CMSTOP21012 ; CERNEP2022222  
Measurement of the differential $ \mathrm{t} \overline{\mathrm{t}} $ production cross section as a function of the jet mass and extraction of the top quark mass in hadronic decays of boosted top quarks  
CMS Collaboration  
2 November 2022  
Eur. Phys. J. C 83 (2023) 560  
Abstract: A measurement of the jet mass distribution in hadronic decays of Lorentzboosted top quarks is presented. The measurement is performed in the lepton+jets channel of top quark pair production ( $ \mathrm{t} \overline{\mathrm{t}} $) events, where the lepton is an electron or muon. The products of the hadronic top quark decay are reconstructed using a single largeradius jet with transverse momentum greater than 400 GeV. The data were collected with the CMS detector at the LHC in protonproton collisions and correspond to an integrated luminosity of 138 fb$ ^{1} $. The differential $ \mathrm{t} \overline{\mathrm{t}} $ production cross section as a function of the jet mass is unfolded to the particle level and is used to extract the top quark mass. The jet mass scale is calibrated using the hadronic W boson decay within the largeradius jet. The uncertainties in the modelling of the final state radiation are reduced by studying angular correlations in the jet substructure. These developments lead to a significant increase in precision, and a top quark mass of 173.06 $ \pm $ 0.84 GeV.  
Links: eprint arXiv:2211.01456 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; Physics Briefing ; CADI line (restricted) ; 
Figures  
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Figure 1:
Distribution in $ m_\text{jet} $ at the particle level after the selection of the fiducial region in the lepton+jets channel of $ \mathrm{t} \overline{\mathrm{t}} $, simulated with POWHEG. The contributions from fully merged events (blue solid) and not merged events (red dashed) are displayed, as well as the sum of the two (black solid). 
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Figure 2:
Distributions in the reconstructed XCone jet $ p_{\mathrm{T}} $ (left) and $ m_\text{jet} $ (right), after the full event selection. The vertical bars on the markers show the statistical uncertainty. The hatched regions show the total uncertainty in the simulation, including the statistical and experimental systematic uncertainties. The lower panels show the ratio of the data to the simulation. The uncertainty bands include the experimental systematic uncertainties and statistical uncertainties in the simulation. In the ratios, the statistical (light grey) and total (dark grey) uncertainties are shown separately. 
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Figure 2a:
Distribution in the reconstructed XCone jet $ p_{\mathrm{T}} $, after the full event selection. The vertical bars on the markers show the statistical uncertainty. The hatched region shows the total uncertainty in the simulation, including the statistical and experimental systematic uncertainties. The lower panel shows the ratio of the data to the simulation. The uncertainty band includes the experimental systematic uncertainties and statistical uncertainties in the simulation. In the ratio, the statistical (light grey) and total (dark grey) uncertainties are shown separately. 
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Figure 2b:
Distribution in the reconstructed XCone jet $ m_\text{jet} $, after the full event selection. The vertical bars on the markers show the statistical uncertainty. The hatched region shows the total uncertainty in the simulation, including the statistical and experimental systematic uncertainties. The lower panel shows the ratio of the data to the simulation. The uncertainty band includes the experimental systematic uncertainties and statistical uncertainties in the simulation. In the ratio, the statistical (light grey) and total (dark grey) uncertainties are shown separately. 
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Figure 3:
Distributions in reconstructed $ p_{\mathrm{T}} $ of the $ p_{\mathrm{T}} $leading XCone subjet (upper left), second XCone subjet (upper right) and third XCone subjet (lower). The vertical bars on the markers show the statistical uncertainty. The hatched regions show the total uncertainty in the simulation, including the statistical and experimental systematic uncertainties. The lower panels show the ratio of the data to the simulation. The uncertainty bands include the experimental systematic uncertainties and statistical uncertainties in the simulation. In the ratios, the statistical (light grey) and total (dark grey) uncertainties are shown separately. 
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Figure 3a:
Distribution in reconstructed $ p_{\mathrm{T}} $ of the $ p_{\mathrm{T}} $leading XCone subjet. The vertical bars on the markers show the statistical uncertainty. The hatched region shows the total uncertainty in the simulation, including the statistical and experimental systematic uncertainties. The lower panel shows the ratio of the data to the simulation. The uncertainty band include the experimental systematic uncertainties and statistical uncertainties in the simulation. In the ratio, the statistical (light grey) and total (dark grey) uncertainties are shown separately. 
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Figure 3b:
Distribution in reconstructed $ p_{\mathrm{T}} $ of the $ p_{\mathrm{T}} $second XCone subjet. The vertical bars on the markers show the statistical uncertainty. The hatched region shows the total uncertainty in the simulation, including the statistical and experimental systematic uncertainties. The lower panel shows the ratio of the data to the simulation. The uncertainty band include the experimental systematic uncertainties and statistical uncertainties in the simulation. In the ratio, the statistical (light grey) and total (dark grey) uncertainties are shown separately. 
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Figure 3c:
Distribution in reconstructed $ p_{\mathrm{T}} $ of the $ p_{\mathrm{T}} $third XCone subjet. The vertical bars on the markers show the statistical uncertainty. The hatched region shows the total uncertainty in the simulation, including the statistical and experimental systematic uncertainties. The lower panel shows the ratio of the data to the simulation. The uncertainty band include the experimental systematic uncertainties and statistical uncertainties in the simulation. In the ratio, the statistical (light grey) and total (dark grey) uncertainties are shown separately. 
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Figure 4:
Peak region of the reconstructed W boson mass in the four regions $ p_{\mathrm{T}}^\mathrm{W} < $ 300 GeV and $ r_{p_{\mathrm{T}}} < $ 0.7 (upper left), $ p_{\mathrm{T}}^\mathrm{W} < $ 300 GeV and $ r_{p_{\mathrm{T}}} > $ 0.7 (upper right), $ p_{\mathrm{T}}^\mathrm{W} > $ 300 GeV and $ r_{p_{\mathrm{T}}} < $ 0.7 (lower left), and $ p_{\mathrm{T}}^\mathrm{W} > $ 300 GeV and $ r_{p_{\mathrm{T}}} > $ 0.7 (lower right). The backgroundsubtracted data and the $ \mathrm{t} \overline{\mathrm{t}} $ simulation are normalised to unit area. For illustration, the $ \mathrm{t} \overline{\mathrm{t}} $ simulation is also shown with the JEC and XCone correction factors varied by one standard deviation. The lower panels show the ratios to the nominal $ \mathrm{t} \overline{\mathrm{t}} $ simulation. 
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Figure 4a:
Peak region of the reconstructed W boson mass in the $ p_{\mathrm{T}}^\mathrm{W} < $ 300 GeV and $ r_{p_{\mathrm{T}}} < $ 0.7 region. The backgroundsubtracted data and the $ \mathrm{t} \overline{\mathrm{t}} $ simulation are normalised to unit area. For illustration, the $ \mathrm{t} \overline{\mathrm{t}} $ simulation is also shown with the JEC and XCone correction factors varied by one standard deviation. The lower panel shows the ratios to the nominal $ \mathrm{t} \overline{\mathrm{t}} $ simulation. 
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Figure 4b:
Peak region of the reconstructed W boson mass in the $ p_{\mathrm{T}}^\mathrm{W} < $ 300 GeV and $ r_{p_{\mathrm{T}}} > $ 0.7 region. The backgroundsubtracted data and the $ \mathrm{t} \overline{\mathrm{t}} $ simulation are normalised to unit area. For illustration, the $ \mathrm{t} \overline{\mathrm{t}} $ simulation is also shown with the JEC and XCone correction factors varied by one standard deviation. The lower panel shows the ratios to the nominal $ \mathrm{t} \overline{\mathrm{t}} $ simulation. 
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Figure 4c:
Peak region of the reconstructed W boson mass in the $ p_{\mathrm{T}}^\mathrm{W} > $ 300 GeV and $ r_{p_{\mathrm{T}}} < $ 0.7 region. The backgroundsubtracted data and the $ \mathrm{t} \overline{\mathrm{t}} $ simulation are normalised to unit area. For illustration, the $ \mathrm{t} \overline{\mathrm{t}} $ simulation is also shown with the JEC and XCone correction factors varied by one standard deviation. The lower panel shows the ratios to the nominal $ \mathrm{t} \overline{\mathrm{t}} $ simulation. 
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Figure 4d:
Peak region of the reconstructed W boson mass in the $ p_{\mathrm{T}}^\mathrm{W} > $ 300 GeV and $ r_{p_{\mathrm{T}}} > $ 0.7 region. The backgroundsubtracted data and the $ \mathrm{t} \overline{\mathrm{t}} $ simulation are normalised to unit area. For illustration, the $ \mathrm{t} \overline{\mathrm{t}} $ simulation is also shown with the JEC and XCone correction factors varied by one standard deviation. The lower panel shows the ratios to the nominal $ \mathrm{t} \overline{\mathrm{t}} $ simulation. 
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Figure 5:
The twodimensional $ \chi^2 $ as a function of $ f^\text{JEC} $ and $ f^\text{XCone} $, obtained from a comparison of backgroundsubtracted data with the predictions from $ \mathrm{t} \overline{\mathrm{t}} $ production in the reconstructed $ m_{\mathrm{W}} $ distributions. The minimum is indicated by a black cross, and the borders of the 68 and 95% CL intervals are shown by the light and dark red ellipses, respectively. 
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Figure 6:
Jet mass distribution of hadronic decays of the W boson, reconstructed from two XCone subjets. The vertical bars on the markers show the statistical uncertainty. The hatched regions show the total uncertainty in the simulation, including the statistical and experimental systematic uncertainties. The lower panel shows the ratio of the data to the simulation. The uncertainty bands include the experimental systematic uncertainties and statistical uncertainties in the simulation. The statistical (light grey) and total (dark grey) uncertainties are shown separately in the ratio. 
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Figure 7:
Mean values of the $ m_\text{jet} $ distribution for t and W boson decays, as a function of the number of primary vertices $ N_{\text{PV}} $ (left). Data (markers) are compared with $ \mathrm{t} \overline{\mathrm{t}} $ simulation (filled areas). The vertical bars and size of the filled areas show the statistical uncertainties in the calculation of the mean values. Jet mass resolution in simulation as a function of particlelevel XConejet $ p_{\mathrm{T}} $, given for different intervals in the number of primary vertices (right). The vertical bars indicate the statistical uncertainties and the horizontal bars indicate the bin width. 
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Figure 7a:
Mean values of the $ m_\text{jet} $ distribution for t and W boson decays, as a function of the number of primary vertices $ N_{\text{PV}} $. Data (markers) are compared with $ \mathrm{t} \overline{\mathrm{t}} $ simulation (filled areas). The vertical bars and size of the filled areas show the statistical uncertainties in the calculation of the mean values. 
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Figure 7b:
Jet mass resolution in simulation as a function of particlelevel XConejet $ p_{\mathrm{T}} $, given for different intervals in the number of primary vertices. The vertical bars indicate the statistical uncertainties and the horizontal bars indicate the bin width. 
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Figure 8:
The normalised distributions in $ \tau_{32} $ for AK8 jets with $ m_\text{jet} > $ 140 GeV from the hadronic decay of boosted top quarks. Shown are distributions for 2016 (left) and the combination of 2017 and 2018 (right). The backgroundsubtracted data are compared to $ \mathrm{t} \overline{\mathrm{t}} $ simulations with the UE tunes CUETP8M2T4 for 2016 and CP5 for the combination of 2017 and 2018, and different values of $ f_\text{FSR} $ are shown as well. The lower panels show the ratio to the $ \mathrm{t} \overline{\mathrm{t}} $ simulation with $ f_\text{FSR}= $ 1. 
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Figure 8a:
The normalised distribution in $ \tau_{32} $ for AK8 jets with $ m_\text{jet} > $ 140 GeV from the hadronic decay of boosted top quarks for 2016. The backgroundsubtracted data are compared to $ \mathrm{t} \overline{\mathrm{t}} $ simulations with the UE tune CUETP8M2T4 and different values of $ f_\text{FSR} $ are shown as well. The lower panel shows the ratio to the $ \mathrm{t} \overline{\mathrm{t}} $ simulation with $ f_\text{FSR}= $ 1. 
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Figure 8b:
The normalised distribution in $ \tau_{32} $ for AK8 jets with $ m_\text{jet} > $ 140 GeV from the hadronic decay of boosted top quarks for the combination of 2017 and 2018. The backgroundsubtracted data are compared to $ \mathrm{t} \overline{\mathrm{t}} $ simulations with the UE tune CP5 and different values of $ f_\text{FSR} $ are shown as well. The lower panel shows the ratio to the $ \mathrm{t} \overline{\mathrm{t}} $ simulation with $ f_\text{FSR}= $ 1. 
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Figure 9:
Relative experimental (left) and model (right) uncertainties in the measurement of $ m_\text{jet} $. Various sources are displayed as coloured lines and compared to the total experimental or model uncertainty, respectively. The uncertainty sources are calculated as the square root of the diagonal entries from the respective covariance matrix, and do not include bintobin correlations. 
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Figure 9a:
Relative experimental uncertainties in the measurement of $ m_\text{jet} $. Various sources are displayed as coloured lines and compared to the total experimental or model uncertainty, respectively. The uncertainty sources are calculated as the square root of the diagonal entries from the respective covariance matrix, and do not include bintobin correlations. 
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Figure 9b:
Relative model uncertainties in the measurement of $ m_\text{jet} $. Various sources are displayed as coloured lines and compared to the total experimental or model uncertainty, respectively. The uncertainty sources are calculated as the square root of the diagonal entries from the respective covariance matrix, and do not include bintobin correlations. 
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Figure 10:
Relative experimental (left) and model (right) uncertainties after normalising the measurement to the total cross section. Various sources are displayed as coloured lines and compared to the total experimental or model uncertainty, respectively. The uncertainty sources are calculated as the square root of the diagonal entries from the respective covariance matrix, and do not include bintobin correlations. 
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Figure 10a:
Relative experimental uncertainties after normalising the measurement to the total cross section. Various sources are displayed as coloured lines and compared to the total experimental or model uncertainty, respectively. The uncertainty sources are calculated as the square root of the diagonal entries from the respective covariance matrix, and do not include bintobin correlations. 
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Figure 10b:
Relative model uncertainties after normalising the measurement to the total cross section. Various sources are displayed as coloured lines and compared to the total experimental or model uncertainty, respectively. The uncertainty sources are calculated as the square root of the diagonal entries from the respective covariance matrix, and do not include bintobin correlations. 
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Figure 11:
Differential $ \mathrm{t} \overline{\mathrm{t}} $ production cross section as a function of $ m_\text{jet} $ compared to predictions obtained with POWHEG: absolute (left) and normalised (right). For the normalised measurement, the data are compared to predictions with different $ m_{\mathrm{t}} $. The vertical bars represent the total uncertainties, and the statistical uncertainties are shown by short horizontal bars. The long horizontal bars reflect the bin widths. Theoretical uncertainties in the prediction are indicated by the bands. The lower panels show the ratio of the theoretical prediction to data. 
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Figure 11a:
Absolute differential $ \mathrm{t} \overline{\mathrm{t}} $ production cross section as a function of $ m_\text{jet} $ compared to predictions obtained with POWHEG. The vertical bars represent the total uncertainties, and the statistical uncertainties are shown by short horizontal bars. The long horizontal bars reflect the bin widths. Theoretical uncertainties in the prediction are indicated by the bands. The lower panel shows the ratio of the theoretical prediction to data. 
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Figure 11b:
Normalised differential $ \mathrm{t} \overline{\mathrm{t}} $ production cross section as a function of $ m_\text{jet} $ compared to predictions obtained with POWHEG. The data are compared to predictions with different $ m_{\mathrm{t}} $. The vertical bars represent the total uncertainties, and the statistical uncertainties are shown by short horizontal bars. The long horizontal bars reflect the bin widths. Theoretical uncertainties in the prediction are indicated by the bands. The lower panel shows the ratio of the theoretical prediction to data. 
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Figure 12:
Correlations between the bins in the unfolding before (left) and after (right) normalising the distribution to the total cross section. Boxes with crosses indicate negative values of the correlation coefficient. 
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Figure 12a:
Correlations between the bins in the unfolding before normalising the distribution to the total cross section. Boxes with crosses indicate negative values of the correlation coefficient. 
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Figure 12b:
Correlations between the bins in the unfolding after normalising the distribution to the total cross section. Boxes with crosses indicate negative values of the correlation coefficient. 
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Figure 13:
Extracted top quark mass from simulation compared to the true value. The vertical error bars show the total uncertainty in the extraction of $ m_{\mathrm{t}} $. 
Tables  
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Table 1:
Total and individual uncertainties in the extraction of $ m_{\mathrm{t}} $ from the normalised differential cross section. The uncertainties are grouped into experimental, model, theory, and statistical uncertainties. Uncertainties from the choice of the PDF, b tagging, the luminosity measurement, and the lepton triggers, identification and reconstruction are smaller than 0.01 GeV and are not listed. 
Summary 
A measurement of the differential top quark pair ($ \mathrm{t} \overline{\mathrm{t}} $) production cross section as a function of the jet mass $ m_\text{jet} $ in hadronic decays of boosted top quarks has been presented. The normalised distribution in $ m_\text{jet} $ is sensitive to the top quark mass $ m_{\mathrm{t}} $, which is measured to be 173.06 $ \pm $ 0.84 GeV. This value is compatible with earlier precision measurements in fully resolved final states. With respect to an earlier CMS analysis, the precision is improved by a factor of more than three. This has been achieved by a dedicated calibration of the jet mass scale, a study of the effects of final state radiation inside largeradius jets, and about 4 times more data. With these improvements, the uncertainty in the extraction of $ m_{\mathrm{t}} $ at high top quark boosts becomes comparable to direct measurements close to the $ \mathrm{t} \overline{\mathrm{t}} $ production threshold. The sources of the leading systematic uncertainties are very different, highlighting the complementarity of this measurement. In addition, the study of boosted top quarks offers the possibility to directly compare the distribution in $ m_\text{jet} $ to analytic calculations. When these calculations become available, the unfolded $ m_\text{jet} $ distribution can be used to measure the top quark pole mass directly. The precisely measured differential cross section as a function of $ m_\text{jet} $ represents an important step towards understanding and resolving the ambiguities between the top quark mass extracted from a direct reconstruction of $ m_{\mathrm{t}} $, and the top quark pole mass. 
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