit nuisance parameter values and relative impacts on the fiducial cross section, for the fit of $ |\eta| $ of the b jet with third-highest $ p_{\mathrm{T}} $ in the $ \geq $5 jets: $ \geq $3b phase space. The nuisance parameters are defined such that the prefit value is zero with unity uncertainty. |
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Figure A2:
Post-fit nuisance parameter values and relative impacts on the fiducial cross section, for the fit of $ |\eta| $ of the subleading extra b jet in the $ \geq $6 jets: $ \geq $4b phase space. The nuisance parameters are defined such that the prefit value is zero with unity uncertainty. |
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Figure A3:
Post-fit nuisance parameter values and relative impacts on the fiducial cross section, for the fit of $ H_{\mathrm{T}} $ of light jets in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light phase space. The nuisance parameters are defined such that the prefit value is zero with unity uncertainty. |
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Figure A4:
Post-fit nuisance parameter values and relative impacts on the fiducial cross section, for the fit of $ \Delta\phi $ between leading light jet and softest b jet in the $ \geq $7 jets: $ \geq $4b, $ \geq $3 light phase space. The nuisance parameters are defined such that the prefit value is zero with unity uncertainty. |
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Figure B1:
Effect of the considered sources of uncertainties on the measurement of the normalized differential cross section of the $ |\eta| $ of the b jet with third-highest $ p_{\mathrm{T}} $ in the $ \geq $5 jets: $ \geq $3b phase space, obtained by combining the impacts of associated nuisance parameters. The last bin of the distribution is not shown, since it has no associated parameter of interest but is constrained by the other bins. The category ``other theory'' includes b quark fragmentation, top quark $ p_{\mathrm{T}} $ modelling, PDF, $ h_{\mathrm{damp}} $, colour reconnection, and underlying event uncertainties. The category ``other experimental'' includes pileup and the integrated luminosity uncertainties. |
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Figure B2:
Effect of the considered sources of uncertainties on the measurement of the normalized differential cross section of the $ |\eta| $ of the subleading extra b jet in the $ \geq $6 jets: $ \geq $4b phase space, obtained by combining the impacts of associated nuisance parameters. The last bin of the distribution is not shown, since it has no associated parameter of interest but is constrained by the other bins. The category ``other theory'' includes b quark fragmentation, top quark $ p_{\mathrm{T}} $ modelling, PDF, $ h_{\mathrm{damp}} $, colour reconnection, and underlying event uncertainties. The category ``other experimental'' includes pileup and the integrated luminosity uncertainties. |
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Figure B3:
Effect of the considered sources of uncertainties on the measurement of the normalized differential cross section of the $ H_{\mathrm{T}} $ of light jets in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light phase space, obtained by combining the impacts of associated nuisance parameters. The last bin of the distribution is not shown, since it has no associated parameter of interest but is constrained by the other bins. The category ``other theory'' includes b quark fragmentation, top quark $ p_{\mathrm{T}} $ modelling, PDF, $ h_{\mathrm{damp}} $, colour reconnection, and underlying event uncertainties. The category ``other experimental'' includes pileup and the integrated luminosity uncertainties. |
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Figure B4:
Effect of the considered sources of uncertainties on the measurement of the normalized differential cross section of the $ \Delta\phi $ between leading light jet and softest b jet in the $ \geq $7 jets: $ \geq $4b, $ \geq $3 light phase space, obtained by combining the impacts of associated nuisance parameters. The last bin of the distribution is not shown, since it has no associated parameter of interest but is constrained by the other bins. The category ``other theory'' includes b quark fragmentation, top quark $ p_{\mathrm{T}} $ modelling, PDF, $ h_{\mathrm{damp}} $, colour reconnection, and underlying event uncertainties. The category ``other experimental'' includes pileup and the integrated luminosity uncertainties. |
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Figure C1:
Correlations between the parameters of interest $ \vec{\mu} $ in the fit of the $ |\eta| $ of the subleading extra b jet in the $ \geq $6 jets: $ \geq $4b phase space. |
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Figure C2:
Correlations between the parameters of interest $ \vec{\mu} $ in the fit of the $ H_{\mathrm{T}} $ of light jets in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light phase space. |
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Figure C3:
Correlations between the parameters of interest $ \vec{\mu} $ in the fit of the $ \Delta\phi $ between leading light jet and softest b jet in the $ \geq $7 jets: $ \geq $4b, $ \geq $3 light phase space. |
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Figure D1:
Ratio of normalized differential cross section predictions of the POWHEG+OL+P8 $\mathrm{t\bar{t}b\bar{b}}$ 4FS modeling approach with different $ \mu_{\mathrm{R}} $ and $ \mu_{\mathrm{F}} $ scale settings relative to the measured normalized differential cross sections for the number of jets (upper) and $ H_{\mathrm{T}} $ of jets (lower) in the $ \geq $5 jets: $ \geq $3b phase space. The systematic (total) uncertainties of the measurement are represented as grey (blue) bands. Variations of the $ \mu_{\mathrm{R}} $ ($ \mu_{\mathrm{F}} $) scale relative to the nominal scale setting are shown in orange (purple). The last bin in the distributions contains the overflow. |
png pdf |
Figure D1-a:
Ratio of normalized differential cross section predictions of the POWHEG+OL+P8 $\mathrm{t\bar{t}b\bar{b}}$ 4FS modeling approach with different $ \mu_{\mathrm{R}} $ and $ \mu_{\mathrm{F}} $ scale settings relative to the measured normalized differential cross sections for the number of jets (upper) and $ H_{\mathrm{T}} $ of jets (lower) in the $ \geq $5 jets: $ \geq $3b phase space. The systematic (total) uncertainties of the measurement are represented as grey (blue) bands. Variations of the $ \mu_{\mathrm{R}} $ ($ \mu_{\mathrm{F}} $) scale relative to the nominal scale setting are shown in orange (purple). The last bin in the distributions contains the overflow. |
png pdf |
Figure D1-b:
Ratio of normalized differential cross section predictions of the POWHEG+OL+P8 $\mathrm{t\bar{t}b\bar{b}}$ 4FS modeling approach with different $ \mu_{\mathrm{R}} $ and $ \mu_{\mathrm{F}} $ scale settings relative to the measured normalized differential cross sections for the number of jets (upper) and $ H_{\mathrm{T}} $ of jets (lower) in the $ \geq $5 jets: $ \geq $3b phase space. The systematic (total) uncertainties of the measurement are represented as grey (blue) bands. Variations of the $ \mu_{\mathrm{R}} $ ($ \mu_{\mathrm{F}} $) scale relative to the nominal scale setting are shown in orange (purple). The last bin in the distributions contains the overflow. |
png pdf |
Figure D2:
Ratio of normalized differential cross section predictions of the POWHEG+OL+P8} $\mathrm{t\bar{t}b\bar{b}}$ 4FS modeling approach with different $ \mu_{\mathrm{R}} $ and $ \mu_{\mathrm{F}} $ scale settings relative to the measured normalized differential cross sections for the extra light jet (upper) and $ H_{\mathrm{T}} $ of light jets (lower) in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light phase space. The systematic (total) uncertainties of the measurement are represented as grey (blue) bands. The systematic (total) uncertainties of the measurement are represented as grey (blue) bands. Variations of the $ \mu_{\mathrm{R}} $ ($ \mu_{\mathrm{F}} $) scale relative to the nominal scale setting are shown in orange (purple). The last bin in the distributions contains the overflow. |
png pdf |
Figure D2-a:
Ratio of normalized differential cross section predictions of the POWHEG+OL+P8} $\mathrm{t\bar{t}b\bar{b}}$ 4FS modeling approach with different $ \mu_{\mathrm{R}} $ and $ \mu_{\mathrm{F}} $ scale settings relative to the measured normalized differential cross sections for the extra light jet (upper) and $ H_{\mathrm{T}} $ of light jets (lower) in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light phase space. The systematic (total) uncertainties of the measurement are represented as grey (blue) bands. The systematic (total) uncertainties of the measurement are represented as grey (blue) bands. Variations of the $ \mu_{\mathrm{R}} $ ($ \mu_{\mathrm{F}} $) scale relative to the nominal scale setting are shown in orange (purple). The last bin in the distributions contains the overflow. |
png pdf |
Figure D2-b:
Ratio of normalized differential cross section predictions of the POWHEG+OL+P8} $\mathrm{t\bar{t}b\bar{b}}$ 4FS modeling approach with different $ \mu_{\mathrm{R}} $ and $ \mu_{\mathrm{F}} $ scale settings relative to the measured normalized differential cross sections for the extra light jet (upper) and $ H_{\mathrm{T}} $ of light jets (lower) in the $ \geq $6 jets: $ \geq $3b, $ \geq $3 light phase space. The systematic (total) uncertainties of the measurement are represented as grey (blue) bands. The systematic (total) uncertainties of the measurement are represented as grey (blue) bands. Variations of the $ \mu_{\mathrm{R}} $ ($ \mu_{\mathrm{F}} $) scale relative to the nominal scale setting are shown in orange (purple). The last bin in the distributions contains the overflow. |
| Tables | |
png pdf |
Table 1:
Generator settings for different modeling approaches of $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ production. The top quark mass value is set to $ m_{\mathrm{t}} = $ 172.5 GeV for all generator setups, and for the generator setups using massive b quarks, the b quark mass value is set to $ m_{\mathrm{b}} = $ 4.75 GeV. In the scale settings, $ H_{\mathrm{T}} $ corresponds to the scalar $ m_{\mathrm{T}} $ sum, $ H_{\mathrm{T}} = \sum_{i=\mathrm{t},\bar{\mathrm{t}},\mathrm{b},\bar{\mathrm{b}},\mathrm{g}} m_{\mathrm{T},i} $, and \smash$ m_{\mathrm{T},i}=\sqrt{\smash[b]{m_i^2+p_{\mathrm{T},i}^2}} $ is the transverse mass. For generators setups using POWHEG the $ h_{\mathrm{damp}} $ value is specified. Other generator setups do not use this parameter and are marked with ($ \text{--} $). |
png pdf |
Table 2:
Generator settings for various minor background samples simulated with POWHEG [34-61-66] or MadGraph-5\_aMC@NLO [32]. The ``Group'' column refers to the grouping of processes in the maximum likelihood fits. |
png pdf |
Table 3:
Description of all measured observables for each of the four fiducial phase space regions. Observables marked as ($ \checkmark^\ast $) rely on the definition of additional b jets, and do not fully correspond to the 6j4b fiducial phase space defined at the particle level, but also require the presence of b jets without top (anti)quarks in their simulated history. |
png pdf |
Table 4:
Summary of the systematic uncertainty sources in the inclusive and differential $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ cross section measurements. The first column lists the source of the uncertainty. The second (third) column indicates the treatment of correlations of the uncertainties between different data-taking periods (processes), where $ \checkmark $ means fully correlated, $ \sim $ means partially correlated (i.e., contains sub-sources that are either fully correlated or uncorrelated), $ \times $ means uncorrelated, and $ \text{--} $ means not applicable. |
png pdf |
Table 5:
Contributions of the considered sources of uncertainty to the total uncertainty in the inclusive cross sections. For each group of uncertainty sources, the impacts of the corresponding nuisance parameters on the total cross section are combined, taking into account their correlation in the fit. The numbers show relative uncertainties (in %). The statistical uncertainty is obtained as the difference, in quadrature, between the total uncertainty and the sum of all systematic uncertainties. |
png pdf |
Table 6:
Measured and predicted inclusive cross sections in the four considered phase space regions (in fb). |
png pdf |
Table E1:
Observed $ z $ score for each of the theoretical predictions in the 5j3b phase space, given the unfolded data and covariance matrix. For the determination of the $ z $ score, only the measurement uncertainties are considered. |
png pdf |
Table E2:
Observed $ z $ score for each of the theoretical predictions in the 6j4b phase space, given the unfolded data and covariance matrix. For the determination of the $ z $ score, only the measurement uncertainties are considered. |
png pdf |
Table E3:
Observed $ z $ score for each of the theoretical predictions in the 6j4b phase space of the observables related to the $ \mathrm{b}\mathrm{b}^{\text{extra}} $ pair, given the unfolded data and covariance matrix. For the determination of the $ z $ score, only the measurement uncertainties are considered. |
png pdf |
Table E4:
Observed $ z $ score for each of the theoretical predictions in the 6j4b phase space of the observables related to the $ \mathrm{b}\mathrm{b}^{\text{add.}} $ pair, given the unfolded data and covariance matrix. For the determination of the $ z $ score, only the measurement uncertainties are considered. |
png pdf |
Table E5:
Observed $ z $ score for each of the theoretical predictions in the 6j3b3l phase space, given the unfolded data and covariance matrix. For the determination of the $ z $ score, only the measurement uncertainties are considered. |
png pdf |
Table E6:
Observed $ z $ score for each of the theoretical predictions in the 7j4b3l phase space, given the unfolded data and covariance matrix. For the determination of the $ z $ score, only the measurement uncertainties are considered. |
| Summary |
| Measurements of inclusive and normalized differential cross sections of the associated production of top quark-antiquark and bottom quark-antiquark pairs, $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $, for events containing an electron or a muon, have been presented. These measurements use proton-proton collision data recorded by the CMS detector at $ \sqrt{s} = $ 13 TeV and correspond to an integrated luminosity of 138 fb$ ^{-1} $. The inclusive cross sections are measured in four fiducial phase space regions requiring different jet, b jet, and light jet multiplicities. With total uncertainties of 6-17%, depending on the phase space, these are the most precise measurements of the $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ cross section to date. The uncertainties are dominated by systematic sources, with the leading uncertainties originating from the calibration of the b tagging and of the jet energy scale, and from the choice of renormalization scale in the signal $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ and background $ \mathrm{t} \bar{\mathrm{t}} $ processes. In most cases, the measured inclusive cross sections exceed the predictions with the chosen generator settings. The only exception is when using a particular choice of dynamic renormalization scale, $ \smash[b]{\mu_{\mathrm{R}}=\frac12 \prod_{i=\mathrm{t},\bar{\mathrm{t}},\mathrm{b},\bar{\mathrm{b}}} m_{\mathrm{T},i}^{1/4}} $, where $ \smash{m_{\mathrm{T},i}^2=m_i^2+p_{\mathrm{T},i}^2} $ are the transverse masses of top and bottom quarks. Differential cross section measurements are performed as a function of several observables in the aforementioned phase space regions. These observables mainly target b jets as well as additional light jets produced in association with the top quark pairs. In the phase space containing events with at least six jets, of which at least four are b tagged, the additional b-jet radiation is probed with two different approaches. The first approach uses observables defined purely at the particle level, without any reference to the top quark decay chains, by selecting the two b jets with the smallest angular separation. The second approach uses explicitly the b jets at the generator level that do not originate from top quark decays and identifies those jets at the detector level with a neural network discriminant. The differential measurements have relative uncertainties in the range of 2-50%, depending on the phase space and the observable. The results are compared to the predictions of several event generator setups, and it is found that none of them simultaneously describe all measured distributions in the various phase space regions. In the more inclusive phase space with five jets and three b jets, the agreement between data and predictions is generally poor, while in the phase space with six jets and four b jets, corresponding to the case in which the two additional b jets in $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ production are resolved, most predictions are compatible with the data within the larger experimental uncertainties. These measurements will help to further tune and refine the theoretical predictions and better assess the validity of the theoretical uncertainties estimated from the various $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ event generators. |
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