CMS-PAS-TOP-14-013 | ||

Measurement of double differential cross sections for top quark pair production in pp collisions at $\sqrt{s} =$ 8 TeV | ||

CMS Collaboration | ||

July 2016 | ||

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Abstract:
Normalized double differential cross sections for top quark pair ($\rm{t\bar{t}}$) 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 using the dilepton ${\rm e}^{\pm}\mu^{\mp}$ decay mode of the $\rm{t\bar{t}}$ system. The $\rm{t\bar{t}}$ cross section is measured as a function of various combinations of two observables characterizing the kinematics of the top quark and the $\rm{t\bar{t}}$ system. The data are compared to calculations in perturbative QCD at next-to-leading order and approximate next-to-next-to-leading order, and to predictions of Monte Carlo event generators that complement fixed-order computations with parton showers, hadronization, and multiple-parton interactions. Overall, a reasonable agreement is observed which is improved when the latest global sets of proton parton distribution functions are used in the predictions. The impact of the measured cross sections constraining the gluon distribution in the proton is demonstrated in a fit of parametrized parton distribution functions to the data.
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Links:
CDS record (PDF) ;
inSPIRE record ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, EPJC 77 (2017) 459.The superseded preliminary plots can be found here. |

Figures | |

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Figure 1:
Distributions of $p_{T}(\rm t)$ (a), $|y(\rm t)|$ (b), $p_{T}({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ (c), $|y({\mathrm{ t } {}\mathrm{ \bar{t} } } )|$ (d) and $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ (e) in events after the kinematic reconstruction. The experimental data with the vertical bars corresponding to the data statistical uncertainties are plotted together with distributions of simulated signal and different background processes. 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 $p_{T}(\rm t)$ (a), $|y(\rm t)|$ (b), $p_{T}({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ (c), $|y({\mathrm{ t } {}\mathrm{ \bar{t} } } )|$ (d) and $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ (e) in events after the kinematic reconstruction. The experimental data with the vertical bars corresponding to the data statistical uncertainties are plotted together with distributions of simulated signal and different background processes. 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-b:
Distributions of $p_{T}(\rm t)$ (a), $|y(\rm t)|$ (b), $p_{T}({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ (c), $|y({\mathrm{ t } {}\mathrm{ \bar{t} } } )|$ (d) and $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ (e) in events after the kinematic reconstruction. The experimental data with the vertical bars corresponding to the data statistical uncertainties are plotted together with distributions of simulated signal and different background processes. 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-c:
Distributions of $p_{T}(\rm t)$ (a), $|y(\rm t)|$ (b), $p_{T}({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ (c), $|y({\mathrm{ t } {}\mathrm{ \bar{t} } } )|$ (d) and $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ (e) in events after the kinematic reconstruction. The experimental data with the vertical bars corresponding to the data statistical uncertainties are plotted together with distributions of simulated signal and different background processes. 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-d:
Distributions of $p_{T}(\rm t)$ (a), $|y(\rm t)|$ (b), $p_{T}({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ (c), $|y({\mathrm{ t } {}\mathrm{ \bar{t} } } )|$ (d) and $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ (e) in events after the kinematic reconstruction. The experimental data with the vertical bars corresponding to the data statistical uncertainties are plotted together with distributions of simulated signal and different background processes. 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-e:
Distributions of $p_{T}(\rm t)$ (a), $|y(\rm t)|$ (b), $p_{T}({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ (c), $|y({\mathrm{ t } {}\mathrm{ \bar{t} } } )|$ (d) and $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ (e) in events after the kinematic reconstruction. The experimental data with the vertical bars corresponding to the data statistical uncertainties are plotted together with distributions of simulated signal and different background processes. 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 2:
Comparison of the measured normalized ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections as a function of ${ {p_{\mathrm {T}}} ({\rm t})}$ in different ${y({\rm t})}$ 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 to the MadGraph+Pythia6 (MG+P) predictions are shown. |

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Figure 3:
Comparison of the measured normalized ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections as a function of ${y({\rm t})}$ 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 ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections 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 ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections 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 ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections 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 ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections 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 ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections as a function of ${ {p_{\mathrm {T}}} ({\rm t})}$ in different ${y({\rm t})}$ ranges to NLO $O(\alpha _s^3)$ and approximate NNLO $O(\alpha _s^4)$ predictions calculated with CT14 and HERAPDF2.0. 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 on the CT14 theoretical predictions represents the scale uncertainties of the NLO predictions and the dark band shows the scale and PDF uncertainties added in quadrature. The dotted line shows NLO predictions calculated with HERAPDF2.0 . The dashed line shows approximate NNLO predictions calculated with CT14 . In the bottom panel the ratios to the CT14 predictions are shown. |

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Figure 9:
Comparison of the measured normalized ${\mathrm{ t } {}\mathrm{ \bar{t} } } $ differential cross sections as a function of ${y({\rm t})}$ in different $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ ranges to NLO $O(\alpha _s^3)$ predictions. Details can be found in the caption of Fig. 8. Approximate NNLO $O(\alpha _s^4)$ predictions are not available for this distribution. |

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Figure 10:
Comparison of the measured normalized ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections as a function of ${y({\mathrm{ t } {}\mathrm{ \bar{t} } } )}$ in different $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ ranges to NLO $O(\alpha _s^3)$ predictions. Details can be found in the caption of Fig. 8. Approximate NNLO $O(\alpha _s^4)$ predictions are not available for this distribution. |

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Figure 11:
Comparison of the measured normalized ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections as a function of ${\Delta \eta (\mathrm{t}, \mathrm{\bar{t}})}$ in different $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ ranges to NLO $O(\alpha _s^3)$ predictions. Details can be found in the caption of Fig. 8. Approximate NNLO $O(\alpha _s^4)$ predictions are not available for this distribution. |

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Figure 12:
Comparison of the measured normalized ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections as a function of ${ {p_{\mathrm {T}}} ({\mathrm{ t } {}\mathrm{ \bar{t} } } )}$ in different $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ ranges to NLO $O(\alpha _s^3)$ predictions. Details can be found in the caption of Fig. 8. Approximate NNLO $O(\alpha _s^4)$ predictions are not available for this distribution. |

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Figure 13:
Comparison of the measured normalized ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections as a function of ${\Delta \phi (\mathrm{t}, \mathrm{\bar{t}})}$ in different $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ ranges to NLO $O(\alpha _s^3)$ predictions. Details can be found in the caption of Fig. 8. Approximate NNLO $O(\alpha _s^4)$ predictions are not available for this distribution. |

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Figure 13-a:
Comparison of the measured normalized ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections as a function of ${\Delta \phi (\mathrm{t}, \mathrm{\bar{t}})}$ in different $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ ranges to NLO $O(\alpha _s^3)$ predictions. Details can be found in the caption of Fig. 8. Approximate NNLO $O(\alpha _s^4)$ predictions are not available for this distribution. |

png pdf |
Figure 13-b:
Comparison of the measured normalized ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections as a function of ${\Delta \phi (\mathrm{t}, \mathrm{\bar{t}})}$ in different $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ ranges to NLO $O(\alpha _s^3)$ predictions. Details can be found in the caption of Fig. 8. Approximate NNLO $O(\alpha _s^4)$ predictions are not available for this distribution. |

png pdf |
Figure 13-c:
Comparison of the measured normalized ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections as a function of ${\Delta \phi (\mathrm{t}, \mathrm{\bar{t}})}$ in different $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ ranges to NLO $O(\alpha _s^3)$ predictions. Details can be found in the caption of Fig. 8. Approximate NNLO $O(\alpha _s^4)$ predictions are not available for this distribution. |

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Figure 13-d:
Comparison of the measured normalized ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ differential cross sections as a function of ${\Delta \phi (\mathrm{t}, \mathrm{\bar{t}})}$ in different $M({\mathrm{ t } {}\mathrm{ \bar{t} } } )$ ranges to NLO $O(\alpha _s^3)$ predictions. Details can be found in the caption of Fig. 8. Approximate NNLO $O(\alpha _s^4)$ predictions are not available for this distribution. |

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Figure 14-a:
The gluon (a), sea quark (b), u valence (c) and d valence quark (d) distributions at $\mu _f^2=$ 30 000 GeV$^2$, as obtained in all variants of the PDF fit, normalized to the results from the fit using the DIS and ${\rm W}^{\pm }$ boson charge asymmetry data only. The total uncertainty of each distribution is shown by a shaded (or hatched) band. 18p stands for the 18-parameter fit as described in the text. |

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Figure 14-b:
The gluon (a), sea quark (b), u valence (c) and d valence quark (d) distributions at $\mu _f^2=$ 30 000 GeV$^2$, as obtained in all variants of the PDF fit, normalized to the results from the fit using the DIS and ${\rm W}^{\pm }$ boson charge asymmetry data only. The total uncertainty of each distribution is shown by a shaded (or hatched) band. 18p stands for the 18-parameter fit as described in the text. |

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Figure 14-c:
The gluon (a), sea quark (b), u valence (c) and d valence quark (d) distributions at $\mu _f^2=$ 30 000 GeV$^2$, as obtained in all variants of the PDF fit, normalized to the results from the fit using the DIS and ${\rm W}^{\pm }$ boson charge asymmetry data only. The total uncertainty of each distribution is shown by a shaded (or hatched) band. 18p stands for the 18-parameter fit as described in the text. |

png pdf |
Figure 14-d:
The gluon (a), sea quark (b), u valence (c) and d valence quark (d) distributions at $\mu _f^2=$ 30 000 GeV$^2$, as obtained in all variants of the PDF fit, normalized to the results from the fit using the DIS and ${\rm W}^{\pm }$ boson charge asymmetry data only. The total uncertainty of each distribution is shown by a shaded (or hatched) band. 18p stands for the 18-parameter fit as described in the text. |

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Figure 15-a:
Fractional total uncertainties of the gluon (a), sea quark (b), u valence (c) and d valence quark (d) distributions at $\mu _f^2=$ 30 000 GeV$^2$, shown by shaded (or hatched) bands, as obtained in all variants of the PDF fit. 18p stands for the 18-parameter fit as described in the text. |

png pdf |
Figure 15-b:
Fractional total uncertainties of the gluon (a), sea quark (b), u valence (c) and d valence quark (d) distributions at $\mu _f^2=$ 30 000 GeV$^2$, shown by shaded (or hatched) bands, as obtained in all variants of the PDF fit. 18p stands for the 18-parameter fit as described in the text. |

png pdf |
Figure 15-c:
Fractional total uncertainties of the gluon (a), sea quark (b), u valence (c) and d valence quark (d) distributions at $\mu _f^2=$ 30 000 GeV$^2$, shown by shaded (or hatched) bands, as obtained in all variants of the PDF fit. 18p stands for the 18-parameter fit as described in the text. |

png pdf |
Figure 15-d:
Fractional total uncertainties of the gluon (a), sea quark (b), u valence (c) and d valence quark (d) distributions at $\mu _f^2=$ 30 000 GeV$^2$, shown by shaded (or hatched) bands, as obtained in all variants of the PDF fit. 18p stands for the 18-parameter fit as described in the text. |

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Figure 16-a:
Same as in Fig. 15 for the variants of the PDF fit using the single differential ${\mathrm {t}\overline {\mathrm {t}}}$ cross sections. |

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Figure 16-b:
Same as in Fig. 15 for the variants of the PDF fit using the single differential ${\mathrm {t}\overline {\mathrm {t}}}$ cross sections. |

png pdf |
Figure 16-c:
Same as in Fig. 15 for the variants of the PDF fit using the single differential ${\mathrm {t}\overline {\mathrm {t}}}$ cross sections. |

png pdf |
Figure 16-d:
Same as in Fig. 15 for the variants of the PDF fit using the single differential ${\mathrm {t}\overline {\mathrm {t}}}$ cross sections. |

png pdf |
Figure 17:
Fractional total uncertainties of the gluon distribution at $\mu _f^2=$ 30 000 GeV$^2$, shown by shaded (or hatched) bands, as obtained in the PDF fit using the DIS and ${\rm W}^{\pm }$ boson charge asymmetry data only, as well as single and double differential ${\mathrm {t}\overline {\mathrm {t}}}$ cross sections. 18p stands for the 18-parameter fit as described in the text. |

Tables | |

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Table 1:
The ${\chi ^2}$ values of double differential normalized ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ cross sections with respect to MC calculations. |

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Table 2:
The ${\chi ^2}$ values of double differential normalized ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ cross sections with respect to NLO $O(\alpha _s^3)$ theoretical calculations [17] using different PDF sets. The ${\chi ^2}$ values that include PDF uncertainties are shown in parenthesis. |

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Table 3:
The ${\chi ^2}$ values of double differential normalized ${\mathrm{ t } {}\mathrm{ \bar{t} } }$ cross sections with respect to approximate NNLO $O(\alpha _s^4)$ theoretical calculations [4,18,65,66] using different PDF sets. |

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Table 4:
The global and partial ${\chi ^2}$/dof values for the data sets in all variants of the PDF fit. The variant of the fit which uses the DIS and ${\rm W}^{\pm }$ boson charge asymmetry data only is denoted as `Nominal', Every double differential ${\mathrm {t}\overline {\mathrm {t}}}$ distribution is added ($+$) to the nominal data, one at a time. For HERA measurements, the energy of the proton beam, $E_{ {\mathrm {p}}}$, is listed for each data set, with electron energy being $E_{ {\mathrm {e}}}=$ 27.5 GeV. The `Correlated ${\chi ^2} $' and `Log penalty $\chi ^2$' entries refer to the ${\chi ^2}$ contributions from the nuisance parameters and from the logarithmic term, respectively, described in the text. |

Summary |

The first measurement of normalized double differential $\mathrm{ t \bar{t} }$ production cross sections in pp collisions at $ \sqrt{s} = $ 8 TeV is presented. The measurement is performed for the ${\rm e}\mu$ final state, using 19.7 fb$^{-1}$ of collision data collected by the CMS detector. The normalized $\mathrm{ t \bar{t} }$ cross section is measured in the full phase space as a function of six different combinations of variables, which describe the top quark or $\mathrm{ t \bar{t} }$ kinematics. The observed trends support the findings reported in the previous single differential $\mathrm{ t \bar{t} }$ measurement, in particular the tendency of a softer distribution of $p_{\mathrm{T}}(\mathrm{t})$ in data compared to the MC predictions. The presented double differential studies reveal a broader distribution of $y(\mathrm{t})$ at high $M(\mathrm{ t \bar{t} })$ in data than in MC and a larger pseudorapidity separation $\Delta \eta (\mathrm{t}, \mathrm{\bar{t}})$ at moderate $M(\mathrm{ t \bar{t} })$ in data compared to MC. The data are in agreement with NLO QCD predictions based on modern PDF sets. The measured double differential cross sections have been incorporated into a PDF fit together with other data from HERA and LHC. A significant impact on the gluon distributions at large values of $x$ is observed, in particular when the distribution of $y({\mathrm{t \bar{t}}})$ in the $M(\mathrm{ t \bar{t} })$ ranges is used. It exceeds the impact of single differential normalized $\mathrm{ t \bar{t} }$ cross sections, thus strongly suggests the use of these measurements in future PDF fits. |

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Compact Muon Solenoid LHC, CERN |