CMS-PAS-TOP-21-012 | ||

Measurement of the jet mass distribution and top quark mass in hadronic decays of boosted top quarks in pp collisions at $\sqrt{s} = $ 13 TeV | ||

CMS Collaboration | ||

May 2022 | ||

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Abstract:
A measurement of the jet mass distribution in hadronic decays of boosted top quarks is presented. The data were collected with the CMS detector at the LHC in pp collisions and correspond to an integrated luminosity of 138 fb$^{-1}$. The measurement is performed in the lepton+jets channel of $\mathrm{t\bar{t}}$ events, where the lepton is an electron or muon. The products of the hadronic top quark decay are reconstructed using a single large-radius jet with transverse momentum greater than 400 GeV. The differential $\mathrm{t\bar{t}}$ 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 $m_\mathrm{t}$. The jet mass is calibrated using the hadronic W boson decay within the large-radius jet. Uncertainties in the modelling of the final state radiation are reduced by studying angular relations of the jet substructure. These developments lead to a significant increase in precision with respect to an earlier measurement, resulting in $m_\mathrm{t} = $ 172.76 $\pm$ 0.81 GeV.
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Links:
CDS record (PDF) ;
Physics Briefing ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, EPJC 83 (2023) 560.The superseded preliminary plots can be found here. |

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 $\mathrm{t\bar{t}}$, simulated with POWHEG. The contributions from fully merged events (blue solid) and not merged events (orange 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 statistical and experimental systematic uncertainties, where the statistical (light grey) and total (dark grey) uncertainties are shown separately in the ratios. |

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Figure 2-a:
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 statistical and experimental systematic uncertainties, where the statistical (light grey) and total (dark grey) uncertainties are shown separately in the ratios. |

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Figure 2-b:
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 statistical and experimental systematic uncertainties, where the statistical (light grey) and total (dark grey) uncertainties are shown separately in the ratios. |

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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 statistical and experimental systematic uncertainties, where the statistical (light grey) and total (dark grey) uncertainties are shown separately in the ratios. |

png pdf |
Figure 3-a:
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 statistical and experimental systematic uncertainties, where the statistical (light grey) and total (dark grey) uncertainties are shown separately in the ratios. |

png pdf |
Figure 3-b:
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 statistical and experimental systematic uncertainties, where the statistical (light grey) and total (dark grey) uncertainties are shown separately in the ratios. |

png pdf |
Figure 3-c:
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 statistical and experimental systematic uncertainties, where the statistical (light grey) and total (dark grey) uncertainties are shown separately in the ratios. |

png pdf |
Figure 4:
Peak region of the reconstructed W boson mass in the four regions $ {{p_{\mathrm {T}}} ^\mathrm{W}} < $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} < $ 0.7 (upper left), $ {{p_{\mathrm {T}}} ^\mathrm{W}} < $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} > $ 0.7 (upper right), $ {{p_{\mathrm {T}}} ^\mathrm{W}} > $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} < $ 0.7 (lower left), and $ {{p_{\mathrm {T}}} ^\mathrm{W}} > $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} > $ 0.7 (lower right). The background-subtracted data are normalised to unit area and compared to the $\mathrm{t\bar{t}}$ simulation with the JEC and XCone correction factors varied by one standard deviation. The lower panels show the ratios to the nominal $\mathrm{t\bar{t}}$ simulation. |

png pdf |
Figure 4-a:
Peak region of the reconstructed W boson mass in the four regions $ {{p_{\mathrm {T}}} ^\mathrm{W}} < $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} < $ 0.7 (upper left), $ {{p_{\mathrm {T}}} ^\mathrm{W}} < $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} > $ 0.7 (upper right), $ {{p_{\mathrm {T}}} ^\mathrm{W}} > $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} < $ 0.7 (lower left), and $ {{p_{\mathrm {T}}} ^\mathrm{W}} > $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} > $ 0.7 (lower right). The background-subtracted data are normalised to unit area and compared to the $\mathrm{t\bar{t}}$ simulation with the JEC and XCone correction factors varied by one standard deviation. The lower panels show the ratios to the nominal $\mathrm{t\bar{t}}$ simulation. |

png pdf |
Figure 4-b:
Peak region of the reconstructed W boson mass in the four regions $ {{p_{\mathrm {T}}} ^\mathrm{W}} < $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} < $ 0.7 (upper left), $ {{p_{\mathrm {T}}} ^\mathrm{W}} < $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} > $ 0.7 (upper right), $ {{p_{\mathrm {T}}} ^\mathrm{W}} > $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} < $ 0.7 (lower left), and $ {{p_{\mathrm {T}}} ^\mathrm{W}} > $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} > $ 0.7 (lower right). The background-subtracted data are normalised to unit area and compared to the $\mathrm{t\bar{t}}$ simulation with the JEC and XCone correction factors varied by one standard deviation. The lower panels show the ratios to the nominal $\mathrm{t\bar{t}}$ simulation. |

png pdf |
Figure 4-c:
Peak region of the reconstructed W boson mass in the four regions $ {{p_{\mathrm {T}}} ^\mathrm{W}} < $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} < $ 0.7 (upper left), $ {{p_{\mathrm {T}}} ^\mathrm{W}} < $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} > $ 0.7 (upper right), $ {{p_{\mathrm {T}}} ^\mathrm{W}} > $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} < $ 0.7 (lower left), and $ {{p_{\mathrm {T}}} ^\mathrm{W}} > $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} > $ 0.7 (lower right). The background-subtracted data are normalised to unit area and compared to the $\mathrm{t\bar{t}}$ simulation with the JEC and XCone correction factors varied by one standard deviation. The lower panels show the ratios to the nominal $\mathrm{t\bar{t}}$ simulation. |

png pdf |
Figure 4-d:
Peak region of the reconstructed W boson mass in the four regions $ {{p_{\mathrm {T}}} ^\mathrm{W}} < $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} < $ 0.7 (upper left), $ {{p_{\mathrm {T}}} ^\mathrm{W}} < $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} > $ 0.7 (upper right), $ {{p_{\mathrm {T}}} ^\mathrm{W}} > $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} < $ 0.7 (lower left), and $ {{p_{\mathrm {T}}} ^\mathrm{W}} > $ 300 GeV and $ {f_{{p_{\mathrm {T}}}}} > $ 0.7 (lower right). The background-subtracted data are normalised to unit area and compared to the $\mathrm{t\bar{t}}$ simulation with the JEC and XCone correction factors varied by one standard deviation. The lower panels show the ratios to the nominal $\mathrm{t\bar{t}}$ simulation. |

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Figure 5:
The two-dimensional $\chi ^2$ as a function of ${f^\text {JEC}}$ and ${f^\text {XCone}}$, obtained from a comparison of background-subtracted data with the predictions from $\mathrm{t\bar{t}}$ 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 statistical and experimental systematic uncertainties, where 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 (upper) and W (lower) decays, as a function of the number of primary vertices (left). Data (markers) are compared with $\mathrm{t\bar{t}}$ 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 particle level XCone jet ${p_{\mathrm {T}}}$, given for different intervals in the number of primary vertices (right). The vertical bars indicate the statistical uncertainties, horizontal bars indicate the bin width. |

png pdf |
Figure 7-a:
Mean values of the ${m_\text {jet}}$ distribution for t (upper) and W (lower) decays, as a function of the number of primary vertices (left). Data (markers) are compared with $\mathrm{t\bar{t}}$ 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 particle level XCone jet ${p_{\mathrm {T}}}$, given for different intervals in the number of primary vertices (right). The vertical bars indicate the statistical uncertainties, horizontal bars indicate the bin width. |

png pdf |
Figure 7-b:
Mean values of the ${m_\text {jet}}$ distribution for t (upper) and W (lower) decays, as a function of the number of primary vertices (left). Data (markers) are compared with $\mathrm{t\bar{t}}$ 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 particle level XCone jet ${p_{\mathrm {T}}}$, given for different intervals in the number of primary vertices (right). The vertical bars indicate the statistical uncertainties, horizontal bars indicate the bin width. |

png pdf |
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 background-subtracted data are compared to $\mathrm{t\bar{t}}$ simulations with different parton shower and UE tunes and different values of ${f_\text {FSR}}$. The bottom panels show the ratio to the $\mathrm{t\bar{t}}$ simulation with $ {f_\text {FSR}} =$ 1. |

png pdf |
Figure 8-a:
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 background-subtracted data are compared to $\mathrm{t\bar{t}}$ simulations with different parton shower and UE tunes and different values of ${f_\text {FSR}}$. The bottom panels show the ratio to the $\mathrm{t\bar{t}}$ simulation with $ {f_\text {FSR}} =$ 1. |

png pdf |
Figure 8-b:
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 background-subtracted data are compared to $\mathrm{t\bar{t}}$ simulations with different parton shower and UE tunes and different values of ${f_\text {FSR}}$. The bottom panels show the ratio to the $\mathrm{t\bar{t}}$ simulation with $ {f_\text {FSR}} =$ 1. |

png pdf |
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 bin-to-bin correlations. |

png pdf |
Figure 9-a:
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 bin-to-bin correlations. |

png pdf |
Figure 9-b:
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 bin-to-bin correlations. |

png pdf |
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 bin-to-bin correlations. |

png pdf |
Figure 10-a:
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 bin-to-bin correlations. |

png pdf |
Figure 10-b:
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 bin-to-bin correlations. |

png pdf |
Figure 11:
Differential (left) and normalised (right) $\mathrm{t\bar{t}}$ production cross section as a function of ${m_\text {jet}}$, compared to predictions obtained with POWHEG. 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 panel shows the ratio of the theoretical prediction to data. |

png pdf |
Figure 11-a:
Differential (left) and normalised (right) $\mathrm{t\bar{t}}$ production cross section as a function of ${m_\text {jet}}$, compared to predictions obtained with POWHEG. 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 panel shows the ratio of the theoretical prediction to data. |

png pdf |
Figure 11-b:
Differential (left) and normalised (right) $\mathrm{t\bar{t}}$ production cross section as a function of ${m_\text {jet}}$, compared to predictions obtained with POWHEG. 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 panel shows the ratio of the theoretical prediction to data. |

png pdf |
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 12-a:
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 12-b:
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 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 statistical, experimental, model and theory uncertainties. Experimental uncertainties from 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 $\mathrm{t\bar{t}}$ 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 extracted with a value of 172.76 $\pm$ 0.81 GeV, compatible with earlier precision measurements with fully resolved final states [11,14,15]. With respect to an earlier analysis [34], 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 large-radius jets, and about 3.7 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 $\mathrm{t\bar{t}}$ production threshold. The sources of the leading systematic uncertainties are very different, highlighting the complementarity of these measurements. In addition, the study of boosted top quarks offers the possibility to directly compare the distribution in ${m_\text{jet}}$ to analytic calculations [32]. 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 ambiguities between the top quark pole mass and the mass extracted from a direct reconstruction of ${m_{\mathrm{t}}}$, where the latter relies on simulations including non-perturbative effects. |

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Compact Muon Solenoid LHC, CERN |