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| CMS-TOP-15-008 ; CERN-EP-2017-050 | ||
| Measurement of the top quark mass in the dileptonic $\mathrm{ t \bar{t} }$ decay channel using the mass observables $M_{\mathrm{ b }\ell}$, $M_{\mathrm{T}2}$, and $M_{\mathrm{ b }\ell\nu}$ in pp collisions at $\sqrt{s} = $ 8 TeV | ||
| CMS Collaboration | ||
| 20 April 2017 | ||
| Phys. Rev. D 96 (2017) 032002 | ||
| Abstract: A measurement of the top quark mass ($M_{\mathrm{ t }}$) in the dileptonic $\mathrm{ t \bar{t} }$ decay channel is performed using data from proton-proton collisions at a center-of-mass energy of 8 TeV. The data was recorded by the CMS experiment at the LHC and corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$. Events are selected with two oppositely charged leptons ($\ell=$ e, $\mu$) and two jets identified as originating from b quarks. The analysis is based on three kinematic observables whose distributions are sensitive to the value of $M_{\mathrm{ t }}$. An invariant mass observable, $M_{\mathrm{ b }\ell}$, and a 'stransverse mass' observable, $M_{\mathrm{T}2}$, are employed in a simultaneous fit to determine the value of $M_{\mathrm{ t }}$ and an overall jet energy scale factor (JSF). A complementary approach is used to construct an invariant mass observable, $M_{\mathrm{ b }\ell\nu}$, that is combined with $M_{\mathrm{T}2}$ to measure $M_{\mathrm{ t }}$. The shapes of the observables, along with their evolutions in $M_{\mathrm{ t }}$ and JSF, are modeled by a nonparametric Gaussian process regression technique. The sensitivity of the observables to the value of $M_{\mathrm{ t }}$ is investigated using a Fisher information density method. The top quark mass is measured to be 172.22 $\pm$ 0.18 (stat) $^{+0.89}_{-0.93}$ (syst) GeV. | ||
| Links: e-print arXiv:1704.06142 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
(Left) the ${M_{\mathrm{ b } \ell }}$ distribution in data and simulation with $ {M_{\mathrm{ t } }^{\text {MC}}}= $ 172.5 GeV, normalized to the number of events in the 8 TeV data set corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$. The lower panel shows the ratio between the data and simulation. Statistical and systematic uncertainties on the distribution in simulation are represented by the shaded area. A description of the systematic uncertainties is given in Section 7. (Right) the ${M_{\mathrm{ b } \ell }}$ distribution shapes in simulation, normalized to unit area, corresponding to three values of $ {M_{\mathrm{ t } }^{\text {MC}}}$ are shown together with the 'local shape sensitivity' function, described in Appendix {sec:sensitivity}. The ${M_{\mathrm{ b } \ell }}$ distributions include two or three values of ${M_{\mathrm{ b } \ell }}$ for each event. The distribution shapes are modeled with a GP regression technique, described in Section 5. |
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Figure 1-a:
The ${M_{\mathrm{ b } \ell }}$ distribution in data and simulation with $ {M_{\mathrm{ t } }^{\text {MC}}}= $ 172.5 GeV, normalized to the number of events in the 8 TeV data set corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$. The lower panel shows the ratio between the data and simulation. Statistical and systematic uncertainties on the distribution in simulation are represented by the shaded area. A description of the systematic uncertainties is given in Section 7. |
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Figure 1-b:
The ${M_{\mathrm{ b } \ell }}$ distribution shapes in simulation, normalized to unit area, corresponding to three values of $ {M_{\mathrm{ t } }^{\text {MC}}}$ are shown together with the 'local shape sensitivity' function, described in Appendix {sec:sensitivity}. The ${M_{\mathrm{ b } \ell }}$ distributions include two or three values of ${M_{\mathrm{ b } \ell }}$ for each event. The distribution shapes are modeled with a GP regression technique, described in Section 5. |
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Figure 2:
The ${M_{\mathrm {T}2}}$ subsystems in the dileptonic ${\mathrm{ t } {}\mathrm{ \bar{t} } } $ event topology. |
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Figure 3:
Following the conventions of Fig. 1, shown are the (left) $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ distribution in data and simulation with $ {M_{\mathrm{ t } }^{\text {MC}}}= $ 172.5 GeV, and (right) $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ distribution shapes in simulation corresponding to three values of ${M_{\mathrm{ t } }^{\text {MC}}}$, along with the 'local shape sensitivity' function. The $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ distributions include one value of $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ for each event if it satisfies the kinematic requirement outlined in Section 4.2. |
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Figure 3-a:
Following the conventions of Fig. 1, shown is the $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ distribution in data and simulation with $ {M_{\mathrm{ t } }^{\text {MC}}}= $ 172.5 GeV. The $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ distribution includes one value of $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ for each event if it satisfies the kinematic requirement outlined in Section 4.2. |
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Figure 3-b:
Following the conventions of Fig. 1, shown is the $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ distribution shapes in simulation corresponding to three values of ${M_{\mathrm{ t } }^{\text {MC}}}$, along with the 'local shape sensitivity' function. The $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ distribution includes one value of $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ for each event if it satisfies the kinematic requirement outlined in Section 4.2. |
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Figure 4:
Following the conventions of Fig. 1, shown are the (left) MAOS ${M_{\mathrm{ b } \ell \nu }}$ distribution in data and simulation with $ {M_{\mathrm{ t } }^{\text {MC}}}=$ 172.5 GeV, and (right) the MAOS ${M_{\mathrm{ b } \ell \nu }}$ distribution shapes in simulation corresponding to three values of $ {M_{\mathrm{ t } }^{\text {MC}}} $, along with the 'local shape sensitivity' function. The MAOS ${M_{\mathrm{ b } \ell \nu }}$ distributions include up to eight values of ${M_{\mathrm{ b } \ell \nu }}$ for each event. |
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Figure 4-a:
Following the conventions of Fig. 1, shown is the MAOS ${M_{\mathrm{ b } \ell \nu }}$ distribution in data and simulation with $ {M_{\mathrm{ t } }^{\text {MC}}}=$ 172.5 GeV. The MAOS ${M_{\mathrm{ b } \ell \nu }}$ distribution includes up to eight values of ${M_{\mathrm{ b } \ell \nu }}$ for each event. |
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Figure 4-b:
Following the conventions of Fig. 1, shown is the MAOS ${M_{\mathrm{ b } \ell \nu }}$ distribution shapes in simulation corresponding to three values of $ {M_{\mathrm{ t } }^{\text {MC}}} $, along with the 'local shape sensitivity' function. The MAOS ${M_{\mathrm{ b } \ell \nu }}$ distribution includes up to eight values of ${M_{\mathrm{ b } \ell \nu }}$ for each event. |
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Figure 5:
The (left) ${M_{\mathrm{ b } \ell }}$ and (right) $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ distributions in simulation with $ {M_{\mathrm{ t } }}= $ 172.5 GeV for several values of JSF. Two or three values are included in the ${M_{\mathrm{ b } \ell }}$ distribution for each event, and one value is included in the $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ distribution if it satisfies the kinematic requirement outlined in Section 4.2. The distributions are normalized to unit area. The three curves corresponding to each of the ${M_{\mathrm{ b } \ell }}$ and $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ distributions are obtained using a GP regression technique described in Section 5. |
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Figure 5-a:
The ${M_{\mathrm{ b } \ell }}$ distribution in simulation with $ {M_{\mathrm{ t } }}= $ 172.5 GeV for several values of JSF. Two or three values are included in the ${M_{\mathrm{ b } \ell }}$ distribution for each event. The distributions are normalized to unit area. The three curves corresponding to each of the ${M_{\mathrm{ b } \ell }}$ distributions are obtained using a GP regression technique described in Section 5. |
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Figure 5-b:
The $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ distribution in simulation with $ {M_{\mathrm{ t } }}= $ 172.5 GeV for several values of JSF. One value is included in the $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ distribution if it satisfies the kinematic requirement outlined in Section 4.2. The distributions are normalized to unit area. The three curves corresponding to each of the $ {M_{\mathrm {T}2}^{\mathrm{ b } \mathrm{ b } }}$ distributions are obtained using a GP regression technique described in Section 5. |
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Figure 6:
Likelihood fit results as a function of $ {M_{\mathrm{ t } }^{\text {MC}}}$ corresponding to the (top) 2D, (center left) 1D, (center right) MAOS, and (bottom) hybrid fits. For each value of $ {M_{\mathrm{ t } }^{\text {MC}}} $, the fit is conducted using 50 pseudo-experimentsin MC simulation. The mean parameter values, $ {M_{\mathrm{ t } }}^{\rm fit}$ and $ {\mathrm {JSF}}^{\rm fit}$, are represented by the points, with statistical uncertainties indicated by the error bars. A best-fit line of the form $y=ax + b$ is shown for each fit configuration. |
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Figure 6-a:
Likelihood fit results as a function of $ {M_{\mathrm{ t } }^{\text {MC}}}$ corresponding to the 2D fit. For each value of $ {M_{\mathrm{ t } }^{\text {MC}}} $, the fit is conducted using 50 pseudo-experimentsin MC simulation. The mean parameter values $ {M_{\mathrm{ t } }}^{\rm fit}$ is represented by the points, with statistical uncertainties indicated by the error bars. A best-fit line of the form $y=ax + b$ is shown for each fit configuration. |
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Figure 6-b:
Likelihood fit results as a function of $ {M_{\mathrm{ t } }^{\text {MC}}}$ corresponding to the 2D fit. For each value of $ {M_{\mathrm{ t } }^{\text {MC}}} $, the fit is conducted using 50 pseudo-experimentsin MC simulation. The mean parameter values $ {\mathrm {JSF}}^{\rm fit}$ is represented by the points, with statistical uncertainties indicated by the error bars. A best-fit line of the form $y=ax + b$ is shown for each fit configuration. |
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Figure 6-c:
Likelihood fit results as a function of $ {M_{\mathrm{ t } }^{\text {MC}}}$ corresponding to the 1D fit. For each value of $ {M_{\mathrm{ t } }^{\text {MC}}} $, the fit is conducted using 50 pseudo-experimentsin MC simulation. The mean parameter values $ {M_{\mathrm{ t } }}^{\rm fit}$ is represented by the points, with statistical uncertainties indicated by the error bars. A best-fit line of the form $y=ax + b$ is shown for each fit configuration. |
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Figure 6-d:
Likelihood fit results as a function of $ {M_{\mathrm{ t } }^{\text {MC}}}$ corresponding to the MAOS fit. For each value of $ {M_{\mathrm{ t } }^{\text {MC}}} $, the fit is conducted using 50 pseudo-experimentsin MC simulation. The mean parameter values $ {M_{\mathrm{ t } }}^{\rm fit}$ is represented by the points, with statistical uncertainties indicated by the error bars. A best-fit line of the form $y=ax + b$ is shown for each fit configuration. |
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Figure 6-e:
Likelihood fit results as a function of $ {M_{\mathrm{ t } }^{\text {MC}}}$ corresponding to the hybrid fit. For each value of $ {M_{\mathrm{ t } }^{\text {MC}}} $, the fit is conducted using 50 pseudo-experimentsin MC simulation. The mean parameter values $ {M_{\mathrm{ t } }}^{\rm fit}$ is represented by the points, with statistical uncertainties indicated by the error bars. A best-fit line of the form $y=ax + b$ is shown for each fit configuration. |
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Figure 7:
Likelihood fit results using 1000 bootstrap pseudo-experiments for the (top) 2D fit, (center left) 1D fit, (center right) MAOS fit. (Bottom) hybrid fit results given by the linear combination in Eq. (9) of the 1D and 2D fits. The error bars represent the statistical uncertainty corresponding to the number of pseudo-experiments in each bin. |
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Figure 7-a:
Likelihood fit results using 1000 bootstrap pseudo-experiments for the 2D fit, for ${M_{\mathrm{ t } }}$. The error bars represent the statistical uncertainty corresponding to the number of pseudo-experiments in each bin. |
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Figure 7-b:
Likelihood fit results using 1000 bootstrap pseudo-experiments for the 2D fit, for JSF. The error bars represent the statistical uncertainty corresponding to the number of pseudo-experiments in each bin. |
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Figure 7-c:
Likelihood fit results using 1000 bootstrap pseudo-experiments for the 1D fit. The error bars represent the statistical uncertainty corresponding to the number of pseudo-experiments in each bin. |
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Figure 7-d:
Likelihood fit results using 1000 bootstrap pseudo-experiments for the MAOS fit. The error bars represent the statistical uncertainty corresponding to the number of pseudo-experiments in each bin. |
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Figure 7-e:
Likelihood fit results using 1000 bootstrap pseudo-experiments for the hybrid fit results given by the linear combination in Eq. (9) of the 1D and 2D fits. The error bars represent the statistical uncertainty corresponding to the number of pseudo-experiments in each bin. |
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Figure 8:
Likelihood fit results corresponding to the 2D fit (left) and hybrid fit (right), obtained using 1000 pseudo-experiments constructed with the bootstrapping technique. The shaded histogram represents the number of pseudo-experiments in each bin of ${M_{\mathrm{ t } }}$ and JSF. Two-dimensional contours corresponding to $-2\Delta \log(\mathcal {L})=$ 1 (4) are shown, allowing the construction of one (two) $\sigma $ statistical intervals in ${M_{\mathrm{ t } }}$ and JSF. The hybrid fit results are given by a linear combination of the 1D and 2D fit results using Eq. (9). |
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Figure 8-a:
Likelihood fit results corresponding to the 2D fit, obtained using 1000 pseudo-experiments constructed with the bootstrapping technique. The shaded histogram represents the number of pseudo-experiments in each bin of ${M_{\mathrm{ t } }}$ and JSF. Two-dimensional contours corresponding to $-2\Delta \log(\mathcal {L})=$ 1 (4) are shown, allowing the construction of one (two) $\sigma $ statistical intervals in ${M_{\mathrm{ t } }}$ and JSF. The hybrid fit results are given by a linear combination of the 1D and 2D fit results using Eq. (9). |
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Figure 8-b:
Likelihood fit results corresponding to the hybrid fit, obtained using 1000 pseudo-experiments constructed with the bootstrapping technique. The shaded histogram represents the number of pseudo-experiments in each bin of ${M_{\mathrm{ t } }}$ and JSF. Two-dimensional contours corresponding to $-2\Delta \log(\mathcal {L})=$ 1 (4) are shown, allowing the construction of one (two) $\sigma $ statistical intervals in ${M_{\mathrm{ t } }}$ and JSF. The hybrid fit results are given by a linear combination of the 1D and 2D fit results using Eq. (9). |
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Figure 9:
Maximum-likelihood fit result in a typical pseudo-experiment of the 2D likelihood fit in data. The best fit parameter values for this pseudo-experimentare $ {M_{\mathrm{ t } }}= $ 171.99 GeV and JSF = 1.007. When the JSF parameter is constrained to be unity in the 1D likelihood fit, the best fit value of ${M_{\mathrm{ t } }}$ is 172.48 GeV. The lower panel shows the ratio between the distribution in data and the best fit distribution in simulation. |
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Figure 9-a:
Maximum-likelihood fit result in a typical pseudo-experiment of the 2D likelihood fit in data. The best fit parameter values for this pseudo-experimentare $ {M_{\mathrm{ t } }}= $ 171.99 GeV and JSF = 1.007. When the JSF parameter is constrained to be unity in the 1D likelihood fit, the best fit value of ${M_{\mathrm{ t } }}$ is 172.48 GeV. The lower panel shows the ratio between the distribution in data and the best fit distribution in simulation. |
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Figure 9-b:
Maximum-likelihood fit result in a typical pseudo-experiment of the 2D likelihood fit in data. The best fit parameter values for this pseudo-experimentare $ {M_{\mathrm{ t } }}= $ 171.99 GeV and JSF = 1.007. When the JSF parameter is constrained to be unity in the 1D likelihood fit, the best fit value of ${M_{\mathrm{ t } }}$ is 172.48 GeV. The lower panel shows the ratio between the distribution in data and the best fit distribution in simulation. |
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Figure 10:
The MAOS ${M_{\mathrm{ b } \ell \nu }}$ distribution corresponding to the maximum-likelihood fit result in a typical pseudo-experimentof the MAOS likelihood fit in data. The best fit value of ${M_{\mathrm{ t } }}$ for this pseudo-experimentis 171.54 GeV. The lower panel shows the ratio between the distribution in data and the best fit distribution in simulation. |
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Figure 11:
Summary of the 1D, 2D, hybrid, and MAOS likelihood fit results using the 2012 data set at $ \sqrt{s} = $ 8 TeV, corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$. A recent dileptonic channel measurement using the 2012 data set and the most recent combination of ${M_{\mathrm{ t } }}$ measurements by CMS [6] are shown for reference. |
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Figure 12:
Demonstration of the GP conditioning process, given in Eqs.(16) and (17), 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 ellipse. The known value of the shape at the training point (square point) determines the mean value of the shape at the test point (round point and vertical line). The distribution of possible values of the shape at the test point is represented by the dashed curve. |
| Tables | |
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Table 1:
Systematic uncertainties for the 2D, 1D, hybrid, and MAOS likelihood fits. The breakdown of JES and b quark fragmentation uncertainties into 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 ${M_{\mathrm{ t } }}$ or JSF. The circled star character highlights the uncertainty sources that are large in at least one of the likelihood fits. |
| Summary |
| A measurement of the top quark mass ($M_{\mathrm{ t }}$) in the dileptonic $\mathrm{ t \bar{t} }$ decay channel is performed using proton-proton collisions at $ \sqrt{s} = $ 8 TeV, corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$. The measurement is based on the mass observables $M_{\mathrm{ b }\ell}$, $M_{\mathrm{T}2}^{\mathrm{ b }\mathrm{ b }}$, and $M_{\mathrm{ b }\ell\nu}$, which allow for mass reconstruction in decay topologies that are kinematically underconstrained. The sensitivity of these observables to the value of $M_{\mathrm{ t }}$ is investigated using a Fisher information density technique. The observables are employed in three versions of an unbinned likelihood fit, where a Gaussian process technique is used to model the corresponding distribution shapes and their evolution in $M_{\mathrm{ t }}$ and an overall jet energy scale factor (JSF). The Gaussian process shapes are nonparametric, and allow for a likelihood fitting framework that gives unbiased results. The 2D fit provides the first simultaneous measurement of $M_{\mathrm{ t }}$ and JSF in the dileptonic channel. It is robust against uncertainties due to the determination of jet energy scale, including the flavor-dependent uncertainty component arising from differences in the response between b jets, light-quark jets, and gluon jets. The fit yields $M_{\mathrm{ t }} =$ 171.56 $\pm$ 0.46 (stat) $^{+1.31}_{-1.25}$ (syst) GeV and JSF = 1.011 $\pm$ 0.006 (stat) $^{+0.015}_{-0.014}$ (syst). The most precise measurement of $M_{\mathrm{ t }}$ is given by a linear combination of this result with a fit in which the JSF is constrained to be unity, yielding a value of 172.22 $\pm$ 0.18 (stat) $^{+0.89}_{-0.93}$ (syst) GeV. |
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