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| CMS-PAS-TOP-15-008 | ||
| Measurement of the top-quark mass in the dileptonic $\mathrm{ t \bar{t} }$ decay channel using the $M_{\mathrm{b}\ell}$, $M_{\mathrm{T}2}$, and $M_{\mathrm{b}\ell\nu}$ observables | ||
| CMS Collaboration | ||
| August 2016 | ||
| Abstract: We report on a measurement of the top-quark mass ($M_{\mathrm{t}}$) in the dileptonic $\mathrm{t}\overline{\mathrm{t}}$ decay channel using events selected from a data sample corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$. The events were recorded by the CMS detector at the LHC in proton-proton collisions at $\sqrt{s} =$ 8 TeV. The analysis is based on three observables whose distribution shapes are sensitive to the value of $M_{\mathrm{t}}$. The $M_{\mathrm{b}\ell}$ invariant mass and $M_{\mathrm{T}2}^{\mathrm{bb}}$ `stransverse mass' observables are employed in a simultaneous fit to determine the value of $M_{\mathrm{t}}$ and an overall jet energy scale factor (JSF). In a complementary approach, the $M_{\mathrm{T}2}$-Assisted On-Shell reconstruction technique is used to construct an $M_{\mathrm{b}\ell\nu}$ invariant mass observable that is combined with $M_{\mathrm{T}2}^{\mathrm{bb}}$ to measure $M_{\mathrm{t}}$. The shapes of the observables, along with their evolutions in $M_{\mathrm{t}}$ and JSF, are modeled by a non-parametric Gaussian Process regression technique. The top-quark mass is measured to be 172.22 $\pm$ 0.18 (stat) $^{+0.89}_{-0.93}$ (syst) GeV. | ||
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CDS record (PDF) ;
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These preliminary results are superseded in this paper, PRD 96 (2017) 032002. The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1-a:
(a) the ${\mathrm {M}_{\mathrm {b}\ell }}$ distribution in data and simulation with $ {\mathrm {M}_{\mathrm {t}}^{\text {MC}}}= $ 172.5 GeV, normalized to the number of events in the 8 TeV dataset corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$. Statistical and systematic uncertainties on the distribution in simulation are represented by the grey shaded area. A description of the systematic uncertainties is given in Section 8. (b) the ${\mathrm {M}_{\mathrm {b}\ell }}$ distribution shapes in simulation corresponding to three values of ${\mathrm {M}_{\mathrm {t}}^{\text {MC}}}$ are shown in grey. The `local shape sensitivity' function, described in Appendix A, is shown in red. |
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Figure 1-b:
(a) the ${\mathrm {M}_{\mathrm {b}\ell }}$ distribution in data and simulation with $ {\mathrm {M}_{\mathrm {t}}^{\text {MC}}}= $ 172.5 GeV, normalized to the number of events in the 8 TeV dataset corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$. Statistical and systematic uncertainties on the distribution in simulation are represented by the grey shaded area. A description of the systematic uncertainties is given in Section 8. (b) the ${\mathrm {M}_{\mathrm {b}\ell }}$ distribution shapes in simulation corresponding to three values of ${\mathrm {M}_{\mathrm {t}}^{\text {MC}}}$ are shown in grey. The `local shape sensitivity' function, described in Appendix A, is shown in red. |
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Figure 2:
${\mathrm {M}_{\mathrm {T}2}}$ subsystems in the dileptonic ${\mathrm {t}\overline {\mathrm {t}}} $ event topology. |
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Figure 3-a:
(a) the ${\mathrm {M}_{\mathrm {T}2}^{\mathrm {bb}}}$ distribution in data and simulation with $ {\mathrm {M}_{\mathrm {t}}^{\text {MC}}}=$ 172.5 GeV, normalized to the number of events in the 8 TeV dataset corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$. Statistical and systematic uncertainties on the distribution in simulation are represented by the grey shaded area. (b) the ${\mathrm {M}_{\mathrm {T}2}^{\mathrm {bb}}}$ distribution shapes in simulation corresponding to three values of ${\mathrm {M}_{\mathrm {t}}^{\text {MC}}}$ are shown in grey. The `local shape sensitivity' function is shown in red. |
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Figure 3-b:
(a) the ${\mathrm {M}_{\mathrm {T}2}^{\mathrm {bb}}}$ distribution in data and simulation with $ {\mathrm {M}_{\mathrm {t}}^{\text {MC}}}=$ 172.5 GeV, normalized to the number of events in the 8 TeV dataset corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$. Statistical and systematic uncertainties on the distribution in simulation are represented by the grey shaded area. (b) the ${\mathrm {M}_{\mathrm {T}2}^{\mathrm {bb}}}$ distribution shapes in simulation corresponding to three values of ${\mathrm {M}_{\mathrm {t}}^{\text {MC}}}$ are shown in grey. The `local shape sensitivity' function is shown in red. |
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Figure 4-a:
(a) the MAOS ${\mathrm {M}_{\mathrm {b}\ell \nu }}$ distribution in data and simulation with $ {\mathrm {M}_{\mathrm {t}}^{\text {MC}}}=$ 172.5 GeV, normalized to the number of events in the 8 TeV dataset corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$. Statistical and systematic uncertainties on the distribution in simulation are represented by the grey shaded area. (b) the MAOS ${\mathrm {M}_{\mathrm {b}\ell \nu }}$ distribution shapes in simulation corresponding to three values of ${\mathrm {M}_{\mathrm {t}}^{\text {MC}}}$ are shown in grey. The `local shape sensitivity' function is shown in red. |
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Figure 4-b:
(a) the MAOS ${\mathrm {M}_{\mathrm {b}\ell \nu }}$ distribution in data and simulation with $ {\mathrm {M}_{\mathrm {t}}^{\text {MC}}}=$ 172.5 GeV, normalized to the number of events in the 8 TeV dataset corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$. Statistical and systematic uncertainties on the distribution in simulation are represented by the grey shaded area. (b) the MAOS ${\mathrm {M}_{\mathrm {b}\ell \nu }}$ distribution shapes in simulation corresponding to three values of ${\mathrm {M}_{\mathrm {t}}^{\text {MC}}}$ are shown in grey. The `local shape sensitivity' function is shown in red. |
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Figure 5-a:
The (left) ${\mathrm {M}_{\mathrm {b}\ell }}$ and (right) ${\mathrm {M}_{\mathrm {T}2}^{\mathrm {bb}}}$ distributions in MC with $ {\mathrm {M}_{\mathrm {t}}}= 172.5$ GeV for several values of JSF. |
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Figure 5-b:
The (left) ${\mathrm {M}_{\mathrm {b}\ell }}$ and (right) ${\mathrm {M}_{\mathrm {T}2}^{\mathrm {bb}}}$ distributions in MC with $ {\mathrm {M}_{\mathrm {t}}}= 172.5$ GeV for several values of JSF. |
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Figure 6:
Demonstration of the GP conditioning process (Eqs. (9) et (10)) for one training point and one test point. The covariance between the value of the shape at the training and test point is represented by the red ellipse. The known value of the shape at the training point (blue square) determines the mean value of the shape at the test point (green circle). |
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Figure 7-a:
Likelihood fit results using 50 pseudo-experiments in MC simulation, with values of ${\mathrm {M}_{\mathrm {t}}^{\text {MC}}}$ ranging from 166.5 to 178.5 GeV. A calibration curve of the form $y=ax + b$ is determined for each fit configuration. Measured values of (a) ${\mathrm {M}_{\mathrm {t}}}$ and (b) JSF are shown for the 2D fit, and measured values of ${\mathrm {M}_{\mathrm {t}}}$ are shown for the (c) 1D, (d) MAOS, and (e) hybrid fits. |
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Figure 7-b:
Likelihood fit results using 50 pseudo-experiments in MC simulation, with values of ${\mathrm {M}_{\mathrm {t}}^{\text {MC}}}$ ranging from 166.5 to 178.5 GeV. A calibration curve of the form $y=ax + b$ is determined for each fit configuration. Measured values of (a) ${\mathrm {M}_{\mathrm {t}}}$ and (b) JSF are shown for the 2D fit, and measured values of ${\mathrm {M}_{\mathrm {t}}}$ are shown for the (c) 1D, (d) MAOS, and (e) hybrid fits. |
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Figure 7-c:
Likelihood fit results using 50 pseudo-experiments in MC simulation, with values of ${\mathrm {M}_{\mathrm {t}}^{\text {MC}}}$ ranging from 166.5 to 178.5 GeV. A calibration curve of the form $y=ax + b$ is determined for each fit configuration. Measured values of (a) ${\mathrm {M}_{\mathrm {t}}}$ and (b) JSF are shown for the 2D fit, and measured values of ${\mathrm {M}_{\mathrm {t}}}$ are shown for the (c) 1D, (d) MAOS, and (e) hybrid fits. |
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Figure 7-d:
Likelihood fit results using 50 pseudo-experiments in MC simulation, with values of ${\mathrm {M}_{\mathrm {t}}^{\text {MC}}}$ ranging from 166.5 to 178.5 GeV. A calibration curve of the form $y=ax + b$ is determined for each fit configuration. Measured values of (a) ${\mathrm {M}_{\mathrm {t}}}$ and (b) JSF are shown for the 2D fit, and measured values of ${\mathrm {M}_{\mathrm {t}}}$ are shown for the (c) 1D, (d) MAOS, and (e) hybrid fits. |
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Figure 7-e:
Likelihood fit results using 50 pseudo-experiments in MC simulation, with values of ${\mathrm {M}_{\mathrm {t}}^{\text {MC}}}$ ranging from 166.5 to 178.5 GeV. A calibration curve of the form $y=ax + b$ is determined for each fit configuration. Measured values of (a) ${\mathrm {M}_{\mathrm {t}}}$ and (b) JSF are shown for the 2D fit, and measured values of ${\mathrm {M}_{\mathrm {t}}}$ are shown for the (c) 1D, (d) MAOS, and (e) hybrid fits. |
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Figure 8-a:
Likelihood fit results using 1k bootstrap pseudo-experiments for the (a,b) 2D fit, (c) 1D fit, (d) MAOS fit. (e) hybrid fit results given by a linear combination of the 1D and 2D fits (Eq. (4)). |
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Figure 8-b:
Likelihood fit results using 1k bootstrap pseudo-experiments for the (a,b) 2D fit, (c) 1D fit, (d) MAOS fit. (e) hybrid fit results given by a linear combination of the 1D and 2D fits (Eq. (4)). |
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Figure 8-c:
Likelihood fit results using 1k bootstrap pseudo-experiments for the (a,b) 2D fit, (c) 1D fit, (d) MAOS fit. (e) hybrid fit results given by a linear combination of the 1D and 2D fits (Eq. (4)). |
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Figure 8-d:
Likelihood fit results using 1k bootstrap pseudo-experiments for the (a,b) 2D fit, (c) 1D fit, (d) MAOS fit. (e) hybrid fit results given by a linear combination of the 1D and 2D fits (Eq. (4)). |
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Figure 8-e:
Likelihood fit results using 1k bootstrap pseudo-experiments for the (a,b) 2D fit, (c) 1D fit, (d) MAOS fit. (e) hybrid fit results given by a linear combination of the 1D and 2D fits (Eq. (4)). |
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Figure 9-a:
Likelihood fit results corresponding to the 2D fit (a) and hybrid fit (b), obtained using 1k pseudo-experiments constructed with the bootstrapping technique. The shaded gray histogram represents the number of pseudo-experiments in each bin of ${\mathrm {M}_{\mathrm {t}}}$ and JSF. Two-dimensional contours corresponding to $-2\Delta \log(\mathcal {L})=1(4)$ are shown in red to indicate the one (two) sigma statistical intervals in ${\mathrm {M}_{\mathrm {t}}}$ and JSF. The hybrid fit results are given by a linear combination of the 1D and 2D fit results using Eq. (14). The correlation coefficient between the ${\mathrm {M}_{\mathrm {t}}}$ and JSF parameters is $-0.94$ in the 2D fit and $-0.40$ in the hybrid fit. |
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Figure 9-b:
Likelihood fit results corresponding to the 2D fit (a) and hybrid fit (b), obtained using 1k pseudo-experiments constructed with the bootstrapping technique. The shaded gray histogram represents the number of pseudo-experiments in each bin of ${\mathrm {M}_{\mathrm {t}}}$ and JSF. Two-dimensional contours corresponding to $-2\Delta \log(\mathcal {L})=1(4)$ are shown in red to indicate the one (two) sigma statistical intervals in ${\mathrm {M}_{\mathrm {t}}}$ and JSF. The hybrid fit results are given by a linear combination of the 1D and 2D fit results using Eq. (14). The correlation coefficient between the ${\mathrm {M}_{\mathrm {t}}}$ and JSF parameters is $-0.94$ in the 2D fit and $-0.40$ in the hybrid fit. |
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Figure 10-a:
Maximum likelihood fit result in a typical pseudo-experiment of the 2D likelihood fit. The best-fit parameter values for this pseudo-experiment are $ {\mathrm {M}_{\mathrm {t}}}=$ 171.99 GeV and $ {\mathrm {JSF}}=$ 1.007. |
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Figure 10-b:
Maximum likelihood fit result in a typical pseudo-experiment of the 2D likelihood fit. The best-fit parameter values for this pseudo-experiment are $ {\mathrm {M}_{\mathrm {t}}}=$ 171.99 GeV and $ {\mathrm {JSF}}=$ 1.007. |
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Figure 11-a:
Maximum likelihood fit result in a typical pseudo-experiment of the 1D likelihood fit. The best-fit value of ${\mathrm {M}_{\mathrm {t}}}$ for this pseudo-experiment is 172.48 GeV. |
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Figure 11-b:
Maximum likelihood fit result in a typical pseudo-experiment of the 1D likelihood fit. The best-fit value of ${\mathrm {M}_{\mathrm {t}}}$ for this pseudo-experiment is 172.48 GeV. |
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Figure 12-a:
Maximum likelihood fit result in a typical pseudo-experiment of the MAOS likelihood fit. The best-fit value of ${\mathrm {M}_{\mathrm {t}}}$ for this pseudo-experiment is 171.54 GeV. |
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Figure 12-b:
Maximum likelihood fit result in a typical pseudo-experiment of the MAOS likelihood fit. The best-fit value of ${\mathrm {M}_{\mathrm {t}}}$ for this pseudo-experiment is 171.54 GeV. |
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Figure 13:
Summary of the 1D, 2D, hybrid, and MAOS likelihood fit results using the CMS 2012 dataset corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$ and $ \sqrt{s} = $ 8 TeV. The most recent combination of ${\mathrm {M}_{\mathrm {t}}}$ measurements by CMS [5] is shown for reference. |
| Tables | |
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Table 1:
Estimate of signal and background composition in MC simulation, normalized to the number of events observed in the full dataset corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$ and $ sqrt {s}= $ 8 TeV . The contributions of these processes to the distribution shapes are shown in Figs. 1, 3, and 4, where the single top, diboson, W+jets, and Drell Yan processes are included in the `non-ttbar bkg' category. The ${\mathrm {t}\overline {\mathrm {t}}} $ category includes: `signal' dilepton events; `mistag' where a light quark or gluon jet is incorrectly selected by the b tagging algorithm; `tau decays' where dilepton events include one $\tau $ in the final state subsequently decaying leptonically; and `hadronic decays' that include events where one of the top quarks decays hadronically. |
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Table 2:
Systematic uncertainties for the 2D, 1D, hybrid, and MAOS likelihood fits. The breakdown of JES uncertainties into four separate components is shown, where the components are added in quadrature to obtain the total. The `up' and `down' variations are given separately, with the sign of each variation indicating the direction of the corresponding shift in ${\mathrm {M}_{\mathrm {t}}}$ or JSF. The $\star$ character highlights the uncertainty sources that are large in at least one of the likelihood fits. |
| Summary |
| We have presented a measurement of the top-quark mass using events in the dileptonic $\mathrm{ t \bar{t} }$ decay channel selected from a dataset corresponding to an integrated luminosity of (lumi)inosity and center of mass energy $ \sqrt{s} = $ 8 TeV. The measurement is based on the ${M_{\mathrm{b}}\ell}$, ${M_{\mathrm{T}2}^{\mathrm{bb}}}$, and MAOS ${M_{\mathrm{b}\ell\nu}}$ observables, which allow for mass reconstruction in decay topologies that are kinematically underconstrained. These observables are employed in three versions of an event-by-event likelihood fit, where a GP technique is used to model the corresponding distribution shapes and their evolution in the ${M_{\mathrm{t}}}$ and JSF parameters. The GP shapes are non-parametric, and allow for a likelihood fitting framework that gives unbiased results. The results for each version of the likelihood fit are summarized in Fig. 13. The 2D fit provides a measurement of ${M_{\mathrm{t}}}$ that is robust against uncertainties due to the determination of JES, yielding 171.56 $\pm$ 0.46 (stat) $^{+1.31}_{-1.25}$ (syst) GeV and 1.011 $\pm$ 0.006 (stat) $^{+0.015}_{-0.014}$ (syst). The most precise measurement of the top quark mass is given by the hybrid fit, which gives 172.22 $\pm$ 0.18 (stat) $^{+0.89}_{-0.93}$ (syst) GeV. |
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