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| CMS-TOP-14-013 ; CERN-EP-2017-030 | ||
| Measurement of double-differential cross sections for top quark pair production in pp collisions at $\sqrt{s} = $ 8 TeV and impact on parton distribution functions | ||
| CMS Collaboration | ||
| 5 March 2017 | ||
| EPJC 77 (2017) 459 | ||
| Abstract: Normalized double-differential cross sections for top quark pair ($ \mathrm{ t \bar{t} } $) production are measured in pp collisions at a centre-of-mass energy of 8 TeV with the CMS experiment at the LHC. The analyzed data correspond to an integrated luminosity of 19.7 fb$^{-1}$. The measurement is performed in the dilepton $\mathrm{ e }^{\pm}\mu^{\mp}$ final state. The $ \mathrm{ t \bar{t} } $ cross section is determined as a function of various pairs of observables characterizing the kinematics of the top quark and $ \mathrm{ t \bar{t} } $ system. The data are compared to calculations using perturbative quantum chromodynamics at next-to-leading and approximate next-to-next-to-leading orders. They are also compared to predictions of Monte Carlo event generators that complement fixed-order computations with parton showers, hadronization, and multiple-parton interactions. Overall agreement is observed with the predictions, which is improved when the latest global sets of proton parton distribution functions are used. The inclusion of the measured $ \mathrm{ t \bar{t} } $ cross sections in a fit of parametrized parton distribution functions is shown to have significant impact on the gluon distribution. | ||
| Links: e-print arXiv:1703.01630 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Distributions of $ {p_{\mathrm {T}}} (\mathrm{ t } )$ (upper left), $y(\mathrm{ t } )$ (upper right), $ {p_{\mathrm {T}}} ({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ (middle left), $y({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ (middle right), and ${M({\mathrm{ t } {}\mathrm{ \bar{t} } } )}$ (lower) in selected events after the kinematic reconstruction. The experimental data with the vertical bars corresponding to their statistical uncertainties are plotted together with distributions of simulated signal and different background processes. The hatched regions correspond to the shape uncertainties in the signal and backgrounds (cf. Section 7). The lower panel in each plot shows the ratio of the observed data event yields to those expected in the simulation. |
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Figure 1-a:
Distributions of $ {p_{\mathrm {T}}} (\mathrm{ t } )$ in selected events after the kinematic reconstruction. The experimental data with the vertical bars corresponding to their statistical uncertainties are plotted together with distributions of simulated signal and different background processes. The hatched regions correspond to the shape uncertainties in the signal and backgrounds (cf. Section 7). The lower panel shows the ratio of the observed data event yields to those expected in the simulation. |
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Figure 1-b:
Distributions of $y(\mathrm{ t } )$ in selected events after the kinematic reconstruction. The experimental data with the vertical bars corresponding to their statistical uncertainties are plotted together with distributions of simulated signal and different background processes. The hatched regions correspond to the shape uncertainties in the signal and backgrounds (cf. Section 7). The lower panel shows the ratio of the observed data event yields to those expected in the simulation. |
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Figure 1-c:
Distributions of $ {p_{\mathrm {T}}} ({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ in selected events after the kinematic reconstruction. The experimental data with the vertical bars corresponding to their statistical uncertainties are plotted together with distributions of simulated signal and different background processes. The hatched regions correspond to the shape uncertainties in the signal and backgrounds (cf. Section 7). The lower panel shows the ratio of the observed data event yields to those expected in the simulation. |
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Figure 1-d:
Distributions of $y({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ in selected events after the kinematic reconstruction. The experimental data with the vertical bars corresponding to their statistical uncertainties are plotted together with distributions of simulated signal and different background processes. The hatched regions correspond to the shape uncertainties in the signal and backgrounds (cf. Section 7). The lower panel shows the ratio of the observed data event yields to those expected in the simulation. |
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Figure 1-e:
Distributions of ${M({\mathrm{ t } {}\mathrm{ \bar{t} } } )}$ in selected events after the kinematic reconstruction. The experimental data with the vertical bars corresponding to their statistical uncertainties are plotted together with distributions of simulated signal and different background processes. The hatched regions correspond to the shape uncertainties in the signal and backgrounds (cf. Section 7). The lower panel shows the ratio of the observed data event yields to those expected in the simulation. |
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Figure 2:
Comparison of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross section as a function of $ { {p_{\mathrm {T}}} (\mathrm{ t } )} $ in different $ {| {y(\mathrm{ t } )} | }$ ranges to MC predictions calculated using MadGraph+PYTHIA6 , POWHEG+PYTHIA6 , POWHEG+HERWIG6 , and MC@NLO+HERWIG6 . The inner vertical bars on the data points represent the statistical uncertainties and the full bars include also the systematic uncertainties added in quadrature. In the bottom panel, the ratios of the data and other simulations to the MadGraph+PYTHIA6 (MG+P) predictions are shown. |
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Figure 3:
Comparison of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross section as a function of $ {| {y(\mathrm{ t } )} | }$ in different $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ ranges to MC predictions. Details can be found in the caption of Fig. 2. |
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Figure 4:
Comparison of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross section as a function of $ {| {y({\mathrm{ t } {}\mathrm{ \bar{t} } } )} | }$ in different of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ ranges to MC predictions. Details can be found in the caption of Fig. 2. |
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Figure 5:
Comparison of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross section as a function of $ {\Delta \eta (\mathrm{ t } ,\mathrm{ \bar{t} } )} $ in different $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ ranges to MC predictions. Details can be found in the caption of Fig. 2. |
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Figure 6:
Comparison of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross section as a function of $ { {p_{\mathrm {T}}} ({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ in different $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ ranges to MC predictions. Details can be found in the caption of Fig. 2. |
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Figure 7:
Comparison of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross section as a function of $ {\Delta \phi (\mathrm{ t } ,\mathrm{ \bar{t} } )} $ in different $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ ranges to MC predictions. Details can be found in the caption of Fig. 2. |
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Figure 8:
Comparison of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross section as a function of $ { {p_{\mathrm {T}}} (\mathrm{ t } )} $ in different $ {| {y(\mathrm{ t } )} | }$ ranges to NLO $\mathcal{O}(\alpha _s^3)$ (MNR) predictions calculated with CT14 and HERAPDF2.0 , and approximate NNLO $\mathcal{O}(\alpha _s^4)$ (DiffTop) prediction calculated with CT14 . The inner vertical bars on the data points represent the statistical uncertainties and the full bars include also the systematic uncertainties added in quadrature. The light band shows the scale uncertainties ($\mu $) for the NLO predictions using CT14 , while the dark band includes also the PDF uncertainties added in quadrature ($\mu + \mathrm {PDF}$). The dotted line shows the NLO predictions calculated with HERAPDF2.0 . The dashed line shows the approximate NNLO predictions calculated with CT14 . In the bottom panel, the ratios of the data and other calculations to the NLO prediction using CT14 are shown. |
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Figure 9:
Comparison of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross section as a function of $ {| {y(\mathrm{ t } )} | }$ in different $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ ranges to NLO $\mathcal{O}(\alpha _s^3)$ predictions. Details can be found in the caption of Fig. 8. Approximate NNLO $\mathcal{O}(\alpha _s^4)$ predictions are not available for this cross section. |
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Figure 10:
Comparison of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross section as a function of $ {| {y({\mathrm{ t } {}\mathrm{ \bar{t} } } )} | }$ in different $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ ranges to NLO $\mathcal{O}(\alpha _s^3)$ predictions. Details can be found in the caption of Fig. 8. Approximate NNLO $\mathcal{O}(\alpha _s^4)$ predictions are not available for this cross section. |
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Figure 11:
Comparison of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross section as a function of $ {\Delta \eta (\mathrm{ t } ,\mathrm{ \bar{t} } )} $ in different $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ ranges to NLO $\mathcal{O}(\alpha _s^3)$ predictions. Details can be found in the caption of Fig. 8. Approximate NNLO $\mathcal{O}(\alpha _s^4)$ predictions are not available for this cross section. |
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Figure 12:
Comparison of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross section as a function of $ { {p_{\mathrm {T}}} ({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ in different $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ ranges to NLO $\mathcal{O}(\alpha _s^3)$ predictions. Details can be found in the caption of Fig. 8. Approximate NNLO $\mathcal{O}(\alpha _s^4)$ predictions are not available for this cross section. |
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Figure 13:
Comparison of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross section as a function of $ {\Delta \phi (\mathrm{ t } ,\mathrm{ \bar{t} } )} $ in different $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ ranges to NLO $\mathcal{O}(\alpha _s^3)$ predictions. Details can be found in the caption of Fig. 8. Approximate NNLO $\mathcal{O}(\alpha _s^4)$ predictions are not available for this cross section. |
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Figure 14:
The gluon (upper left), sea quark (upper right), u valence quark (lower left), and d valence quark (lower right) PDFs at $\mu _\mathrm {f}^2= $ 30 000 GeV$ ^2$, as obtained in all variants of the PDF fit, normalized to the results from the fit using the HERA DIS and CMS $ {\mathrm{ W } ^\pm } $ boson charge asymmetry measurements only. The shaded, hatched, and dotted areas represent the total uncertainty in each of the fits. |
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Figure 14-a:
The gluon PDF at $\mu _\mathrm {f}^2= $ 30 000 GeV$ ^2$, as obtained in all variants of the PDF fit, normalized to the results from the fit using the HERA DIS and CMS $ {\mathrm{ W } ^\pm } $ boson charge asymmetry measurements only. The shaded, hatched, and dotted areas represent the total uncertainty in each of the fits. |
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Figure 14-b:
The sea quark PDF at $\mu _\mathrm {f}^2= $ 30 000 GeV$ ^2$, as obtained in all variants of the PDF fit, normalized to the results from the fit using the HERA DIS and CMS $ {\mathrm{ W } ^\pm } $ boson charge asymmetry measurements only. The shaded, hatched, and dotted areas represent the total uncertainty in each of the fits. |
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Figure 14-c:
The u valence quark PDF at $\mu _\mathrm {f}^2= $ 30 000 GeV$ ^2$, as obtained in all variants of the PDF fit, normalized to the results from the fit using the HERA DIS and CMS $ {\mathrm{ W } ^\pm } $ boson charge asymmetry measurements only. The shaded, hatched, and dotted areas represent the total uncertainty in each of the fits. |
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Figure 14-d:
The d valence quark PDF at $\mu _\mathrm {f}^2= $ 30 000 GeV$ ^2$, as obtained in all variants of the PDF fit, normalized to the results from the fit using the HERA DIS and CMS $ {\mathrm{ W } ^\pm } $ boson charge asymmetry measurements only. The shaded, hatched, and dotted areas represent the total uncertainty in each of the fits. |
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Figure 15:
Relative total uncertainties of the gluon (upper left), sea quark (upper right), u valence quark (lower left), and d valence quark (lower right) distributions at $\mu _\mathrm {f}^2= $ 30 000 GeV$ ^2$, shown by shaded, hatched, and dotted areas, as obtained in all variants of the PDF fit. |
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Figure 15-a:
Relative total uncertainties of the gluon distribution at $\mu _\mathrm {f}^2= $ 30 000 GeV$ ^2$, shown by shaded, hatched, and dotted areas, as obtained in all variants of the PDF fit. |
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Figure 15-b:
Relative total uncertainties of the sea quark distribution at $\mu _\mathrm {f}^2= $ 30 000 GeV$ ^2$, shown by shaded, hatched, and dotted areas, as obtained in all variants of the PDF fit. |
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Figure 15-c:
Relative total uncertainties of the u valence quark distribution at $\mu _\mathrm {f}^2= $ 30 000 GeV$ ^2$, shown by shaded, hatched, and dotted areas, as obtained in all variants of the PDF fit. |
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Figure 15-d:
Relative total uncertainties of the d valence quark distribution at $\mu _\mathrm {f}^2= $ 30 000 GeV$ ^2$, shown by shaded, hatched, and dotted areas, as obtained in all variants of the PDF fit. |
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Figure 16:
The gluon distribution at $\mu _\mathrm {f}^2= $ 30 000 GeV$ ^2$, as obtained from the PDF fit to the HERA DIS data and CMS $ {\mathrm{ W } ^\pm } $ boson charge asymmetry measurements (shaded area), the CMS inclusive jet production cross sections (hatched area), and the $ {\mathrm{ W } ^\pm } $ boson charge asymmetry plus the double-differential $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ cross section (dotted area). All presented PDFs are normalized to the results from the fit using the DIS and $ {\mathrm{ W } ^\pm } $ boson charge asymmetry measurements. The shaded, hatched, and dotted areas represent the total uncertainty in each of the fits. |
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Figure 17:
The same as in Fig. 15 for the variants of the PDF fit using the single-differential $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ cross sections. |
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Figure 17-a:
The same as in Fig. 15-a for the variants of the PDF fit using the single-differential $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ cross sections. |
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Figure 17-b:
The same as in Fig. 15-b for the variants of the PDF fit using the single-differential $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ cross sections. |
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Figure 17-c:
The same as in Fig. 15-c for the variants of the PDF fit using the single-differential $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ cross sections. |
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Figure 17-d:
The same as in Fig. 15-d for the variants of the PDF fit using the single-differential $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ cross sections. |
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Figure 18:
Relative total uncertainties of the gluon distribution at $\mu _\mathrm {f}^2= $ 30 000 GeV$^2$, shown by shaded (or hatched) bands, as obtained in the PDF fit using the DIS and $ {\mathrm{ W } ^\pm } $ boson charge asymmetry data only, as well as single- and double-differential $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ cross sections. |
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Figure 19:
The gluon distribution (left) and its fractional total uncertainty (right) at $\mu _\mathrm {f}^2= $ 30 000 GeV$ ^2$, as obtained in the PDF fit at NNLO using the DIS and $ {\mathrm{ W } ^\pm } $ boson charge asymmetry data only, as well as $ {y(\mathrm{ t } )} $ cross sections. The distributions shown in the left panel are normalized to the results from the fit using the DIS and $ {\mathrm{ W } ^\pm } $ boson charge asymmetry data only. The total uncertainty of each distribution is shown by a shaded (or hatched) band. |
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Figure 19-a:
The gluon distribution at $\mu _\mathrm {f}^2= $ 30 000 GeV$ ^2$, as obtained in the PDF fit at NNLO using the DIS and $ {\mathrm{ W } ^\pm } $ boson charge asymmetry data only, as well as $ {y(\mathrm{ t } )} $ cross sections. The distributions shown are normalized to the results from the fit using the DIS and $ {\mathrm{ W } ^\pm } $ boson charge asymmetry data only. The total uncertainty of each distribution is shown by a shaded (or hatched) band. |
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Figure 19-b:
The fractional total uncertainty of the gluon distribution at $\mu _\mathrm {f}^2= $ 30 000 GeV$ ^2$, as obtained in the PDF fit at NNLO using the DIS and $ {\mathrm{ W } ^\pm } $ boson charge asymmetry data only, as well as $ {y(\mathrm{ t } )} $ cross sections. The total uncertainty of each distribution is shown by a shaded (or hatched) band. |
| Tables | |
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Table 1:
The $ {\chi ^2} $ values and dof of the measured normalized double-differential $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ cross sections with respect to the various MC predictions. |
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Table 2:
The $ {\chi ^2} $ values and dof of the double-differential normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ cross sections with respect to NLO $\mathcal{O}(\alpha _s^3)$ theoretical calculations [18] using different PDF sets. The $ {\chi ^2} $ values that include PDF uncertainties are shown in parentheses. |
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Table 3:
The $ {\chi ^2} $ values and dof of the double-differential normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ cross sections with respect to approximate NNLO $\mathcal{O}(\alpha _s^4)$ theoretical calculations [19,4,69,70] using different PDF sets. |
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Table 4:
The global and partial $ {\chi ^2} $/dof values for all variants of the PDF fit. The variant of the fit that uses the DIS and $ {\mathrm{ W } ^\pm } $ boson charge asymmetry data only is denoted as `Nominal fit'. Each double-differential $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ cross section is added ($+$) to the nominal data, one at a time. For the HERA measurements, the energy of the proton beam, $E_{\mathrm{ p } }$, is listed for each data set, with the electron energy being $E_{\mathrm{ e } }=27.5 GeV $, CC and NC stand for charged and neutral current, respectively. The correlated $ {\chi ^2} $ and the log-penalty $\chi ^2$ entries refer to the $ {\chi ^2} $ contributions from the nuisance parameters and from the logarithmic term, respectively, as described in the text. |
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Table 5:
The measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections in different bins of $ {y(\mathrm{ t } )} $ and $ { {p_{\mathrm {T}}} (\mathrm{ t } )} $ , along with their relative statistical and systematic uncertainties. |
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Table 6:
The correlation matrix of statistical uncertainties for the normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections as a function of $ {y(\mathrm{ t } )} $ and $ { {p_{\mathrm {T}}} (\mathrm{ t } )} $ . The values are expressed as percentages. For bin indices see Table 5. |
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Table 7:
Sources and values of the relative systematic uncertainties in percent of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections as a function of $ {y(\mathrm{ t } )} $ and $ { {p_{\mathrm {T}}} (\mathrm{ t } )} $ . For bin indices see Table 5. |
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Table 8:
The measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections in different bins of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ {y(\mathrm{ t } )} $ , along with their relative statistical and systematic uncertainties. |
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Table 9:
The correlation matrix of statistical uncertainties for the normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections as a function of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ {y(\mathrm{ t } )} $ . The values are expressed as percentages. For bin indices see Table 8. |
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Table 10:
Sources and values of the relative systematic uncertainties in percent of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections as a function of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ {y(\mathrm{ t } )} $ . For bin indices see Table 8. |
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Table 11:
The measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections in different bins of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ {y({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ , along with their relative statistical and systematic uncertainties. |
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Table 12:
The correlation matrix of statistical uncertainties for the normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections as a function of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ {y({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ . The values are expressed as percentages. For bin indices see Table 11. |
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Table 13:
Sources and values of the relative systematic uncertainties in percent of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections as a function of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ {y({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ . For bin indices see Table 11. |
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Table 14:
The measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections in different bins of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ {\Delta \eta (\mathrm{ t } ,\mathrm{ \bar{t} } )} $ , along with their relative statistical and systematic uncertainties. |
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Table 15:
The correlation matrix of statistical uncertainties for the normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections as a function of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ {\Delta \eta (\mathrm{ t } ,\mathrm{ \bar{t} } )} $ . The values are expressed as percentages. For bin indices see Table 14. |
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Table 16:
Sources and values of the relative systematic uncertainties in percent of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections as a function of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ {\Delta \eta (\mathrm{ t } ,\mathrm{ \bar{t} } )} $ . For bin indices see Table 14. |
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Table 17:
The measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections in different bins of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ { {p_{\mathrm {T}}} ({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ , along with their relative statistical and systematic uncertainties. |
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Table 18:
The correlation matrix of statistical uncertainties for the normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections as a function of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ { {p_{\mathrm {T}}} ({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ . The values are expressed as percentages. For bin indices see Table 17. |
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Table 19:
Sources and values of the relative systematic uncertainties in percent of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections as a function of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ { {p_{\mathrm {T}}} ({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ . For bin indices see Table 17. |
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Table 20:
The measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections in different bins of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ {\Delta \phi (\mathrm{ t } ,\mathrm{ \bar{t} } )} $ , along with their relative statistical and systematic uncertainties. |
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Table 21:
The correlation matrix of statistical uncertainties for the normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections as a function of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ {\Delta \phi (\mathrm{ t } ,\mathrm{ \bar{t} } )} $ . The values are expressed as percentages. For bin indices see Table 20. |
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Table 22:
Sources and values of the relative systematic uncertainties in percent of the measured normalized $ {\mathrm{ t } {}\mathrm{ \bar{t} } } $ double-differential cross sections as a function of $ {M({\mathrm{ t } {}\mathrm{ \bar{t} } } )} $ and $ {\Delta \phi (\mathrm{ t } ,\mathrm{ \bar{t} } )} $ . For bin indices see Table 20. |
| Summary |
|
A measurement of normalized double-differential $ \mathrm{ t \bar{t} } $ production cross sections in pp collisions at $ \sqrt{s} = $ 8 TeV has been presented. The measurement is performed in the $\mathrm{ e }^{\pm}\mu^{\mp}$ final state, using data collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 19.7 fb$^{-1}$. The normalized $ \mathrm{ t \bar{t} } $ cross section is measured in the full phase space as a function of different pairs of kinematic variables describing the top quark or $ \mathrm{ t \bar{t} } $ system. None of the tested MC models is able to correctly describe all the double-differential distributions. The data exhibit a softer transverse momentum $p_{\mathrm{T}}({\mathrm{t}})$ distribution, compared to the Monte Carlo predictions, as was reported in previous single-differential $ \mathrm{ t \bar{t} } $ cross section measurements. The double-differential studies reveal a broader distribution of rapidity $y({\mathrm{t}})$ at high $ \mathrm{ t \bar{t} } $ invariant mass $ M(\mathrm{ t \bar{t} }) $ and a larger pseudorapidity separation $ \Delta \eta (\mathrm{ t \bar{t} }) $ at moderate $ M(\mathrm{ t \bar{t} }) $ in data compared to simulation. The data are in reasonable agreement with next-to-leading-order predictions of quantum chromodynamics using recent sets of parton distribution functions (PDFs). The measured double-differential cross sections have been incorporated into a PDF fit, together with other data from HERA and the LHC. Including the $ \mathrm{ t \bar{t} } $ data, one observes a significant reduction in the uncertainties in the gluon distribution at large values of parton momentum fraction $x$, in particular when using the double-differential $ \mathrm{ t \bar{t} } $ cross section as a function of $ y (\mathrm{ t \bar{t} }) $ and $ M(\mathrm{ t \bar{t} }) $. The constraints provided by these data are competitive with those from inclusive jet data. This improvement exceeds that from using single-differential $ \mathrm{ t \bar{t} } $ cross section data, thus strongly suggesting the use of the double-differential $ \mathrm{ t \bar{t} } $ measurements in PDF fits. |
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