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| CMS-TOP-23-003 ; CERN-EP-2024-005 | ||
| Review of top quark mass measurements in CMS | ||
| CMS Collaboration | ||
| 3 March 2024 | ||
| Accepted for publication in Physics Reports | ||
| Abstract: The top quark mass is one of the most intriguing parameters of the standard model (SM). Its value indicates a Yukawa coupling close to unity, and the resulting strong ties to the Higgs physics make the top quark mass a crucial ingredient for understanding essential aspects of the electroweak sector of the SM. While it is such an important parameter of the SM, its measurement and interpretation in terms of the Lagrangian parameter are challenging. The CMS Collaboration has performed multiple measurements of the top quark mass, addressing these challenges from different angles: highly precise `direct' measurements, using the top quark decay products, as well as `indirect' measurements aiming at accurate interpretations in terms of the Lagrangian parameter. Recent mass measurements using Lorentz-boosted top quarks are particularly promising, opening a new avenue of measurements based on top quark decay products contained in a single particle jet, with superior prospects for accurate theoretical interpretations. Moreover, dedicated studies of the dominant uncertainties in the modelling of the signal processes have been performed. This review offers the first comprehensive overview of these measurements performed by the CMS Collaboration using the data collected at centre-of-mass energies of 7, 8, and 13 TeV. | ||
| Links: e-print arXiv:2403.01313 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; Physics Briefing ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Summary of CMS measurements of the $ \mathrm{t} \overline{\mathrm{t}} $ production cross section as a function of $ \sqrt{s} $ compared to the NNLO QCD calculation complemented with NNLL resummation (TOP++ v2.0 [77]). The theory band represents uncertainties due to the renormalisation and factorisation scales, parton distribution functions, and the strong coupling. The measurements and the theoretical calculation are quoted at $ m_{\mathrm{t}}= $ 172.5 GeV. Measurements made at the same $ \sqrt{s} $ are slightly offset for clarity. An enlarged inset is included to highlight the difference between 13 and 13.6 TeV predictions and results. Figure taken from Ref. [82]. |
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Figure 2:
Summary of single top quark production cross section measurements by CMS. Theoretical calculations for $ t $-channel, $ s $-channel, and W-associated production are courtesy of N. Kidonakis [88,89]. |
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Figure 3:
Reconstructed top quark mass resolution with and without the HITFIT/KINFITTER kinematic reconstruction in the lepton+jets (left) and all-jets (right) channels. Multiple reconstruction options with and without kinematic fit are represented by lines of different colour, and ``correct'' denotes the correct parton-jet assignments as discussed in the text. The HITFIT/KINFITTER reconstruction with a cutoff on $ P_{\text{gof}} $ is used for measuring the top quark mass [61,62,62]. |
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Figure 3-a:
Reconstructed top quark mass resolution with and without the HITFIT/KINFITTER kinematic reconstruction in the lepton+jets (left) and all-jets (right) channels. Multiple reconstruction options with and without kinematic fit are represented by lines of different colour, and ``correct'' denotes the correct parton-jet assignments as discussed in the text. The HITFIT/KINFITTER reconstruction with a cutoff on $ P_{\text{gof}} $ is used for measuring the top quark mass [61,62,62]. |
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Figure 3-b:
Reconstructed top quark mass resolution with and without the HITFIT/KINFITTER kinematic reconstruction in the lepton+jets (left) and all-jets (right) channels. Multiple reconstruction options with and without kinematic fit are represented by lines of different colour, and ``correct'' denotes the correct parton-jet assignments as discussed in the text. The HITFIT/KINFITTER reconstruction with a cutoff on $ P_{\text{gof}} $ is used for measuring the top quark mass [61,62,62]. |
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Figure 4:
Reconstructed $ \mathrm{t} \overline{\mathrm{t}} $ mass bias (left) and resolution (right) with and without the HITFIT kinematic reconstruction in the lepton+jets channel, as functions of the $ \mathrm{t} \overline{\mathrm{t}} $ invariant mass at generator level. Multiple reconstruction options with and without kinematic fit are represented by lines of different colour, and ``correct'' denotes the correct parton-jet assignments as discussed in the text. The HITFIT reconstruction with a cutoff on $ P_{\text{gof}} $ is used for measuring the top quark mass [61]. |
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Figure 4-a:
Reconstructed $ \mathrm{t} \overline{\mathrm{t}} $ mass bias (left) and resolution (right) with and without the HITFIT kinematic reconstruction in the lepton+jets channel, as functions of the $ \mathrm{t} \overline{\mathrm{t}} $ invariant mass at generator level. Multiple reconstruction options with and without kinematic fit are represented by lines of different colour, and ``correct'' denotes the correct parton-jet assignments as discussed in the text. The HITFIT reconstruction with a cutoff on $ P_{\text{gof}} $ is used for measuring the top quark mass [61]. |
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Figure 4-b:
Reconstructed $ \mathrm{t} \overline{\mathrm{t}} $ mass bias (left) and resolution (right) with and without the HITFIT kinematic reconstruction in the lepton+jets channel, as functions of the $ \mathrm{t} \overline{\mathrm{t}} $ invariant mass at generator level. Multiple reconstruction options with and without kinematic fit are represented by lines of different colour, and ``correct'' denotes the correct parton-jet assignments as discussed in the text. The HITFIT reconstruction with a cutoff on $ P_{\text{gof}} $ is used for measuring the top quark mass [61]. |
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Figure 5:
Reconstructed $ \mathrm{t} \overline{\mathrm{t}} $ mass bias (left) and resolution (right) with and without the KINFITTER kinematic reconstruction in the all-jet channel, as functions of the $ \mathrm{t} \overline{\mathrm{t}} $ invariant mass at generator level. Multiple reconstruction options with and without kinematic fit are represented by lines of different colour, and ``correct'' denotes the correct parton-jet assignments as discussed in the text. The KINFITTER reconstruction with a cutoff on $ P_{\text{gof}} $ is used for measuring the top quark mass [62]. |
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Figure 5-a:
Reconstructed $ \mathrm{t} \overline{\mathrm{t}} $ mass bias (left) and resolution (right) with and without the KINFITTER kinematic reconstruction in the all-jet channel, as functions of the $ \mathrm{t} \overline{\mathrm{t}} $ invariant mass at generator level. Multiple reconstruction options with and without kinematic fit are represented by lines of different colour, and ``correct'' denotes the correct parton-jet assignments as discussed in the text. The KINFITTER reconstruction with a cutoff on $ P_{\text{gof}} $ is used for measuring the top quark mass [62]. |
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Figure 5-b:
Reconstructed $ \mathrm{t} \overline{\mathrm{t}} $ mass bias (left) and resolution (right) with and without the KINFITTER kinematic reconstruction in the all-jet channel, as functions of the $ \mathrm{t} \overline{\mathrm{t}} $ invariant mass at generator level. Multiple reconstruction options with and without kinematic fit are represented by lines of different colour, and ``correct'' denotes the correct parton-jet assignments as discussed in the text. The KINFITTER reconstruction with a cutoff on $ P_{\text{gof}} $ is used for measuring the top quark mass [62]. |
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Figure 6:
The reconstruction efficiencies for the full kinematic reconstruction (FKR, blue circles) and loose kinematic reconstruction (LKR, orange squares) are shown as functions of the invariant mass, transverse momentum, and rapidity of the reconstructed $ \mathrm{t} \overline{\mathrm{t}} $ system. The averaged efficiencies are 92 (96)% for the FKR (LKR). The corresponding parton-generator-level distributions, normalised to unit area, for $ \mathrm{t} \overline{\mathrm{t}} $ production are represented by the grey shaded areas, shown on the logarithmic scale (right $ y $ axis). The POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulated samples are used. |
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Figure 6-a:
The reconstruction efficiencies for the full kinematic reconstruction (FKR, blue circles) and loose kinematic reconstruction (LKR, orange squares) are shown as functions of the invariant mass, transverse momentum, and rapidity of the reconstructed $ \mathrm{t} \overline{\mathrm{t}} $ system. The averaged efficiencies are 92 (96)% for the FKR (LKR). The corresponding parton-generator-level distributions, normalised to unit area, for $ \mathrm{t} \overline{\mathrm{t}} $ production are represented by the grey shaded areas, shown on the logarithmic scale (right $ y $ axis). The POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulated samples are used. |
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Figure 6-b:
The reconstruction efficiencies for the full kinematic reconstruction (FKR, blue circles) and loose kinematic reconstruction (LKR, orange squares) are shown as functions of the invariant mass, transverse momentum, and rapidity of the reconstructed $ \mathrm{t} \overline{\mathrm{t}} $ system. The averaged efficiencies are 92 (96)% for the FKR (LKR). The corresponding parton-generator-level distributions, normalised to unit area, for $ \mathrm{t} \overline{\mathrm{t}} $ production are represented by the grey shaded areas, shown on the logarithmic scale (right $ y $ axis). The POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulated samples are used. |
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Figure 6-c:
The reconstruction efficiencies for the full kinematic reconstruction (FKR, blue circles) and loose kinematic reconstruction (LKR, orange squares) are shown as functions of the invariant mass, transverse momentum, and rapidity of the reconstructed $ \mathrm{t} \overline{\mathrm{t}} $ system. The averaged efficiencies are 92 (96)% for the FKR (LKR). The corresponding parton-generator-level distributions, normalised to unit area, for $ \mathrm{t} \overline{\mathrm{t}} $ production are represented by the grey shaded areas, shown on the logarithmic scale (right $ y $ axis). The POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulated samples are used. |
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Figure 7:
The biases (solid lines), as defined in the text, for the full kinematic reconstruction (FKR, blue) and loose kinematic reconstruction (LKR, orange) are shown for the invariant mass, transverse momentum, and rapidity of the $ \mathrm{t} \overline{\mathrm{t}} $ system, as a function of the same variables at the generator level. The corresponding parton-generator-level distributions, normalised to unit area, for $ \mathrm{t} \overline{\mathrm{t}} $ production are represented by the grey shaded areas, shown on the logarithmic scale (right $ y $ axis). The POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulated samples are used. |
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Figure 7-a:
The biases (solid lines), as defined in the text, for the full kinematic reconstruction (FKR, blue) and loose kinematic reconstruction (LKR, orange) are shown for the invariant mass, transverse momentum, and rapidity of the $ \mathrm{t} \overline{\mathrm{t}} $ system, as a function of the same variables at the generator level. The corresponding parton-generator-level distributions, normalised to unit area, for $ \mathrm{t} \overline{\mathrm{t}} $ production are represented by the grey shaded areas, shown on the logarithmic scale (right $ y $ axis). The POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulated samples are used. |
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Figure 7-b:
The biases (solid lines), as defined in the text, for the full kinematic reconstruction (FKR, blue) and loose kinematic reconstruction (LKR, orange) are shown for the invariant mass, transverse momentum, and rapidity of the $ \mathrm{t} \overline{\mathrm{t}} $ system, as a function of the same variables at the generator level. The corresponding parton-generator-level distributions, normalised to unit area, for $ \mathrm{t} \overline{\mathrm{t}} $ production are represented by the grey shaded areas, shown on the logarithmic scale (right $ y $ axis). The POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulated samples are used. |
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Figure 7-c:
The biases (solid lines), as defined in the text, for the full kinematic reconstruction (FKR, blue) and loose kinematic reconstruction (LKR, orange) are shown for the invariant mass, transverse momentum, and rapidity of the $ \mathrm{t} \overline{\mathrm{t}} $ system, as a function of the same variables at the generator level. The corresponding parton-generator-level distributions, normalised to unit area, for $ \mathrm{t} \overline{\mathrm{t}} $ production are represented by the grey shaded areas, shown on the logarithmic scale (right $ y $ axis). The POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulated samples are used. |
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Figure 8:
The resolutions (solid lines), as defined in the text, for the full kinematic reconstruction (FKR, blue) and loose kinematic reconstruction (LKR, orange) are shown as functions of the invariant mass, transverse momentum, and rapidity of the $ \mathrm{t} \overline{\mathrm{t}} $ system at the generator level. The corresponding parton-generator-level distributions, normalised to unit area, for $ \mathrm{t} \overline{\mathrm{t}} $ production are represented by the grey shaded areas, shown on the logarithmic scale (right $ y $ axis). The POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulated samples are used. |
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Figure 8-a:
The resolutions (solid lines), as defined in the text, for the full kinematic reconstruction (FKR, blue) and loose kinematic reconstruction (LKR, orange) are shown as functions of the invariant mass, transverse momentum, and rapidity of the $ \mathrm{t} \overline{\mathrm{t}} $ system at the generator level. The corresponding parton-generator-level distributions, normalised to unit area, for $ \mathrm{t} \overline{\mathrm{t}} $ production are represented by the grey shaded areas, shown on the logarithmic scale (right $ y $ axis). The POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulated samples are used. |
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Figure 8-b:
The resolutions (solid lines), as defined in the text, for the full kinematic reconstruction (FKR, blue) and loose kinematic reconstruction (LKR, orange) are shown as functions of the invariant mass, transverse momentum, and rapidity of the $ \mathrm{t} \overline{\mathrm{t}} $ system at the generator level. The corresponding parton-generator-level distributions, normalised to unit area, for $ \mathrm{t} \overline{\mathrm{t}} $ production are represented by the grey shaded areas, shown on the logarithmic scale (right $ y $ axis). The POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulated samples are used. |
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Figure 8-c:
The resolutions (solid lines), as defined in the text, for the full kinematic reconstruction (FKR, blue) and loose kinematic reconstruction (LKR, orange) are shown as functions of the invariant mass, transverse momentum, and rapidity of the $ \mathrm{t} \overline{\mathrm{t}} $ system at the generator level. The corresponding parton-generator-level distributions, normalised to unit area, for $ \mathrm{t} \overline{\mathrm{t}} $ production are represented by the grey shaded areas, shown on the logarithmic scale (right $ y $ axis). The POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulated samples are used. |
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Figure 9:
The correlation between $ \rho_{\text{gen}} $ and $ \rho_{\text{reco}} $ is shown for the regression NN reconstruction method (left). The $ \rho_{\text{reco}} $ resolution, defined in the text, as a function of $ \rho_{\text{gen}} $ (right) for the full (blue line) and loose (orange line) kinematic reconstructions and the regression NN (red line) methods. The number of events per bin in the left plot is shown by the colour scale. Figure taken from Ref. [69]. |
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Figure 9-a:
The correlation between $ \rho_{\text{gen}} $ and $ \rho_{\text{reco}} $ is shown for the regression NN reconstruction method (left). The $ \rho_{\text{reco}} $ resolution, defined in the text, as a function of $ \rho_{\text{gen}} $ (right) for the full (blue line) and loose (orange line) kinematic reconstructions and the regression NN (red line) methods. The number of events per bin in the left plot is shown by the colour scale. Figure taken from Ref. [69]. |
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Figure 9-b:
The correlation between $ \rho_{\text{gen}} $ and $ \rho_{\text{reco}} $ is shown for the regression NN reconstruction method (left). The $ \rho_{\text{reco}} $ resolution, defined in the text, as a function of $ \rho_{\text{gen}} $ (right) for the full (blue line) and loose (orange line) kinematic reconstructions and the regression NN (red line) methods. The number of events per bin in the left plot is shown by the colour scale. Figure taken from Ref. [69]. |
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Figure 10:
Distributions of the jet multiplicity $ N_{\text{Jets}} $ [134] (left) and the jet substructure observable $ \Delta R_{\mathrm{g}} $, the angle between the groomed subjets, normalised to the number of jets [135] (right) in $ \mathrm{t} \overline{\mathrm{t}} $ events at 13 TeV (black symbols). The data are compared to the MC simulation setups used in Run-1, early Run-2, and Run-2 legacy analyses, presented by bands of different style and colour. The uncertainty bands include ME scale, ME-PS matching, ISR, and FSR uncertainties. |
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Figure 10-a:
Distributions of the jet multiplicity $ N_{\text{Jets}} $ [134] (left) and the jet substructure observable $ \Delta R_{\mathrm{g}} $, the angle between the groomed subjets, normalised to the number of jets [135] (right) in $ \mathrm{t} \overline{\mathrm{t}} $ events at 13 TeV (black symbols). The data are compared to the MC simulation setups used in Run-1, early Run-2, and Run-2 legacy analyses, presented by bands of different style and colour. The uncertainty bands include ME scale, ME-PS matching, ISR, and FSR uncertainties. |
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Figure 10-b:
Distributions of the jet multiplicity $ N_{\text{Jets}} $ [134] (left) and the jet substructure observable $ \Delta R_{\mathrm{g}} $, the angle between the groomed subjets, normalised to the number of jets [135] (right) in $ \mathrm{t} \overline{\mathrm{t}} $ events at 13 TeV (black symbols). The data are compared to the MC simulation setups used in Run-1, early Run-2, and Run-2 legacy analyses, presented by bands of different style and colour. The uncertainty bands include ME scale, ME-PS matching, ISR, and FSR uncertainties. |
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Figure 11:
Left: Ratio of data to POWHEG+PYTHIA-8 (early Run-2) predictions for top quark $ p_{\mathrm{T}} $ in the dilepton (red symbols) and lepton+jets (blue symbols) channels along with an exponential fit (solid line). Right: Distribution of the transverse momentum of hadronically decaying top quark as measured by CMS [139] (black symbols) compared to MC simulations for the generator setups used in Run-1, early Run-2, and Run-2 legacy analyses, presented by bands of different styles. The uncertainty bands include ME scale, ME-PS matching, ISR, and FSR uncertainties. |
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Figure 11-a:
Left: Ratio of data to POWHEG+PYTHIA-8 (early Run-2) predictions for top quark $ p_{\mathrm{T}} $ in the dilepton (red symbols) and lepton+jets (blue symbols) channels along with an exponential fit (solid line). Right: Distribution of the transverse momentum of hadronically decaying top quark as measured by CMS [139] (black symbols) compared to MC simulations for the generator setups used in Run-1, early Run-2, and Run-2 legacy analyses, presented by bands of different styles. The uncertainty bands include ME scale, ME-PS matching, ISR, and FSR uncertainties. |
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Figure 11-b:
Left: Ratio of data to POWHEG+PYTHIA-8 (early Run-2) predictions for top quark $ p_{\mathrm{T}} $ in the dilepton (red symbols) and lepton+jets (blue symbols) channels along with an exponential fit (solid line). Right: Distribution of the transverse momentum of hadronically decaying top quark as measured by CMS [139] (black symbols) compared to MC simulations for the generator setups used in Run-1, early Run-2, and Run-2 legacy analyses, presented by bands of different styles. The uncertainty bands include ME scale, ME-PS matching, ISR, and FSR uncertainties. |
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Figure 12:
Left: The pseudorapidity density of charged hadrons, $ \mathrm{d} N_{\text{ch}}/\mathrm{d}\eta $, using data from about 170\,000 MB events from inelastic pp collisions using both hit pairs and reconstructed tracks by the CMS experiment [142] at $ \sqrt{s} = $ 13 TeV. Right: The charged-particle $ p_{\mathrm{T}}^{\text{sum}} $ density in the azimuthal region transverse to the direction of the leading charged particle as a function of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment [143] at $ \sqrt{s} = $ 13 TeV. The predictions of the CMS UE tunes from Run-1 to Run-2 legacy evaluated at 13 TeV are compared with data. The coloured bands represent the variations of the tunes, and error bars on the data points represent the total experimental uncertainty in the data including the model uncertainty. Both distributions are normalised to the total number of events. |
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Figure 12-a:
Left: The pseudorapidity density of charged hadrons, $ \mathrm{d} N_{\text{ch}}/\mathrm{d}\eta $, using data from about 170\,000 MB events from inelastic pp collisions using both hit pairs and reconstructed tracks by the CMS experiment [142] at $ \sqrt{s} = $ 13 TeV. Right: The charged-particle $ p_{\mathrm{T}}^{\text{sum}} $ density in the azimuthal region transverse to the direction of the leading charged particle as a function of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment [143] at $ \sqrt{s} = $ 13 TeV. The predictions of the CMS UE tunes from Run-1 to Run-2 legacy evaluated at 13 TeV are compared with data. The coloured bands represent the variations of the tunes, and error bars on the data points represent the total experimental uncertainty in the data including the model uncertainty. Both distributions are normalised to the total number of events. |
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Figure 12-b:
Left: The pseudorapidity density of charged hadrons, $ \mathrm{d} N_{\text{ch}}/\mathrm{d}\eta $, using data from about 170\,000 MB events from inelastic pp collisions using both hit pairs and reconstructed tracks by the CMS experiment [142] at $ \sqrt{s} = $ 13 TeV. Right: The charged-particle $ p_{\mathrm{T}}^{\text{sum}} $ density in the azimuthal region transverse to the direction of the leading charged particle as a function of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment [143] at $ \sqrt{s} = $ 13 TeV. The predictions of the CMS UE tunes from Run-1 to Run-2 legacy evaluated at 13 TeV are compared with data. The coloured bands represent the variations of the tunes, and error bars on the data points represent the total experimental uncertainty in the data including the model uncertainty. Both distributions are normalised to the total number of events. |
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Figure 13:
Left: Normalised differential cross section as a function of $ \sum p_{\mathrm{T}} $ of charged particles in the UE in $ \mathrm{t} \overline{\mathrm{t}} $ events, compared to the predictions of different models. The data (coloured boxes) are compared to the nominal POWHEG+PYTHIA-8 predictions and to the expectations obtained from varied $ \alpha_\mathrm{S}^{\text{ISR}}(m_{\mathrm{Z}}) $ or $ \alpha_\mathrm{S}^{\text{FSR}}(m_{\mathrm{Z}}) $ POWHEG+PYTHIA-8 setups (markers). In the case of the POWHEG+PYTHIA-8 setup, the error bar represents the envelope obtained by varying the main parameters of the CEUP8M2T4 tune, according to their uncertainties. This envelope includes the variation of the CR model, $ \alpha_\mathrm{S}^{\text{ISR}}(m_{\mathrm{Z}}) $, $ \alpha_\mathrm{S}^{\text{FSR}}(m_{\mathrm{Z}}) $, the $ h_{\text{damp}} $ parameter, and the $ \mu_{\mathrm{r}} $/$ \mu_{\mathrm{f}} $ scales at the ME level. Right: The different panels show the ratio between each model tested and the data. The shaded (hatched) band represents the total (statistical) uncertainty of the data, while the error bars represent either the total uncertainty of the POWHEG+PYTHIA-8 setup, or the statistical uncertainty of the other MC simulation setups. Figures taken from Ref. [144]. |
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Figure 13-a:
Left: Normalised differential cross section as a function of $ \sum p_{\mathrm{T}} $ of charged particles in the UE in $ \mathrm{t} \overline{\mathrm{t}} $ events, compared to the predictions of different models. The data (coloured boxes) are compared to the nominal POWHEG+PYTHIA-8 predictions and to the expectations obtained from varied $ \alpha_\mathrm{S}^{\text{ISR}}(m_{\mathrm{Z}}) $ or $ \alpha_\mathrm{S}^{\text{FSR}}(m_{\mathrm{Z}}) $ POWHEG+PYTHIA-8 setups (markers). In the case of the POWHEG+PYTHIA-8 setup, the error bar represents the envelope obtained by varying the main parameters of the CEUP8M2T4 tune, according to their uncertainties. This envelope includes the variation of the CR model, $ \alpha_\mathrm{S}^{\text{ISR}}(m_{\mathrm{Z}}) $, $ \alpha_\mathrm{S}^{\text{FSR}}(m_{\mathrm{Z}}) $, the $ h_{\text{damp}} $ parameter, and the $ \mu_{\mathrm{r}} $/$ \mu_{\mathrm{f}} $ scales at the ME level. Right: The different panels show the ratio between each model tested and the data. The shaded (hatched) band represents the total (statistical) uncertainty of the data, while the error bars represent either the total uncertainty of the POWHEG+PYTHIA-8 setup, or the statistical uncertainty of the other MC simulation setups. Figures taken from Ref. [144]. |
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Figure 13-b:
Left: Normalised differential cross section as a function of $ \sum p_{\mathrm{T}} $ of charged particles in the UE in $ \mathrm{t} \overline{\mathrm{t}} $ events, compared to the predictions of different models. The data (coloured boxes) are compared to the nominal POWHEG+PYTHIA-8 predictions and to the expectations obtained from varied $ \alpha_\mathrm{S}^{\text{ISR}}(m_{\mathrm{Z}}) $ or $ \alpha_\mathrm{S}^{\text{FSR}}(m_{\mathrm{Z}}) $ POWHEG+PYTHIA-8 setups (markers). In the case of the POWHEG+PYTHIA-8 setup, the error bar represents the envelope obtained by varying the main parameters of the CEUP8M2T4 tune, according to their uncertainties. This envelope includes the variation of the CR model, $ \alpha_\mathrm{S}^{\text{ISR}}(m_{\mathrm{Z}}) $, $ \alpha_\mathrm{S}^{\text{FSR}}(m_{\mathrm{Z}}) $, the $ h_{\text{damp}} $ parameter, and the $ \mu_{\mathrm{r}} $/$ \mu_{\mathrm{f}} $ scales at the ME level. Right: The different panels show the ratio between each model tested and the data. The shaded (hatched) band represents the total (statistical) uncertainty of the data, while the error bars represent either the total uncertainty of the POWHEG+PYTHIA-8 setup, or the statistical uncertainty of the other MC simulation setups. Figures taken from Ref. [144]. |
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Figure 14:
Measured distribution of the pull angle in $ \mathrm{t} \overline{\mathrm{t}} $ events taken at 8 TeV recorded by ATLAS [154] (points with vertical error bars) compared to MC simulations for the generator setups used in Run-1, early Run-2, and Run-2 legacy analyses, presented by bands of different styles. The uncertainty bands illustrate the uncertainties resulting from colour reconnection effects, as estimated by variations described in the main text. The same variations are applied in CMS top quark mass measurements. |
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Figure 15:
Normalised $ \mathrm{t} \overline{\mathrm{t}} $ differential cross section for the pull angle between jets from the W boson in hadronic top quark decays, calculated from the charged constituents of the jets, measured by the ATLAS experiment using $ \sqrt{s} = $ 8 TeV data [154] to investigate colour flow (left). The predictions from POWHEG+PYTHIA-8 using different tune configurations are compared with data. The statistical uncertainties in the predictions are represented by the coloured band and the vertical bars. The coloured band and error bars on the data points represent the total experimental uncertainty in the data. The invariant mass reconstructed from the hadronically decaying top quark candidates at the generator level (right). The coloured band and the vertical bars represent the statistical uncertainty in the predictions. Figures adapted from Ref. [152]. |
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Figure 15-a:
Normalised $ \mathrm{t} \overline{\mathrm{t}} $ differential cross section for the pull angle between jets from the W boson in hadronic top quark decays, calculated from the charged constituents of the jets, measured by the ATLAS experiment using $ \sqrt{s} = $ 8 TeV data [154] to investigate colour flow (left). The predictions from POWHEG+PYTHIA-8 using different tune configurations are compared with data. The statistical uncertainties in the predictions are represented by the coloured band and the vertical bars. The coloured band and error bars on the data points represent the total experimental uncertainty in the data. The invariant mass reconstructed from the hadronically decaying top quark candidates at the generator level (right). The coloured band and the vertical bars represent the statistical uncertainty in the predictions. Figures adapted from Ref. [152]. |
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Figure 15-b:
Normalised $ \mathrm{t} \overline{\mathrm{t}} $ differential cross section for the pull angle between jets from the W boson in hadronic top quark decays, calculated from the charged constituents of the jets, measured by the ATLAS experiment using $ \sqrt{s} = $ 8 TeV data [154] to investigate colour flow (left). The predictions from POWHEG+PYTHIA-8 using different tune configurations are compared with data. The statistical uncertainties in the predictions are represented by the coloured band and the vertical bars. The coloured band and error bars on the data points represent the total experimental uncertainty in the data. The invariant mass reconstructed from the hadronically decaying top quark candidates at the generator level (right). The coloured band and the vertical bars represent the statistical uncertainty in the predictions. Figures adapted from Ref. [152]. |
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Figure 16:
Distribution of the b quark fragmentation function normalised to the number of b hadrons measured by ALEPH in $ \mathrm{e}^+ \mathrm{e}^- $ collisions at $ \sqrt{s}= $ 91.2 GeV [156] (black symbols with vertical error bars showing the total measurement uncertainties) compared to $ \mathrm{e}^+ \mathrm{e}^- $ MC simulations for the generator setups used in Run-1, early Run-2, and Run-2 legacy analyses, presented by bands of different styles (left). The uncertainty bands are constructed around the default prediction and illustrate the b quark fragmentation uncertainties. The measured semileptonic branching ratios of b hadrons [1] (black symbols) compared to the values in the generator setups (coloured symbols) and their uncertainties, illustrated by shaded bands (right). |
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Figure 16-a:
Distribution of the b quark fragmentation function normalised to the number of b hadrons measured by ALEPH in $ \mathrm{e}^+ \mathrm{e}^- $ collisions at $ \sqrt{s}= $ 91.2 GeV [156] (black symbols with vertical error bars showing the total measurement uncertainties) compared to $ \mathrm{e}^+ \mathrm{e}^- $ MC simulations for the generator setups used in Run-1, early Run-2, and Run-2 legacy analyses, presented by bands of different styles (left). The uncertainty bands are constructed around the default prediction and illustrate the b quark fragmentation uncertainties. The measured semileptonic branching ratios of b hadrons [1] (black symbols) compared to the values in the generator setups (coloured symbols) and their uncertainties, illustrated by shaded bands (right). |
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Figure 16-b:
Distribution of the b quark fragmentation function normalised to the number of b hadrons measured by ALEPH in $ \mathrm{e}^+ \mathrm{e}^- $ collisions at $ \sqrt{s}= $ 91.2 GeV [156] (black symbols with vertical error bars showing the total measurement uncertainties) compared to $ \mathrm{e}^+ \mathrm{e}^- $ MC simulations for the generator setups used in Run-1, early Run-2, and Run-2 legacy analyses, presented by bands of different styles (left). The uncertainty bands are constructed around the default prediction and illustrate the b quark fragmentation uncertainties. The measured semileptonic branching ratios of b hadrons [1] (black symbols) compared to the values in the generator setups (coloured symbols) and their uncertainties, illustrated by shaded bands (right). |
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Figure 17:
Momenta of the self-energy quantum corrections in the top quark rest frame (red segments), absorbed into the top quark mass parameter in the pole (very left), MSR and $ \mathrm{\overline{MS}} $ schemes for different mass renormalisation scales with respect to the charm and bottom quark masses. The red segments extend to infinite momenta for all top quark mass schemes. The loops inside the red segments illustrate contributions of the virtual top, charm, or bottom quark loops, and $ n_{\mathrm{q}} $ stands for the number of quarks lighter than quark $ \mathrm{q} $, indicating that the MSR and the $ \mathrm{\overline{MS}} $ masses run with different flavour numbers between flavour thresholds, as does the strong coupling constant $ \alpha_\mathrm{S} $. Figure taken from Ref. [188]. |
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Figure 18:
Left: The distribution of the reconstructed top quark mass $ m_{\mathrm{t}}^\text{reco} $ using the jet assignment from the kinematic fit, but the reconstructed jet momenta and no addition selection. Right: The distribution of the top quark mass from the kinematic fit $ m_{\mathrm{t}}^\text{fit} $ with the $ P_{\text{gof}} > $ 0.2 selection. Data are shown as points with vertical error bars showing the statistical uncertainties. The coloured histograms show the simulated signal and background contributions. The simulated signal is decomposed into the contributions from correct, wrong, or unmatched permutations as introduced in Section 2.3. The uncertainty in the predicted $ \mathrm{t} \overline{\mathrm{t}} $ cross section is indicated by the hatched area. In the figures, the default value of $ m_{\mathrm{t}}^\text{gen}= $ 172.5 GeV is used. The reduction of permutations with wrongly assigned jets and the much narrower peak are clearly visible in the $ m_{\mathrm{t}}^\text{fit} $ measurement. Figures taken from Ref. [48]. |
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Figure 18-a:
Left: The distribution of the reconstructed top quark mass $ m_{\mathrm{t}}^\text{reco} $ using the jet assignment from the kinematic fit, but the reconstructed jet momenta and no addition selection. Right: The distribution of the top quark mass from the kinematic fit $ m_{\mathrm{t}}^\text{fit} $ with the $ P_{\text{gof}} > $ 0.2 selection. Data are shown as points with vertical error bars showing the statistical uncertainties. The coloured histograms show the simulated signal and background contributions. The simulated signal is decomposed into the contributions from correct, wrong, or unmatched permutations as introduced in Section 2.3. The uncertainty in the predicted $ \mathrm{t} \overline{\mathrm{t}} $ cross section is indicated by the hatched area. In the figures, the default value of $ m_{\mathrm{t}}^\text{gen}= $ 172.5 GeV is used. The reduction of permutations with wrongly assigned jets and the much narrower peak are clearly visible in the $ m_{\mathrm{t}}^\text{fit} $ measurement. Figures taken from Ref. [48]. |
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Figure 18-b:
Left: The distribution of the reconstructed top quark mass $ m_{\mathrm{t}}^\text{reco} $ using the jet assignment from the kinematic fit, but the reconstructed jet momenta and no addition selection. Right: The distribution of the top quark mass from the kinematic fit $ m_{\mathrm{t}}^\text{fit} $ with the $ P_{\text{gof}} > $ 0.2 selection. Data are shown as points with vertical error bars showing the statistical uncertainties. The coloured histograms show the simulated signal and background contributions. The simulated signal is decomposed into the contributions from correct, wrong, or unmatched permutations as introduced in Section 2.3. The uncertainty in the predicted $ \mathrm{t} \overline{\mathrm{t}} $ cross section is indicated by the hatched area. In the figures, the default value of $ m_{\mathrm{t}}^\text{gen}= $ 172.5 GeV is used. The reduction of permutations with wrongly assigned jets and the much narrower peak are clearly visible in the $ m_{\mathrm{t}}^\text{fit} $ measurement. Figures taken from Ref. [48]. |
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Figure 19:
Contours of the likelihood of $ m_{\mathrm{t}} $ and $ \text{JSF} $ values for single events in the Run-1 CMS measurement [53]. |
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Figure 19-a:
Contours of the likelihood of $ m_{\mathrm{t}} $ and $ \text{JSF} $ values for single events in the Run-1 CMS measurement [53]. |
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Figure 19-b:
Contours of the likelihood of $ m_{\mathrm{t}} $ and $ \text{JSF} $ values for single events in the Run-1 CMS measurement [53]. |
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Figure 19-c:
Contours of the likelihood of $ m_{\mathrm{t}} $ and $ \text{JSF} $ values for single events in the Run-1 CMS measurement [53]. |
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Figure 19-d:
Contours of the likelihood of $ m_{\mathrm{t}} $ and $ \text{JSF} $ values for single events in the Run-1 CMS measurement [53]. |
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Figure 20:
The difference between the measured and generated $ m_{\mathrm{t}} $ values, divided by the uncertainty reported by the fit from pseudo-experiments without (red) or with (blue) the additional nuisance parameters for the finite sample sizes. Also included in the legend are the $ \mu $ and $ \sigma $ parameters of Gaussian functions (red and blue lines) fit to the histograms. Figure taken from Ref. [71]. |
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Figure 21:
The distributions of the top quark mass from the kinematic fit for the $ P_{\text{gof}} > $ 0.2 category (left) and of the invariant mass of the lepton and the jet assigned to the top quark decaying in the lepton+jets channel for the $ P_{\text{gof}} < $ 0.2 category (right). Data are shown as points with vertical error bars showing the statistical uncertainties. The coloured histograms show the simulated signal and background contributions. The simulated signal is decomposed into the contributions from correct, wrong, or unmatched permutations, as introduced in Section 2.3. The uncertainty bands contain statistical uncertainties in the simulation, normalisation uncertainties due to the integrated luminosity and cross section, JES correction, and all uncertainties that are evaluated from event-based weights. A large part of the depicted uncertainties in the expected event yields are correlated. The lower panels show the ratio of data to the prediction. In the figures, the default value of $ m_{\mathrm{t}}^\text{gen}= $ 172.5 GeV is used. Figures taken from Ref. [71]. |
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Figure 21-a:
The distributions of the top quark mass from the kinematic fit for the $ P_{\text{gof}} > $ 0.2 category (left) and of the invariant mass of the lepton and the jet assigned to the top quark decaying in the lepton+jets channel for the $ P_{\text{gof}} < $ 0.2 category (right). Data are shown as points with vertical error bars showing the statistical uncertainties. The coloured histograms show the simulated signal and background contributions. The simulated signal is decomposed into the contributions from correct, wrong, or unmatched permutations, as introduced in Section 2.3. The uncertainty bands contain statistical uncertainties in the simulation, normalisation uncertainties due to the integrated luminosity and cross section, JES correction, and all uncertainties that are evaluated from event-based weights. A large part of the depicted uncertainties in the expected event yields are correlated. The lower panels show the ratio of data to the prediction. In the figures, the default value of $ m_{\mathrm{t}}^\text{gen}= $ 172.5 GeV is used. Figures taken from Ref. [71]. |
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Figure 21-b:
The distributions of the top quark mass from the kinematic fit for the $ P_{\text{gof}} > $ 0.2 category (left) and of the invariant mass of the lepton and the jet assigned to the top quark decaying in the lepton+jets channel for the $ P_{\text{gof}} < $ 0.2 category (right). Data are shown as points with vertical error bars showing the statistical uncertainties. The coloured histograms show the simulated signal and background contributions. The simulated signal is decomposed into the contributions from correct, wrong, or unmatched permutations, as introduced in Section 2.3. The uncertainty bands contain statistical uncertainties in the simulation, normalisation uncertainties due to the integrated luminosity and cross section, JES correction, and all uncertainties that are evaluated from event-based weights. A large part of the depicted uncertainties in the expected event yields are correlated. The lower panels show the ratio of data to the prediction. In the figures, the default value of $ m_{\mathrm{t}}^\text{gen}= $ 172.5 GeV is used. Figures taken from Ref. [71]. |
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Figure 22:
The distributions of $ m_{\mathrm{W}}^\text{reco} $ (upper left), $ m_{\ell\mathrm{b}}^\text{reco}/m_{\mathrm{t}}^\text{fit} $ (upper right), and $ R_{\mathrm{b}\mathrm{q}}^\text{reco} $ (lower) for the $ P_{\text{gof}} > $ 0.2 category. Symbols and patterns are the same as in Fig. 21. In the figures, the default value of $ m_{\mathrm{t}}^\text{gen}= $ 172.5 GeV is used. Figures taken from Ref. [71]. |
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Figure 22-a:
The distributions of $ m_{\mathrm{W}}^\text{reco} $ (upper left), $ m_{\ell\mathrm{b}}^\text{reco}/m_{\mathrm{t}}^\text{fit} $ (upper right), and $ R_{\mathrm{b}\mathrm{q}}^\text{reco} $ (lower) for the $ P_{\text{gof}} > $ 0.2 category. Symbols and patterns are the same as in Fig. 21. In the figures, the default value of $ m_{\mathrm{t}}^\text{gen}= $ 172.5 GeV is used. Figures taken from Ref. [71]. |
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Figure 22-b:
The distributions of $ m_{\mathrm{W}}^\text{reco} $ (upper left), $ m_{\ell\mathrm{b}}^\text{reco}/m_{\mathrm{t}}^\text{fit} $ (upper right), and $ R_{\mathrm{b}\mathrm{q}}^\text{reco} $ (lower) for the $ P_{\text{gof}} > $ 0.2 category. Symbols and patterns are the same as in Fig. 21. In the figures, the default value of $ m_{\mathrm{t}}^\text{gen}= $ 172.5 GeV is used. Figures taken from Ref. [71]. |
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Figure 22-c:
The distributions of $ m_{\mathrm{W}}^\text{reco} $ (upper left), $ m_{\ell\mathrm{b}}^\text{reco}/m_{\mathrm{t}}^\text{fit} $ (upper right), and $ R_{\mathrm{b}\mathrm{q}}^\text{reco} $ (lower) for the $ P_{\text{gof}} > $ 0.2 category. Symbols and patterns are the same as in Fig. 21. In the figures, the default value of $ m_{\mathrm{t}}^\text{gen}= $ 172.5 GeV is used. Figures taken from Ref. [71]. |
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Figure 23:
Comparison of the expected total uncertainty in $ m_{\mathrm{t}} $ in the combined lepton+jets channel and for different observable categories defined in Table 4. Figure taken from Ref. [71]. |
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Figure 24:
Summary of the direct $ m_{\mathrm{t}} $ measurements in the lepton+jets channel by the CMS Collaboration. The left panel shows the measured value of $ m_{\mathrm{t}} $ (marker) with statistical (black bars) and total (grey bars) uncertainties. The right panel displays a breakdown of contributing uncertainty groups and their impact on the uncertainty in the measurement. The two results at 13 TeV are derived from the same data. The figure is compiled from Refs. [48,53,61,71]. |
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Figure 25:
Comparison of the CMS direct $ m_{\mathrm{t}} $ measurements from the Run-2 data collected in 2016 at $ \sqrt{s} = $ 13 TeV to the best Run-1 measurements at $ \sqrt{s} = $ 8 TeV in each channel. The horizontal bars display the total uncertainty in the measurements and the red band shows the uncertainty in the Run-1 combination [72]. The figure is compiled from Refs. [53,61,71,60,63,69,62,72]. |
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Figure 26:
Difference of the $ m_{\mathrm{t}} $ extracted after calibration in each bin and from the inclusive sample as a function of the invariant mass of the $ \mathrm{t} \overline{\mathrm{t}} $ system $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ (left) and the $ \Delta R $ between the light-quark jets $ \Delta R_{\mathrm{q}{\overline{\mathrm{q}}{\prime}} } $ (right), obtained from the hybrid fit [61], compared to different generator models. The filled circles represent the data, and the other symbols are for the simulations. For reasons of clarity, the horizontal bars indicating the bin widths are shown only for the data points and each of the simulations is shown as a single offset point with a vertical error bar representing its statistical uncertainty. The statistical uncertainty of the data is displayed by the inner error bars. For the outer error bars, the systematic uncertainties are added in quadrature. Figures taken from Ref. [61]. |
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Figure 26-a:
Difference of the $ m_{\mathrm{t}} $ extracted after calibration in each bin and from the inclusive sample as a function of the invariant mass of the $ \mathrm{t} \overline{\mathrm{t}} $ system $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ (left) and the $ \Delta R $ between the light-quark jets $ \Delta R_{\mathrm{q}{\overline{\mathrm{q}}{\prime}} } $ (right), obtained from the hybrid fit [61], compared to different generator models. The filled circles represent the data, and the other symbols are for the simulations. For reasons of clarity, the horizontal bars indicating the bin widths are shown only for the data points and each of the simulations is shown as a single offset point with a vertical error bar representing its statistical uncertainty. The statistical uncertainty of the data is displayed by the inner error bars. For the outer error bars, the systematic uncertainties are added in quadrature. Figures taken from Ref. [61]. |
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Figure 26-b:
Difference of the $ m_{\mathrm{t}} $ extracted after calibration in each bin and from the inclusive sample as a function of the invariant mass of the $ \mathrm{t} \overline{\mathrm{t}} $ system $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ (left) and the $ \Delta R $ between the light-quark jets $ \Delta R_{\mathrm{q}{\overline{\mathrm{q}}{\prime}} } $ (right), obtained from the hybrid fit [61], compared to different generator models. The filled circles represent the data, and the other symbols are for the simulations. For reasons of clarity, the horizontal bars indicating the bin widths are shown only for the data points and each of the simulations is shown as a single offset point with a vertical error bar representing its statistical uncertainty. The statistical uncertainty of the data is displayed by the inner error bars. For the outer error bars, the systematic uncertainties are added in quadrature. Figures taken from Ref. [61]. |
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Figure 27:
Feynman diagrams of the $ t $-channel single top quark production at LO corresponding to five- (left) and four-flavour (right) schemes, assuming five (u, d, s, c, b) or four (u, d, s, c) active quark flavours in the proton, respectively. At NLO in perturbative QCD, the right diagram is also part of the five-flavour scheme. |
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Figure 27-a:
Feynman diagrams of the $ t $-channel single top quark production at LO corresponding to five- (left) and four-flavour (right) schemes, assuming five (u, d, s, c, b) or four (u, d, s, c) active quark flavours in the proton, respectively. At NLO in perturbative QCD, the right diagram is also part of the five-flavour scheme. |
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Figure 27-b:
Feynman diagrams of the $ t $-channel single top quark production at LO corresponding to five- (left) and four-flavour (right) schemes, assuming five (u, d, s, c, b) or four (u, d, s, c) active quark flavours in the proton, respectively. At NLO in perturbative QCD, the right diagram is also part of the five-flavour scheme. |
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Figure 28:
Normalised differential cross section of the $ t $-channel single top quark production as a function of the $ p_{\mathrm{T}} $ of the parton-level top quark (left) and the W boson (right). Figures taken from Ref. [204]. |
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Figure 28-a:
Normalised differential cross section of the $ t $-channel single top quark production as a function of the $ p_{\mathrm{T}} $ of the parton-level top quark (left) and the W boson (right). Figures taken from Ref. [204]. |
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Figure 28-b:
Normalised differential cross section of the $ t $-channel single top quark production as a function of the $ p_{\mathrm{T}} $ of the parton-level top quark (left) and the W boson (right). Figures taken from Ref. [204]. |
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Figure 29:
The uncertainty in $ m_{\mathrm{t}} $ from the statistical and profiled systematic components (red) and uncertainty in the $ m_{\mathrm{t}} $ calibration (blue) as a function of the cutoff on the BDT score. Figure taken from Ref. [67]. |
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Figure 30:
Data-to-simulation comparison of the reconstructed top quark mass (left) and postfit $ \zeta=\ln(m_{\mathrm{t}}/$ 1 GeV (right) distributions after BDT selection. The lower panel in the left plot shows the data-to-simulation ratios for each bin, while the lower panel in the right plot shows the normalised residuals or pulls, determined using the bin contents of the data distributions (after background QCD subtraction) and the $ F(\zeta) $ values evaluated at the centre of the bins. Figures taken from Ref. [67]. |
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Figure 30-a:
Data-to-simulation comparison of the reconstructed top quark mass (left) and postfit $ \zeta=\ln(m_{\mathrm{t}}/$ 1 GeV (right) distributions after BDT selection. The lower panel in the left plot shows the data-to-simulation ratios for each bin, while the lower panel in the right plot shows the normalised residuals or pulls, determined using the bin contents of the data distributions (after background QCD subtraction) and the $ F(\zeta) $ values evaluated at the centre of the bins. Figures taken from Ref. [67]. |
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Figure 30-b:
Data-to-simulation comparison of the reconstructed top quark mass (left) and postfit $ \zeta=\ln(m_{\mathrm{t}}/$ 1 GeV (right) distributions after BDT selection. The lower panel in the left plot shows the data-to-simulation ratios for each bin, while the lower panel in the right plot shows the normalised residuals or pulls, determined using the bin contents of the data distributions (after background QCD subtraction) and the $ F(\zeta) $ values evaluated at the centre of the bins. Figures taken from Ref. [67]. |
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Figure 31:
Summary of $ m_{\mathrm{t}} $ measurements in single top quark events. The left panel shows the measured value of $ m_{\mathrm{t}} $ (marker) with statistical (thick bars) and total (thin bars) uncertainties. In the case of the 13 TeV measurement [67], the statistical component of the uncertainty includes contributions from the statistical and profiled systematic uncertainties. The right panel displays a breakdown of contributing uncertainty groups and their impact on the uncertainty in the measurement. The figure is compiled from Refs. [58,67]. |
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Figure 32:
Summary of $ \Delta m_{\mathrm{t}} $ measurements in $ \mathrm{t} \overline{\mathrm{t}} $ and single top quark events. The left panel shows the measured value of $ \Delta m_{\mathrm{t}} $ (marker) with statistical (thick bars) and total (thin bars) uncertainties. In the case of the single top quark measurement [67], the statistical component of the uncertainty includes contributions from the statistical and profiled systematic uncertainties. The right panel displays a breakdown of contributing uncertainty groups and their impact on the uncertainty in the measurement. The figure is compiled from Refs. [209,210,67]. |
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Figure 33:
Predicted $ \sigma_{{\mathrm{t}\overline{\mathrm{t}}} } $ as a function of the top quark pole mass, using different PDF sets (red shaded band and red lines of different styles), compared to the cross section measured by CMS assuming $ m_{\mathrm{t}}^{\text{MC}}=m_{\mathrm{t}}^{\text{pole}} $ (blue shaded band). The uncertainties in the measured $ \sigma_{{\mathrm{t}\overline{\mathrm{t}}} } $ as well as the scale and PDF uncertainties in the prediction with NNPDF-2.3 [126] are illustrated by the filled band. The $ m_{\mathrm{t}}^{\text{MC}} $ result obtained in direct measurements to that date is shown as hatched area. The inner (solid) area of the vertical band corresponds to the quoted experimental uncertainty in $ m_{\mathrm{t}}^{\text{MC}} $, while the outer (hatched) area additionally accounts for a possible difference between this value and $ m_{\mathrm{t}}^{\text{pole}} $. Figure taken from Ref. [52]. |
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Figure 34:
Values of $ m_{\mathrm{t}}^{\text{pole}} $ obtained by using measured $ \sigma_{{\mathrm{t}\overline{\mathrm{t}}} } $ together with the prediction at NNLO+NNLL using different NNLO PDF sets. The filled symbols represent the results obtained when using the world average of $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $, while the open symbols indicate the results obtained with the default $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $ value of the respective PDF set. The inner error bars include the uncertainties in the measured cross section and in the LHC beam energy, as well as the PDF and scale uncertainties in the predicted cross section. The outer error bars additionally account for the uncertainty in the $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $ value used for a specific prediction. For comparison, the most precise $ m_{\mathrm{t}}^{\text{MC}} $ to that date is shown as vertical band, where the inner (solid) area corresponds to the original uncertainty of the direct $ m_{\mathrm{t}} $ average, while the outer (hatched) area additionally accounts for the possible difference between $ m_{\mathrm{t}}^{\text{MC}} $ and $ m_{\mathrm{t}}^{\text{pole}} $. Figure taken from Ref. [52]. |
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Figure 35:
Likelihood for the predicted dependence of $ \sigma_{{\mathrm{t}\overline{\mathrm{t}}} } $ on $ m_{\mathrm{t}}^{\text{pole}} $ for 7 and 8 TeV determined with TOP++, using the NNPDF-3.0 PDF set. The measured dependencies on the mass are given by the dashed lines, their 1 $ \sigma $ uncertainties are represented by the dotted lines. The extracted mass at each value of $ \sqrt{s} $ is indicated by a black point, with its $ \pm $ 1 standard deviation uncertainty constructed from the continuous contour, corresponding to $ -2\Delta\log(L_{\text{pred}}L_{\text{exp}})= $ 1. Figure taken from Ref. [54]. |
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Figure 36:
Absolute (left) and shape (right) distributions of $ m_{\ell\mathrm{b}}^\text{min} $ for $ \mathrm{t} \overline{\mathrm{t}} $ production at the LHC at $ \sqrt{s} = $ 8 TeV after detector simulation and event selection in the $ \mathrm{e}\mu $ channel. The central prediction (black symbols) is obtained at the value of $ m_{\mathrm{t}}^{\text{MC}} $ of 172.5 GeV, denoted as $ m_{\mathrm{t}}^0 $. Predictions assuming different $ m_{\mathrm{t}}^{\text{MC}} $ values are shown by different colours. |
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Figure 36-a:
Absolute (left) and shape (right) distributions of $ m_{\ell\mathrm{b}}^\text{min} $ for $ \mathrm{t} \overline{\mathrm{t}} $ production at the LHC at $ \sqrt{s} = $ 8 TeV after detector simulation and event selection in the $ \mathrm{e}\mu $ channel. The central prediction (black symbols) is obtained at the value of $ m_{\mathrm{t}}^{\text{MC}} $ of 172.5 GeV, denoted as $ m_{\mathrm{t}}^0 $. Predictions assuming different $ m_{\mathrm{t}}^{\text{MC}} $ values are shown by different colours. |
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Figure 36-b:
Absolute (left) and shape (right) distributions of $ m_{\ell\mathrm{b}}^\text{min} $ for $ \mathrm{t} \overline{\mathrm{t}} $ production at the LHC at $ \sqrt{s} = $ 8 TeV after detector simulation and event selection in the $ \mathrm{e}\mu $ channel. The central prediction (black symbols) is obtained at the value of $ m_{\mathrm{t}}^{\text{MC}} $ of 172.5 GeV, denoted as $ m_{\mathrm{t}}^0 $. Predictions assuming different $ m_{\mathrm{t}}^{\text{MC}} $ values are shown by different colours. |
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Figure 37:
Data (points) compared to pre-fit (left) and post-fit (right) $ m_{\ell\mathrm{b}}^\text{min} $ distributions of the expected signal and backgrounds from simulation (shaded histograms) used in the simultaneous fit of $ \sigma_{{\mathrm{t}\overline{\mathrm{t}}} } $ and $ m_{\mathrm{t}}^{\text{MC}} $. Events with exactly one b-tagged jets are shown. The hatched bands correspond to the total uncertainty in the sum of the predicted yields. The ratios of data to the sum of the predicted yields are shown in the lower panel. Here, the solid grey band represents the contribution of the statistical uncertainty. Figures taken from Ref. [63]. |
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Figure 37-a:
Data (points) compared to pre-fit (left) and post-fit (right) $ m_{\ell\mathrm{b}}^\text{min} $ distributions of the expected signal and backgrounds from simulation (shaded histograms) used in the simultaneous fit of $ \sigma_{{\mathrm{t}\overline{\mathrm{t}}} } $ and $ m_{\mathrm{t}}^{\text{MC}} $. Events with exactly one b-tagged jets are shown. The hatched bands correspond to the total uncertainty in the sum of the predicted yields. The ratios of data to the sum of the predicted yields are shown in the lower panel. Here, the solid grey band represents the contribution of the statistical uncertainty. Figures taken from Ref. [63]. |
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Figure 37-b:
Data (points) compared to pre-fit (left) and post-fit (right) $ m_{\ell\mathrm{b}}^\text{min} $ distributions of the expected signal and backgrounds from simulation (shaded histograms) used in the simultaneous fit of $ \sigma_{{\mathrm{t}\overline{\mathrm{t}}} } $ and $ m_{\mathrm{t}}^{\text{MC}} $. Events with exactly one b-tagged jets are shown. The hatched bands correspond to the total uncertainty in the sum of the predicted yields. The ratios of data to the sum of the predicted yields are shown in the lower panel. Here, the solid grey band represents the contribution of the statistical uncertainty. Figures taken from Ref. [63]. |
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Figure 38:
Normalised pulls and constraints of the nuisance parameters related to the modelling uncertainties for the simultaneous fit of $ \sigma_{{\mathrm{t}\overline{\mathrm{t}}} } $ and $ m_{\mathrm{t}}^{\text{MC}} $. The markers denote the fitted value, while the inner vertical bars represent the constraint and the outer vertical bars denote the additional uncertainty as determined from pseudo-experiments. The constraint is defined as the ratio of the post-fit uncertainty to the pre-fit uncertainty of a given nuisance parameter, while the normalised pull is the difference between the post-fit and the pre-fit values of the nuisance parameter normalised to its pre-fit uncertainty. The horizontal lines at $ \pm $ 1 represent the pre-fit uncertainty. Figure taken from Ref. [63]. |
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Figure 39:
Values of $ m_{\mathrm{t}}(m_{\mathrm{t}}) $ obtained from comparing the $ \sigma_{{\mathrm{t}\overline{\mathrm{t}}} } $ measurement to the theoretical NNLO predictions using different PDF sets. The inner horizontal bars on the points represent the quadratic sum of the experimental, PDF, and $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $ uncertainties, while the outer horizontal bars give the total uncertainties. Figure taken from Ref. [63]. |
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Figure 40:
Values of $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $ obtained in the comparison of the $ \sigma_{{\mathrm{t}\overline{\mathrm{t}}} } $ measurement to the NNLO prediction using different PDFs, as functions of the $ m_{\mathrm{t}}(m_{\mathrm{t}}) $ value used in the theoretical calculation. The results from using the different PDFs are shown by the bands with different shadings, with the band width corresponding to the quadratic sum of the experimental and PDF uncertainties in $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $. The resulting measured values of $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $ are shown by the different style points at the $ m_{\mathrm{t}}(m_{\mathrm{t}}) $ values used for each PDF. The inner vertical bars on the points represent the quadratic sum of the experimental and PDF uncertainties in $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $, while the outer vertical bars show the total uncertainties. Figure taken from Ref. [63]. |
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Figure 41:
Left: profile likelihood unfolding of the $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution. The signal sample is split into subprocesses in bins of parton-level $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $, and the signal corresponding to bin $ k $ in $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ is denoted with ``Signal ($ \mu_{\mathrm{k}} $)''. The vertical bars represent the statistical uncertainty in the data, while the hashed band is the total uncertainty in the MC simulation. Right: unfolded $ \mathrm{t} \overline{\mathrm{t}} $ cross section as a function of $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $, compared to theoretical predictions in the $ \mathrm{\overline{MS}} $ scheme for different values of $ m_{\mathrm{t}}(m_{\mathrm{t}}) $. The vertical bars correspond to the total uncertainty in the unfolded cross section. Here, the bin centres for the unfolded cross section are defined as the average $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ in the POWHEG+PYTHIA-8 simulation. Figures taken from Ref. [65]. |
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Figure 41-a:
Left: profile likelihood unfolding of the $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution. The signal sample is split into subprocesses in bins of parton-level $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $, and the signal corresponding to bin $ k $ in $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ is denoted with ``Signal ($ \mu_{\mathrm{k}} $)''. The vertical bars represent the statistical uncertainty in the data, while the hashed band is the total uncertainty in the MC simulation. Right: unfolded $ \mathrm{t} \overline{\mathrm{t}} $ cross section as a function of $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $, compared to theoretical predictions in the $ \mathrm{\overline{MS}} $ scheme for different values of $ m_{\mathrm{t}}(m_{\mathrm{t}}) $. The vertical bars correspond to the total uncertainty in the unfolded cross section. Here, the bin centres for the unfolded cross section are defined as the average $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ in the POWHEG+PYTHIA-8 simulation. Figures taken from Ref. [65]. |
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Figure 41-b:
Left: profile likelihood unfolding of the $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ distribution. The signal sample is split into subprocesses in bins of parton-level $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $, and the signal corresponding to bin $ k $ in $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ is denoted with ``Signal ($ \mu_{\mathrm{k}} $)''. The vertical bars represent the statistical uncertainty in the data, while the hashed band is the total uncertainty in the MC simulation. Right: unfolded $ \mathrm{t} \overline{\mathrm{t}} $ cross section as a function of $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $, compared to theoretical predictions in the $ \mathrm{\overline{MS}} $ scheme for different values of $ m_{\mathrm{t}}(m_{\mathrm{t}}) $. The vertical bars correspond to the total uncertainty in the unfolded cross section. Here, the bin centres for the unfolded cross section are defined as the average $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ in the POWHEG+PYTHIA-8 simulation. Figures taken from Ref. [65]. |
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Figure 42:
Running of the top quark mass as a function of $ \mu_{\mathrm{m}}=m_{{\mathrm{t}\overline{\mathrm{t}}} }/ $ 2 obtained with a bin-by-bin dynamic scale $ \mu_{\mathrm{k}}/ $ 2 (full circles), compared to the central values of the results of Ref. [65] obtained with a constant scale $ \mu_{\mathrm{m}}=\mu_{\mathrm{k}} $ (hollow squares) and to those of the NNLO results of Ref. [241] (hollow triangles). As in Ref. [65], the error bars indicate the combination of experimental, extrapolation, and PDF uncertainties in the NLO extraction with bin-by-bin dynamic scale. The full treatment of the QCD scale variations can be found in Ref. [241]. The assumptions on the renormalisation and factorisation scales adopted in the different interpretations are summarised in Table 6. The uncertainties in the three results, which are mostly correlated, are given in the respective references and are of comparable size. |
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Figure 43:
The fractional uncertainties in the gluon distribution function of the proton as a function of $ x $ at factorisation scale $ \mu_{\mathrm{f}}^2= $ 10$^5$ GeV$^{2}$ from a QCD analysis using the DIS and CMS muon charge asymmetry measurements (hatched area), and also including the CMS $ \sigma_{{\mathrm{t}\overline{\mathrm{t}}} } $ results at $ \sqrt{s} = $ 5.02 TeV (solid area). The relative uncertainties are found after the two gluon distributions have been normalised to unity. The solid line shows the ratio of the gluon distribution function found from the fit with the CMS $ \sigma_{{\mathrm{t}\overline{\mathrm{t}}} } $ measurements included to that found without. Figure taken from Ref. [242]. |
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Figure 44:
Comparison of the measured $ [N_{\text{jet}}^{0,1+},m_{{\mathrm{t}\overline{\mathrm{t}}} },y_{{\mathrm{t}\overline{\mathrm{t}}} }] $ cross sections to NLO predictions obtained using different $ m_{\mathrm{t}}^{\text{pole}} $ values. For each theoretical prediction, values of $ \chi^2 $ and dof for the comparison to the data are reported. Figure taken from Ref. [64]. |
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Figure 45:
The theoretical uncertainties for $ [N_{\text{jet}}^{0,1+},m_{{\mathrm{t}\overline{\mathrm{t}}} },y_{{\mathrm{t}\overline{\mathrm{t}}} }] $ cross sections, arising from the scale, PDF, $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $, and $ m_{\mathrm{t}} $ variations, as well as the total theoretical uncertainties obtained from variations in $ \mu_{\mathrm{r}} $ and $ \mu_{\mathrm{f}} $, with their bin-averaged values shown in brackets. The bins are the same as in Fig. 44. Figure taken from Ref. [64]. |
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Figure 46:
The extracted values and their correlations for $ \alpha_\mathrm{S} $ and $ m_{\mathrm{t}}^{\text{pole}} $ (upper left), $ \alpha_\mathrm{S} $ and gluon PDF (lower left), and $ m_{\mathrm{t}}^{\text{pole}} $ and gluon PDF (lower, right). The gluon PDF is shown at the scale $ \mu_{\mathrm{f}}^2= $ 30 000 GeV$^{2}$ for several values of $ x $. For the extracted values of $ \alpha_\mathrm{S} $ and $ m_{\mathrm{t}}^{\text{pole}} $, the additional uncertainties arising from the dependence on the scale are shown. The correlation coefficients $ \rho $ as defined in Ref. [64] are displayed. Furthermore, values of $ \alpha_\mathrm{S} $ ($ m_{\mathrm{t}}^{\text{pole}} $, gluon PDF) extracted using fixed values of $ m_{\mathrm{t}}^{\text{pole}}(\alpha_\mathrm{S}) $ are displayed as dashed, dotted, or dash-dotted lines. The world average values $ \alpha_\mathrm{S}(m_{\mathrm{Z}})= $ 0.1181 $ \pm $ 0.0011 and $ m_{\mathrm{t}}^{\text{pole}}= $ 173.1 $ \pm $ 0.9 GeV from Ref. [252] are shown for reference. Figure taken from Ref. [64]. |
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Figure 47:
Left: Sensitivity $ \mathcal{S} $ to the value of $ m_{\mathrm{t}}^{\text{pole}} $ for $ \mathrm{t} \overline{\mathrm{t}} $ (blue) and $ {\mathrm{t}\overline{\mathrm{t}}} \text{+jet} $ production (orange). Figure taken from Ref. [69]. Right: The distribution of $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ at the parton level as given by the POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulation as a function of $ \rho $ at parton level, obtained in Ref. [69]. |
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Figure 47-a:
Left: Sensitivity $ \mathcal{S} $ to the value of $ m_{\mathrm{t}}^{\text{pole}} $ for $ \mathrm{t} \overline{\mathrm{t}} $ (blue) and $ {\mathrm{t}\overline{\mathrm{t}}} \text{+jet} $ production (orange). Figure taken from Ref. [69]. Right: The distribution of $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ at the parton level as given by the POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulation as a function of $ \rho $ at parton level, obtained in Ref. [69]. |
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Figure 47-b:
Left: Sensitivity $ \mathcal{S} $ to the value of $ m_{\mathrm{t}}^{\text{pole}} $ for $ \mathrm{t} \overline{\mathrm{t}} $ (blue) and $ {\mathrm{t}\overline{\mathrm{t}}} \text{+jet} $ production (orange). Figure taken from Ref. [69]. Right: The distribution of $ m_{{\mathrm{t}\overline{\mathrm{t}}} } $ at the parton level as given by the POWHEG+PYTHIA-8 $ \mathrm{t} \overline{\mathrm{t}} $ simulation as a function of $ \rho $ at parton level, obtained in Ref. [69]. |
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Figure 48:
The measured normalised $ {\mathrm{t}\overline{\mathrm{t}}} \text{+jet} $ differential cross section (closed symbols) as a function of $ \rho $. The vertical error bars (shaded areas) show the statistical (statistical plus systematic) uncertainty. The data are compared to theoretical predictions and the POWHEG+PYTHIA-8 simulation, either using alternative values of $ m_{\mathrm{t}} $ (left panel), shown by the solid lines, or two alternative PDF sets (right), shown by the hatched areas. In the lower panels, the ratio of the predictions to the measurement is shown. Figures taken from Ref. [69]. |
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Figure 48-a:
The measured normalised $ {\mathrm{t}\overline{\mathrm{t}}} \text{+jet} $ differential cross section (closed symbols) as a function of $ \rho $. The vertical error bars (shaded areas) show the statistical (statistical plus systematic) uncertainty. The data are compared to theoretical predictions and the POWHEG+PYTHIA-8 simulation, either using alternative values of $ m_{\mathrm{t}} $ (left panel), shown by the solid lines, or two alternative PDF sets (right), shown by the hatched areas. In the lower panels, the ratio of the predictions to the measurement is shown. Figures taken from Ref. [69]. |
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Figure 48-b:
The measured normalised $ {\mathrm{t}\overline{\mathrm{t}}} \text{+jet} $ differential cross section (closed symbols) as a function of $ \rho $. The vertical error bars (shaded areas) show the statistical (statistical plus systematic) uncertainty. The data are compared to theoretical predictions and the POWHEG+PYTHIA-8 simulation, either using alternative values of $ m_{\mathrm{t}} $ (left panel), shown by the solid lines, or two alternative PDF sets (right), shown by the hatched areas. In the lower panels, the ratio of the predictions to the measurement is shown. Figures taken from Ref. [69]. |
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Figure 49:
Percentiles of maximum angular distance between the top quark decay partons as a function of the top quark $ p_{\mathrm{T}} $ obtained from $ \mathrm{t} \overline{\mathrm{t}} $ simulation. The filled bands indicate the areas that are populated by 70, 80, and 90% of all simulated $ \mathrm{t} \overline{\mathrm{t}} $ events, where the decay partons have at least $ p_{\mathrm{T}} > $ 20 GeV. The most probable value (MPV) is shown as a dashed line, and two functional forms are shown that approximate the $ p_{\mathrm{T}} $-dependence of $ \Delta R_{\text{max}} $. Figure taken from Ref. [271]. |
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Figure 50:
Display of a simulated $ \mathrm{t} \overline{\mathrm{t}} $ event. Each point marks the position of a particle at the particle level in the $ \eta\text{-}\phi $ plane. Decay products of the top quarks are highlighted with triangles or larger circles. The red triangles mark the three quarks from the hadronic decay; the black triangle, black circle, and open circle correspond to the b quark, charged lepton, and neutrino from the leptonic top quark decay, respectively. The jet areas are shown as coloured shapes. The left panel shows the first clustering step with $ N= $ 2 and $ R= $ 1.2, while the right panel shows the subjet clustering. |
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Figure 50-a:
Display of a simulated $ \mathrm{t} \overline{\mathrm{t}} $ event. Each point marks the position of a particle at the particle level in the $ \eta\text{-}\phi $ plane. Decay products of the top quarks are highlighted with triangles or larger circles. The red triangles mark the three quarks from the hadronic decay; the black triangle, black circle, and open circle correspond to the b quark, charged lepton, and neutrino from the leptonic top quark decay, respectively. The jet areas are shown as coloured shapes. The left panel shows the first clustering step with $ N= $ 2 and $ R= $ 1.2, while the right panel shows the subjet clustering. |
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Figure 50-b:
Display of a simulated $ \mathrm{t} \overline{\mathrm{t}} $ event. Each point marks the position of a particle at the particle level in the $ \eta\text{-}\phi $ plane. Decay products of the top quarks are highlighted with triangles or larger circles. The red triangles mark the three quarks from the hadronic decay; the black triangle, black circle, and open circle correspond to the b quark, charged lepton, and neutrino from the leptonic top quark decay, respectively. The jet areas are shown as coloured shapes. The left panel shows the first clustering step with $ N= $ 2 and $ R= $ 1.2, while the right panel shows the subjet clustering. |
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Figure 51:
Normalised jet mass distribution at the particle level for the two-step XCone clustering (blue solid) used in Ref. [66,70] and CA jets with $ R= $ 1.2 (red dotted) used in Ref. [59]. Only events where all top quark decay products are within $ \Delta R= $ 0.4 to any XCone subjet or within $ \Delta R= $ 1.2 to the CA jet are shown. |
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Figure 52:
Normalised differential $ \mathrm{t} \overline{\mathrm{t}} $ production cross section as a function of $ m_{\text{jet}} $. Data (markers) are compared to predictions for different $ m_{\mathrm{t}} $ obtained from simulation (lines). The bars on the markers display the statistical (inner bars) and total (outer bars) uncertainties. The theoretical uncertainty is shown as coloured area. Figure taken from Ref. [70]. |
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Figure 53:
Summary of the $ m_{\mathrm{t}} $ extraction in $ m_{\text{jet}} $ measurements. The left panel shows the extracted value of $ m_{\mathrm{t}} $ (marker) with statistical (thick bars) and total (thin bars) uncertainties. The right panel displays a breakdown of contributing uncertainty groups and their impact on the uncertainty in the $ m_{\mathrm{t}} $ extraction. The figure is compiled from Refs. [59,66,70]. |
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Figure 54:
Overview of top quark mass measurement results published by the CMS Collaboration. The markers display the respective measured value of $ m_{\mathrm{t}} $ with the statistical (inner) and total (outer) uncertainties shown as horizontal error bars. The measurements are categorised into Lagrangian mass extractions from cross section measurements and direct measurements of $ m_{\mathrm{t}}^{\text{MC}} $ and are compared to the combined cross section measurement of the ATLAS and CMS Collaborations (red) and a CMS combination of Run-1 results (blue). Similar labelling as in Table 1 is used. The figure is compiled from Refs. [47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72]. |
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Figure 55:
The resolution of the $ \mu+\mathrm{J}/\psi $ mass for the CMS Phase-2 upgraded detector, for the two PU scenarios, and for the Run-2 (Phase-0) detector. Figure taken from Ref. [290]. |
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Figure 56:
Total uncertainty in $ m_{\mathrm{t}} $ obtained with a selection of different measurement methods and their projections for expected running conditions in Run-2 + Run-3 and at the HL-LHC. The projections are based on $ m_{\mathrm{t}} $ measurements performed during the LHC Run-1, also listed in Table 1: the $ \mathrm{J}/\psi $ [56], total $ \mathrm{t} \overline{\mathrm{t}} $ cross section [54] in the dilepton channel, secondary vertex [55], single top quark [58], and lepton+jets direct [53] measurements. These projections do not fully account for improvements in the performance of the upgraded CMS detector. Figure taken from Ref. [294]. |
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Figure 57:
Left: The projected total experimental uncertainty in the top quark pair production cross section as a function of the uncertainty in the integrated luminosity, for two experimental scenarios, assuming no reduction of the experimental uncertainties with respect to Run-2 and a reduction of the uncertainties following the recommendations outlined in Ref [295]. Right: The projected relative uncertainties in the extracted values of $ m_{\mathrm{t}} $ (dotted lines) and $ \alpha_\mathrm{S} $ (solid lines) as a function of the uncertainty in the integrated luminosity, comparing the case of the full uncertainty in the prediction and no uncertainty in the prediction. The results are obtained assuming a reduction of the uncertainties in the measurement to 1.5%. Figure taken from Ref. [296]. |
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Figure 57-a:
Left: The projected total experimental uncertainty in the top quark pair production cross section as a function of the uncertainty in the integrated luminosity, for two experimental scenarios, assuming no reduction of the experimental uncertainties with respect to Run-2 and a reduction of the uncertainties following the recommendations outlined in Ref [295]. Right: The projected relative uncertainties in the extracted values of $ m_{\mathrm{t}} $ (dotted lines) and $ \alpha_\mathrm{S} $ (solid lines) as a function of the uncertainty in the integrated luminosity, comparing the case of the full uncertainty in the prediction and no uncertainty in the prediction. The results are obtained assuming a reduction of the uncertainties in the measurement to 1.5%. Figure taken from Ref. [296]. |
png pdf |
Figure 57-b:
Left: The projected total experimental uncertainty in the top quark pair production cross section as a function of the uncertainty in the integrated luminosity, for two experimental scenarios, assuming no reduction of the experimental uncertainties with respect to Run-2 and a reduction of the uncertainties following the recommendations outlined in Ref [295]. Right: The projected relative uncertainties in the extracted values of $ m_{\mathrm{t}} $ (dotted lines) and $ \alpha_\mathrm{S} $ (solid lines) as a function of the uncertainty in the integrated luminosity, comparing the case of the full uncertainty in the prediction and no uncertainty in the prediction. The results are obtained assuming a reduction of the uncertainties in the measurement to 1.5%. Figure taken from Ref. [296]. |
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Figure 58:
Projected cumulative differential $ \mathrm{t} \overline{\mathrm{t}} $ distributions for HL-LHC scenario as functions of rapidity and invariant mass of the $ \mathrm{t} \overline{\mathrm{t}} $ pair. Figure taken from Ref. [297]. |
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Figure 59:
The relative gluon PDF uncertainties of the original and profiled ABMP16 (left), CT14 (middle), and NNPDF-3.1 (right) sets. Figure taken from Ref. [297]. |
png pdf |
Figure 59-a:
The relative gluon PDF uncertainties of the original and profiled ABMP16 (left), CT14 (middle), and NNPDF-3.1 (right) sets. Figure taken from Ref. [297]. |
png pdf |
Figure 59-b:
The relative gluon PDF uncertainties of the original and profiled ABMP16 (left), CT14 (middle), and NNPDF-3.1 (right) sets. Figure taken from Ref. [297]. |
png pdf |
Figure 59-c:
The relative gluon PDF uncertainties of the original and profiled ABMP16 (left), CT14 (middle), and NNPDF-3.1 (right) sets. Figure taken from Ref. [297]. |
png pdf |
Figure 60:
Scan of the jet $ p_{\mathrm{T}} $ threshold in the measurements of the jet mass against integrated luminosity resulting in the same event yield in data after the full selection as in the most recent measurement [70]. The projection is obtained by scanning the jet $ p_{\mathrm{T}} $ spectrum observed in data. The markers correspond to 138 fb$ ^{-1} $ of LHC Run-2 data used in Ref. [70], to an estimated data set for the combination of Run-2 and Run-3, and to the HL-LHC scenario. For simplicity a constant centre-of-mass energy of 13 TeV and a similar detector acceptance to Run-2 are assumed in all scenarios. |
| Tables | |
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Table 1:
List of all CMS $ m_{\mathrm{t}} $ measurements by using different analysis methods in chronological order of publication. The summary of these measurements is also depicted in Fig. 54. The analyses are categorised as direct mass measurements (a), indirect extraction of the Lagrangian mass (b), or boosted measurements (c), as explained in the text. The analysis methods of the publications marked with a star (*) are covered in the following sections of this review. All acronyms are defined in Appendix 7. |
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Table 2:
Overview of CMS MC setups for $ \mathrm{t} \overline{\mathrm{t}} $ production used in analyses of Run-1 and Run-2 data, and their associated modelling uncertainties. Variations marked with a dagger ($ \dagger $) are evaluated via event weights, which mitigates the uncertainty associated with the size of MC samples without the need for additional simulations. |
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Table 3:
Typical object definitions, and configuration parameters used for defining top quarks at the particle level (pseudo-top candidate). The pseudo-top candidate definition is not universal and may be optimised for the production mode, final state, the variable, and the phase space being studied. The details of particle-level top quark definitions adopted in the RIVET [179,180] framework by CMS codes are described in Ref. [178] as a fundamental aspect for current and future measurements of differential production cross sections in both $ \mathrm{t} \overline{\mathrm{t}} $ and single-top quark production. |
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Table 4:
The overall list of different input histograms and their inclusion in a certain histogram set. A histogram marked with ``$ \times $'' is included in a set (measurement). |
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Table 5:
Advancement in analysis strategies between Run-1 [58] and Run-2 [67] measurements of $ m_{\mathrm{t}} $ in single top events. Primary improvements that resulted in a higher precision in the Run-2 measurement are highlighted in bold. |
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Table 6:
Summary of scale choices for $ \mu_{\mathrm{r}} $, $ \mu_{\mathrm{f}} $, and $ \mu_{\mathrm{m}} $ for the three different extractions of the running of the top quark mass. The NLO fixed scale corresponds to the result of Ref. [65], while the NNLO result is described in Ref. [241]. The NLO bin-by-bin dynamic result, instead, is obtained in the scope of this review work. |
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Table 7:
A list of the event categories and distributions used in the maximum likelihood fit. |
| Summary |
| Measurements of the top quark mass have been an essential part of the CMS research programme since the first data were recorded in 2010, with more than 20 journal publications that reveal different aspects related to this fundamental parameter of the standard model. A growing understanding of theoretical and experimental issues on the way towards increasing precision in $ m_{\mathrm{t}} $, demanded by matching the accuracy of other electroweak parameters, were followed by steady improvements in analysis techniques. Different complementary methods have been used for measurements of $ m_{\mathrm{t}} $, affected by different sources of theoretical and experimental systematic uncertainties. An impressive sub-GeV precision has been achieved, despite the challenging environment of high-energy pp collisions at the LHC, where events are affected by QCD and electroweak radiation, the underlying event and an unprecedented level of pileup interactions. This success, and a clear perspective of experimental improvements envisaged for the HL-LHC, give confidence in reaching the ultimate precision in $ m_{\mathrm{t}} $ achievable at a hadron collider in the next decade. This experimental goal requires that the necessary theoretical developments will take place, including advancements in the description of the top quark beyond the picture of a free particle, matching higher-order calculations to resummations and hadronisation models, and calculating corrections at the threshold of $ \mathrm{t} \overline{\mathrm{t}} $ production. The precise determination of $ m_{\mathrm{t}} $ is an ongoing endeavor that fosters a close collaboration of the experimental and theoretical communities, with bright prospects in the coming years. |
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