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| CMS-TOP-18-004 ; CERN-EP-2019-028 | ||
| Measurement of $\mathrm{t\bar{t}}$ normalised multi-differential cross sections in pp collisions at $\sqrt{s} = $ 13 TeV, and simultaneous determination of the strong coupling strength, top quark pole mass, and parton distribution functions | ||
| CMS Collaboration | ||
| 10 April 2019 | ||
| Eur. Phys. J. C 80 (2020) 658 | ||
| Abstract: Normalised multi-differential cross sections for top quark pair ($\mathrm{t\bar{t}}$) production are measured in proton-proton collisions at a centre-of-mass energy of 13 TeV using events containing two oppositely charged leptons. The analysed data were recorded with the CMS detector in 2016 and correspond to an integrated luminosity of 35.9 fb$^{-1}$. The double-differential $\mathrm{t\bar{t}}$ cross section is measured as a function of the kinematic properties of the top quark and of the $\mathrm{t\bar{t}}$ system at parton level in the full phase space. A triple-differential measurement is performed as a function of the invariant mass and rapidity of the $\mathrm{t\bar{t}}$ system and the multiplicity of additional jets at particle level. The data are compared to predictions of Monte Carlo event generators that complement next-to-leading-order (NLO) quantum chromodynamics (QCD) calculations with parton showers. Together with a fixed-order NLO QCD calculation, the triple-differential measurement is used to extract values of the strong coupling strength ${\alpha_S}$ and the top quark pole mass ($m_{\mathrm{t}}^{\text{pole}}$) using several sets of parton distribution functions (PDFs). Furthermore, a simultaneous fit of the PDFs, ${\alpha_S}$, and $m_{\mathrm{t}}^{\text{pole}}$ is performed at NLO, demonstrating that the new data have significant impact on the gluon PDF, and at the same time allow an accurate determination of ${\alpha_S}$ and $m_{\mathrm{t}}^{\text{pole}}$. | ||
| Links: e-print arXiv:1904.05237 [hep-ex] (PDF) ; CDS record ; inSPIRE 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}\overline {\mathrm {t}}}})$ (middle left), $y({{\mathrm {t}\overline {\mathrm {t}}}})$ (middle right), ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$ (lower left), and ${N_{\text {jet}}}$ (lower right) in selected events after the kinematic reconstruction, at detector level. 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 estimated shape uncertainties in the signal and backgrounds (as detailed in 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:
Distribution of $ {p_{\mathrm {T}}} ({\mathrm {t}})$ in selected events after the kinematic reconstruction, at detector level. 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 estimated shape uncertainties in the signal and backgrounds (as detailed in 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:
Distribution of $y({\mathrm {t}})$ in selected events after the kinematic reconstruction, at detector level. 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 estimated shape uncertainties in the signal and backgrounds (as detailed in 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:
Distribution of $ {p_{\mathrm {T}}} ({{\mathrm {t}\overline {\mathrm {t}}}})$ in selected events after the kinematic reconstruction, at detector level. 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 estimated shape uncertainties in the signal and backgrounds (as detailed in 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:
Distribution of $y({{\mathrm {t}\overline {\mathrm {t}}}})$ in selected events after the kinematic reconstruction, at detector level. 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 estimated shape uncertainties in the signal and backgrounds (as detailed in 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:
Distribution of ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$ in selected events after the kinematic reconstruction, at detector level. 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 estimated shape uncertainties in the signal and backgrounds (as detailed in 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-f:
Distribution of ${N_{\text {jet}}}$ in selected events after the kinematic reconstruction, at detector level. 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 estimated shape uncertainties in the signal and backgrounds (as detailed in 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:
Distributions of $y({{\mathrm {t}\overline {\mathrm {t}}}})$ (left) and ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$ (right) in selected events after the loose kinematic reconstruction. Details can be found in the caption of Fig. 1. |
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Figure 2-a:
Distribution of $y({{\mathrm {t}\overline {\mathrm {t}}}})$ in selected events after the loose kinematic reconstruction. Details can be found in the caption of Fig. 1. |
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Figure 2-b:
Distribution of ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$ in selected events after the loose kinematic reconstruction. Details can be found in the caption of Fig. 1. |
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Figure 3:
Comparison of the measured [ ${y({\mathrm {t}})}$, ${{p_{\mathrm {T}}} ({\mathrm {t}})}$ ] cross sections {to the theoretical predictions calculated using POWHEG + PYTHIA (`POW+PYT'), POWHEG + HERWIG++ (`POW+HER'), and MG5\_aMC@NLO + PYTHIA (`MG5+PYT') event generators.} The inner vertical bars on the data points represent the statistical uncertainties and the full bars include also the systematic uncertainties added in quadrature. For each MC model, values of ${\chi ^2}$ which take into account the bin-to-bin correlations and dof for the comparison with the data are reported. The hatched regions correspond to the theoretical uncertainties in POWHEG + PYTHIA (see Section 7). In the lower panel, the ratios of the data and other simulations to the `POW+PYT' predictions are shown. |
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Figure 4:
Comparison of the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({\mathrm {t}})}$ ] cross sections {to the theoretical predictions calculated using MC event generators} (further details can be found in the Fig. 3 caption). |
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Figure 5:
Comparison of the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections {to the theoretical predictions calculated using MC event generators} (further details can be found in the Fig. 3 caption). |
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Figure 6:
Comparison of the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${\Delta \eta ({\mathrm {t}}, {\overline {\mathrm {t}}})}$ ] cross sections {to the theoretical predictions calculated using MC event generators} (further details can be found in the Fig. 3 caption). |
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Figure 7:
Comparison of the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${\Delta \phi ({\mathrm {t}}, {\overline {\mathrm {t}}})}$ ] cross sections {to the theoretical predictions calculated using MC event generators} (further details can be found in the Fig. 3 caption). |
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Figure 8:
Comparison of the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${{p_{\mathrm {T}}} ({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections {to the theoretical predictions calculated using MC event generators} (further details can be found in the Fig. 3 caption). |
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Figure 9:
Comparison of the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${{p_{\mathrm {T}}} ({\mathrm {t}})}$ ] cross sections {to the theoretical predictions calculated using MC event generators} (further details can be found in the Fig. 3 caption). |
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Figure 10:
Comparison of the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections {to the theoretical predictions calculated using MC event generators} (further details can be found in the Fig. 3 caption). |
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Figure 11:
Comparison of the measured [ ${N^{0,1,2+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections {to the theoretical predictions calculated using MC event generators} (further details can be found in the Fig. 3 caption). |
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Figure 12:
Assessment of compatibility of various MC predictions with the data. The plot show the $p$-values of ${\chi ^2}$-tests between data and predictions. Only the data uncertainties are taken into account in the ${\chi ^2}$-tests while uncertainties on the theoretical calculations are ignored. Points with $p \le $ 0.001 are shown at $p = $ 0.001. |
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Figure 13:
The theoretical uncertainties for [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] (upper) and [ ${N^{0,1,2+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] (lower) cross sections, arising from PDF, ${{\alpha _S} (m_{{\mathrm {Z}}})}$, and ${m_{{\mathrm {t}}}^{\text {pole}}}$ variations, as well as the total theoretical uncertainties, with their bin-averaged values shown in brackets. The bins are the same as in Figs. 10 and 11. |
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Figure 13-a:
The theoretical uncertainties for [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections, arising from PDF, ${{\alpha _S} (m_{{\mathrm {Z}}})}$, and ${m_{{\mathrm {t}}}^{\text {pole}}}$ variations, as well as the total theoretical uncertainties, with their bin-averaged values shown in brackets. The bins are the same as in Figs. 10 and 11. |
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Figure 13-b:
The theoretical uncertainties for [ ${N^{0,1,2+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections, arising from PDF, ${{\alpha _S} (m_{{\mathrm {Z}}})}$, and ${m_{{\mathrm {t}}}^{\text {pole}}}$ variations, as well as the total theoretical uncertainties, with their bin-averaged values shown in brackets. The bins are the same as in Figs. 10 and 11. |
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Figure 14:
Comparison of the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections to NLO predictions obtained using different PDF sets (further details can be found in Fig. 3). For each theoretical prediction, values of ${\chi ^2}$ and dof for the comparison to the data are reported, while additional ${\chi ^2}$ values that include PDF uncertainties are shown in parentheses. |
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Figure 15:
Comparison of the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections to NLO predictions obtained using different $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ values (further details can be found in Fig. 3). For each theoretical prediction, values of ${\chi ^2}$ and dof for the comparison to the data are reported. |
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Figure 16:
Comparison of the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections to NLO predictions obtained using different ${m_{{\mathrm {t}}}^{\text {pole}}}$ values (further details can be found in Fig. 3). For each theoretical prediction, values of ${\chi ^2}$ and dof for the comparison to the data are reported. |
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Figure 17:
The $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ (left) and ${m_{{\mathrm {t}}}^{\text {pole}}}$ (right) extraction at NLO from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using different PDF sets. The extracted $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ and ${m_{{\mathrm {t}}}^{\text {pole}}}$ values are reported for each PDF set, and the estimated minimum ${\chi ^2}$ value is shown in brackets. Further details are given in the text. |
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Figure 17-a:
The $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ extraction at NLO from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using different PDF sets. The extracted $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ and ${m_{{\mathrm {t}}}^{\text {pole}}}$ values are reported for each PDF set, and the estimated minimum ${\chi ^2}$ value is shown in brackets. Further details are given in the text. |
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Figure 17-b:
The ${m_{{\mathrm {t}}}^{\text {pole}}}$ extraction at NLO from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using different PDF sets. The extracted $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ and ${m_{{\mathrm {t}}}^{\text {pole}}}$ values are reported for each PDF set, and the estimated minimum ${\chi ^2}$ value is shown in brackets. Further details are given in the text. |
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Figure 18:
The ${{\alpha _S} (m_{{\mathrm {Z}}})}$ (left) and $ {m_{{\mathrm {t}}}^{\text {pole}}} $ (right) values extracted at NLO using different PDFs. The contributions to the total uncertainty arising from the data, PDF, scale, and $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ uncertainties are shown separately. The world average values $ {{\alpha _S} (m_{{\mathrm {Z}}})} = $ 0.1181 $\pm$ 0.0011 and $ {m_{{\mathrm {t}}}^{\text {pole}}} = $ 173.1 $\pm$ 0.9 GeV from Ref. [94] are shown for reference. |
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Figure 18-a:
The ${{\alpha _S} (m_{{\mathrm {Z}}})}$ values extracted at NLO using different PDFs. The contributions to the total uncertainty arising from the data, PDF, scale, and $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ uncertainties are shown separately. The world average value $ {{\alpha _S} (m_{{\mathrm {Z}}})} = $ 0.1181 $\pm$ 0.0011 from Ref. [94] is shown for reference. |
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Figure 18-b:
The $ {m_{{\mathrm {t}}}^{\text {pole}}} $ values extracted at NLO using different PDFs. The contributions to the total uncertainty arising from the data, PDF, scale, and $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ uncertainties are shown separately. The world average value $ {m_{{\mathrm {t}}}^{\text {pole}}} = $ 173.1 $\pm$ 0.9 GeV from Ref. [94] is shown for reference. |
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Figure 19:
Comparison of the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections to the NLO predictions using the parameter values from the simultaneous PDF, ${\alpha _S}$, and ${m_{{\mathrm {t}}}^{\text {pole}}}$ fit (further details can be found in Fig. 3). Values of ${\chi ^2}$ and dof are reported. |
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Figure 20:
Comparison of the measured [ ${y({\mathrm {t}})}$, ${{p_{\mathrm {T}}} ({\mathrm {t}})}$ ] cross sections to the NLO predictions using the parameter values from the simultaneous PDF, ${\alpha _S}$ and ${m_{{\mathrm {t}}}^{\text {pole}}}$ fit of the [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections, as well as the predictions obtained using the NNPDF3.1 and ABMP16 PDF sets with different values of ${m_{{\mathrm {t}}}^{\text {pole}}}$ (see Fig. 3 for further details). In the lower panel, the ratios of the data and theoretical predictions to the predictions from the fit are shown. For each theoretical prediction, values of ${\chi ^2}$ and dof for the comparison to the data are reported. |
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Figure 21:
$\Delta \chi ^2 = \chi ^2 - \chi ^2_{\text {min}}$ as a function of ${{\alpha _S} (m_{{\mathrm {Z}}})}$ in the QCD analysis using the HERA DIS data only, or HERA and ${{\mathrm {t}\overline {\mathrm {t}}}}$ data. |
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Figure 22:
The PDFs with their total uncertainties in the fit using the HERA DIS data only, and the HERA DIS and ${{\mathrm {t}\overline {\mathrm {t}}}}$ data. The results are normalised to the PDFs obtained using the HERA DIS data only. |
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Figure 22-a:
The $xu_{\text{V}}(x)$ PDF with total uncertainties in the fit using the HERA DIS data only, and the HERA DIS and ${{\mathrm {t}\overline {\mathrm {t}}}}$ data. The results are normalised to the PDFs obtained using the HERA DIS data only. |
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Figure 22-b:
The $xd_{\text{V}}(x)$ PDF with total uncertainties in the fit using the HERA DIS data only, and the HERA DIS and ${{\mathrm {t}\overline {\mathrm {t}}}}$ data. The results are normalised to the PDFs obtained using the HERA DIS data only. |
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Figure 22-c:
The $xg(x)$ PDF with total uncertainties in the fit using the HERA DIS data only, and the HERA DIS and ${{\mathrm {t}\overline {\mathrm {t}}}}$ data. The results are normalised to the PDFs obtained using the HERA DIS data only. |
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Figure 22-d:
The $x\Sigma(x)$ PDF with total uncertainties in the fit using the HERA DIS data only, and the HERA DIS and ${{\mathrm {t}\overline {\mathrm {t}}}}$ data. The results are normalised to the PDFs obtained using the HERA DIS data only. |
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Figure 23:
The relative total PDF uncertainties in the fit using the HERA DIS data only, and the HERA DIS and ${{\mathrm {t}\overline {\mathrm {t}}}}$ data. |
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Figure 23-a:
The relative total $x\Sigma(x)$ PDF uncertainties in the fit using the HERA DIS data only, and the HERA DIS and ${{\mathrm {t}\overline {\mathrm {t}}}}$ data. |
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Figure 23-b:
The relative total PDF uncertainties in the fit using the HERA DIS data only, and the HERA DIS and ${{\mathrm {t}\overline {\mathrm {t}}}}$ data. |
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Figure 23-c:
The relative total PDF uncertainties in the fit using the HERA DIS data only, and the HERA DIS and ${{\mathrm {t}\overline {\mathrm {t}}}}$ data. |
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Figure 23-d:
The relative total PDF uncertainties in the fit using the HERA DIS data only, and the HERA DIS and ${{\mathrm {t}\overline {\mathrm {t}}}}$ data. |
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Figure 24:
{The extracted values and their correlations for ${\alpha _S}$ and ${m_{{\mathrm {t}}}^{\text {pole}}}$ (upper left), ${\alpha _S}$ 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 GeV$ ^2$ for several values of $x$. For the extracted ${\alpha _S}$ and ${m_{{\mathrm {t}}}^{\text {pole}}}$ values, also shown are the additional uncertainties arising from the dependence on scale variations (see Eq. (8) and Table 2). The correlation coefficients $\rho $ are also displayed. Furthermore, values of ${\alpha _S}({m_{{\mathrm {t}}}^{\text {pole}}}$, gluon PDF) extracted using fixed values of ${m_{{\mathrm {t}}}^{\text {pole}}} ({\alpha _S})$ are displayed as dashed, dotted, or dash-dotted lines. The world average values $ {{\alpha _S} (m_{{\mathrm {Z}}})} = $ 0.1181 $\pm$ 0.0011 and $ {m_{{\mathrm {t}}}^{\text {pole}}} = $ 173.1 $\pm$ 0.9 GeV from Ref. [94] are shown for reference.} |
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Figure B1:
The $\alpha _s$ extraction from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using varied scale and ${m_{{\mathrm {t}}}^{\text {pole}}}$ settings, and CT14 (upper), HERAPDF2.0 (middle), and ABMP16 (lower) PDF sets. Details can be found in the caption of Fig. 17. |
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Figure B1-a:
The $\alpha _s$ extraction from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using varied scale and ${m_{{\mathrm {t}}}^{\text {pole}}}$ settings, and the CT14 PDF set. Details can be found in the caption of Fig. 17. |
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Figure B1-b:
The $\alpha _s$ extraction from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using varied scale and ${m_{{\mathrm {t}}}^{\text {pole}}}$ settings, and the CT14 PDF set. Details can be found in the caption of Fig. 17. |
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Figure B1-c:
The $\alpha _s$ extraction from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using varied scale and ${m_{{\mathrm {t}}}^{\text {pole}}}$ settings, and the HERAPDF2.0 PDF set. Details can be found in the caption of Fig. 17. |
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Figure B1-d:
The $\alpha _s$ extraction from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using varied scale and ${m_{{\mathrm {t}}}^{\text {pole}}}$ settings, and the HERAPDF2.0 PDF set. Details can be found in the caption of Fig. 17. |
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Figure B1-e:
The $\alpha _s$ extraction from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using varied scale and ${m_{{\mathrm {t}}}^{\text {pole}}}$ settings, and the ABMP16 PDF set. Details can be found in the caption of Fig. 17. |
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Figure B1-f:
The $\alpha _s$ extraction from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using varied scale and ${m_{{\mathrm {t}}}^{\text {pole}}}$ settings, and the ABMP16 PDF set. Details can be found in the caption of Fig. 17. |
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Figure B2:
The $ {m_{{\mathrm {t}}}^{\text {pole}}} $ extraction from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using varied scale and $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ settings, and CT14 (upper), HERAPDF2.0 (middle), and ABMP16 (lower) PDF sets. Details can be found in the caption of Fig. 17. |
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Figure B2-a:
The $ {m_{{\mathrm {t}}}^{\text {pole}}} $ extraction from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using varied scale and $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ settings, and the CT14 PDF set. Details can be found in the caption of Fig. 17. |
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Figure B2-b:
The $ {m_{{\mathrm {t}}}^{\text {pole}}} $ extraction from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using varied scale and $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ settings, and the CT14 PDF set. Details can be found in the caption of Fig. 17. |
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Figure B2-c:
The $ {m_{{\mathrm {t}}}^{\text {pole}}} $ extraction from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using varied scale and $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ settings, and the HERAPDF2.0 PDF set. Details can be found in the caption of Fig. 17. |
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Figure B2-d:
The $ {m_{{\mathrm {t}}}^{\text {pole}}} $ extraction from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using varied scale and $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ settings, and the HERAPDF2.0 PDF set. Details can be found in the caption of Fig. 17. |
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Figure B2-e:
The $ {m_{{\mathrm {t}}}^{\text {pole}}} $ extraction from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using varied scale and $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ settings, and the ABMP16 PDF set. Details can be found in the caption of Fig. 17. |
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Figure B2-f:
The $ {m_{{\mathrm {t}}}^{\text {pole}}} $ extraction from the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections using varied scale and $ {{\alpha _S} (m_{{\mathrm {Z}}})} $ settings, and the ABMP16 PDF set. Details can be found in the caption of Fig. 17. |
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Figure B3:
The ${{\alpha _S} (m_{{\mathrm {Z}}})}$ (left) and ${m_{{\mathrm {t}}}^{\text {pole}}}$ (right) values extracted using different single-differential cross sections, for ${N_{\text {jet}}}$ (upper), ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$ (middle), and $ {| {y({{\mathrm {t}\overline {\mathrm {t}}}})} |}$ (lower) measurements. For central values outside the displayed ${m_{{\mathrm {t}}}^{\text {pole}}}$ range, no result is shown. Details can be found in the caption of Fig. 18. |
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Figure B3-a:
The ${{\alpha _S} (m_{{\mathrm {Z}}})}$ values extracted using different single-differential cross sections, for the ${N_{\text {jet}}}$ measurement. Details can be found in the caption of Fig. 18. |
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Figure B3-b:
The ${m_{{\mathrm {t}}}^{\text {pole}}}$ values extracted using different single-differential cross sections, for the ${N_{\text {jet}}}$ measurement. For central values outside the displayed ${m_{{\mathrm {t}}}^{\text {pole}}}$ range, no result is shown. Details can be found in the caption of Fig. 18. |
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Figure B3-c:
The ${{\alpha _S} (m_{{\mathrm {Z}}})}$ values extracted using different single-differential cross sections, for the ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$ measurement. Details can be found in the caption of Fig. 18. |
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Figure B3-d:
The ${m_{{\mathrm {t}}}^{\text {pole}}}$ values extracted using different single-differential cross sections, for the ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$ measurement. For central values outside the displayed ${m_{{\mathrm {t}}}^{\text {pole}}}$ range, no result is shown. Details can be found in the caption of Fig. 18. |
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Figure B3-e:
The ${{\alpha _S} (m_{{\mathrm {Z}}})}$ values extracted using different single-differential cross sections, for the $ {| {y({{\mathrm {t}\overline {\mathrm {t}}}})} |}$ measurement. Details can be found in the caption of Fig. 18. |
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Figure B3-f:
The ${m_{{\mathrm {t}}}^{\text {pole}}}$ values extracted using different single-differential cross sections, for the $ {| {y({{\mathrm {t}\overline {\mathrm {t}}}})} |}$ measurement. For central values outside the displayed ${m_{{\mathrm {t}}}^{\text {pole}}}$ range, no result is shown. Details can be found in the caption of Fig. 18. |
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Figure B4:
The ${{\alpha _S} (m_{{\mathrm {Z}}})}$ (left) and $ {m_{{\mathrm {t}}}^{\text {pole}}} $ (right) values extracted from the triple-differential [ ${N^{0,1,2+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections. Details can be found in the caption of Fig. 18. |
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Figure B4-a:
The ${{\alpha _S} (m_{{\mathrm {Z}}})}$ values extracted from the triple-differential [ ${N^{0,1,2+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections. Details can be found in the caption of Fig. 18. |
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Figure B4-b:
The $ {m_{{\mathrm {t}}}^{\text {pole}}} $ values extracted from the triple-differential [ ${N^{0,1,2+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections. Details can be found in the caption of Fig. 18. |
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Figure B5:
The ${{\alpha _S} (m_{{\mathrm {Z}}})}$ (left) and $ {m_{{\mathrm {t}}}^{\text {pole}}} $ (right) values extracted from the triple-differential [ ${{{p_{\mathrm {T}}} ({{\mathrm {t}\overline {\mathrm {t}}}})}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$}] cross sections. Details can be found in the caption of Fig. 18. |
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Figure B5-a:
The ${{\alpha _S} (m_{{\mathrm {Z}}})}$ values extracted from the triple-differential [ ${{{p_{\mathrm {T}}} ({{\mathrm {t}\overline {\mathrm {t}}}})}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$}] cross sections. Details can be found in the caption of Fig. 18. |
png pdf |
Figure B5-b:
The $ {m_{{\mathrm {t}}}^{\text {pole}}} $ values extracted from the triple-differential [ ${{{p_{\mathrm {T}}} ({{\mathrm {t}\overline {\mathrm {t}}}})}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$}] cross sections. Details can be found in the caption of Fig. 18. |
png pdf |
Figure C1:
Comparison of the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections obtained using different values of ${m_{{\mathrm {t}}}^{\text {MC}}}$ to NLO predictions obtained using different ${m_{{\mathrm {t}}}^{\text {pole}}}$ values (further details can be found in Fig. 3). |
| Tables | |
png pdf |
Table 1:
The ${\chi ^2}$ values (taking into account data uncertainties and ignoring theoretical uncertainties) and dof of the measured cross sections with respect {to the predictions of various MC generators.} |
png pdf |
Table 2:
The individual contributions to the uncertainties for the ${{\alpha _S} (m_{{\mathrm {Z}}})}$ and ${m_{{\mathrm {t}}}^{\text {pole}}}$ determination. |
png pdf |
Table 3:
The global and partial ${\chi ^2}$/dof values for all variants of the QCD analysis. The variant of the fit that uses the HERA DIS only is denoted as `Nominal fit'. 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 standing 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. |
png pdf |
Table A1:
The measured [ ${y({\mathrm {t}})}$, ${{p_{\mathrm {T}}} ({\mathrm {t}})}$ ] cross sections, along with their relative statistical and systematic uncertainties. |
png pdf |
Table A2:
The correlation matrix of statistical uncertainties for the measured [ ${y({\mathrm {t}})}$, ${{p_{\mathrm {T}}} ({\mathrm {t}})}$ ] cross sections. The values are expressed as percentages. For bin indices see A.1. |
png pdf |
Table A3:
Sources and values of the relative systematic uncertainties in percent of the measured [ ${y({\mathrm {t}})}$, ${{p_{\mathrm {T}}} ({\mathrm {t}})}$ ] cross sections. For bin indices see A.1. |
png pdf |
Table A4:
A.3 continued. |
png pdf |
Table A5:
A.3 continued. |
png pdf |
Table A6:
The measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({\mathrm {t}})}$ ] cross sections, along with their relative statistical and systematic uncertainties. |
png pdf |
Table A7:
The correlation matrix of statistical uncertainties for the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({\mathrm {t}})}$ ] cross sections. The values are expressed as percentages. For bin indices see A.6. |
png pdf |
Table A8:
Sources and values of the relative systematic uncertainties in percent of the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({\mathrm {t}})}$ ] cross sections. For bin indices see A.6. |
png pdf |
Table A9:
A.8 continued. |
png pdf |
Table A10:
A.8 continued. |
png pdf |
Table A11:
The measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections, along with their relative statistical and systematic uncertainties. |
png pdf |
Table A12:
The correlation matrix of statistical uncertainties for the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections. The values are expressed as percentages. For bin indices see A.11. |
png pdf |
Table A13:
Sources and values of the relative systematic uncertainties in percent of the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections. For bin indices see A.11. |
png pdf |
Table A14:
A.13 continued. |
png pdf |
Table A15:
A.13 continued. |
png pdf |
Table A16:
The measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${\Delta \eta ({\mathrm {t}}, {\overline {\mathrm {t}}})}$ ] cross sections, along with their relative statistical and systematic uncertainties. |
png pdf |
Table A17:
The correlation matrix of statistical uncertainties for the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${\Delta \eta ({\mathrm {t}}, {\overline {\mathrm {t}}})}$ ] cross sections. The values are expressed as percentages. For bin indices see A.16. |
png pdf |
Table A18:
Sources and values of the relative systematic uncertainties in percent of the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${\Delta \eta ({\mathrm {t}}, {\overline {\mathrm {t}}})}$ ] cross sections. For bin indices see A.16. |
png pdf |
Table A19:
A.18 continued. |
png pdf |
Table A20:
A.18 continued. |
png pdf |
Table A21:
The measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${\Delta \phi ({\mathrm {t}}, {\overline {\mathrm {t}}})}$ ] cross sections, along with their relative statistical and systematic uncertainties. |
png pdf |
Table A22:
The correlation matrix of statistical uncertainties for the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${\Delta \phi ({\mathrm {t}}, {\overline {\mathrm {t}}})}$ ] cross sections. The values are expressed as percentages. For bin indices see A.21. |
png pdf |
Table A23:
Sources and values of the relative systematic uncertainties in percent of the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${\Delta \phi ({\mathrm {t}}, {\overline {\mathrm {t}}})}$ ] cross sections. For bin indices see A.21. |
png pdf |
Table A24:
A.23 continued. |
png pdf |
Table A25:
A.23 continued. |
png pdf |
Table A26:
The measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${{p_{\mathrm {T}}} ({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections, along with their relative statistical and systematic uncertainties. |
png pdf |
Table A27:
The correlation matrix of statistical uncertainties for the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${{p_{\mathrm {T}}} ({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections. The values are expressed as percentages. For bin indices see A.26. |
png pdf |
Table A28:
Sources and values of the relative systematic uncertainties in percent of the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${{p_{\mathrm {T}}} ({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections. For bin indices see A.26. |
png pdf |
Table A29:
A.28 continued. |
png pdf |
Table A30:
A.28 continued. |
png pdf |
Table A31:
The measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${{p_{\mathrm {T}}} ({\mathrm {t}})}$ ] cross sections, along with their relative statistical and systematic uncertainties. |
png pdf |
Table A32:
The correlation matrix of statistical uncertainties for the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${{p_{\mathrm {T}}} ({\mathrm {t}})}$ ] cross sections. The values are expressed as percentages. For bin indices see A.31. |
png pdf |
Table A33:
Sources and values of the relative systematic uncertainties in percent of the measured [ ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${{p_{\mathrm {T}}} ({\mathrm {t}})}$ ] cross sections. For bin indices see A.31. |
png pdf |
Table A34:
A.33 continued. |
png pdf |
Table A35:
A.33 continued. |
png pdf |
Table A36:
The measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections, along with their relative statistical and systematic uncertainties, and NP corrections (see Section 9). |
png pdf |
Table A37:
The correlation matrix of statistical uncertainties for the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections. The values are expressed as percentages. For bin indices see A.36. |
png pdf |
Table A38:
Sources and values of the relative systematic uncertainties in percent of the measured [ ${N^{0,1+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections. For bin indices see A.36. |
png pdf |
Table A39:
A.38 continued. |
png pdf |
Table A40:
A.38 continued. |
png pdf |
Table A41:
The measured [ ${N^{0,1,2+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections, along with their relative statistical and systematic uncertainties, and NP corrections (see Section 9). |
png pdf |
Table A42:
The correlation matrix of statistical uncertainties for the measured [ ${N^{0,1,2+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections. The values are expressed as percentages. For bin indices see A.41. |
png pdf |
Table A43:
Sources and values of the relative systematic uncertainties in percent of the measured [ ${N^{0,1,2+}_{\text {jet}}}$, ${M({{\mathrm {t}\overline {\mathrm {t}}}})}$, ${y({{\mathrm {t}\overline {\mathrm {t}}}})}$ ] cross sections. For bin indices see A.41. |
png pdf |
Table A44:
A.43 continued. |
png pdf |
Table A45:
A.43 continued. |
png pdf |
Table A46:
A.43 continued. |
png pdf |
Table A47:
A.43 continued. |
| Summary |
|
A measurement was presented of normalised multi-differential $\mathrm{t\bar{t}}$ production cross sections in pp collisions at $\sqrt{s} = $ 13 TeV, performed using events containing two oppositely charged leptons (electron or muon). The analysed data were recorded in 2016 with the CMS detector at the LHC, and correspond to an integrated luminosity of 35.9 fb$^{-1}$. The normalised $\mathrm{t\bar{t}}$ cross section is measured in the full phase space as a function of different pairs of kinematic variables that describe either the top quark or the $\mathrm{t\bar{t}}$ system. None of the central predictions of the tested Monte Carlo models is able to correctly describe all the distributions. The data exhibit softer transverse momentum ${p_{\mathrm{T}}}(t)$ distributions than given by the theoretical predictions, as was reported in previous single-differential and double-differential $\mathrm{t\bar{t}}$ cross section measurements. The effect of the softer ${p_{\mathrm{T}}}(t)$ spectra in the data relative to the predictions is enhanced at larger values of the invariant mass of the $\mathrm{t\bar{t}}$ system. {The predicted ${p_{\mathrm{T}}}(t)$ slopes are strongly sensitive to the parton distribution functions (PDFs) and the top quark pole mass $m_{\mathrm{t}}^{\text{pole}}$ value used in the calculations, and the description of the data can be improved by changing these parameters. The measured $\mathrm{t\bar{t}}$ cross sections as a function of the invariant mass and rapidity of the $\mathrm{t\bar{t}}$ system, and the multiplicity of additional jets, have been incorporated into two specific fits of QCD parameters at next-to-leading order, after applying corrections for nonperturbative effects, together with the inclusive deep inelastic scattering data from HERA. When fitting only $\alpha_S$ and $m_{\mathrm{t}}^{\text{pole}}$ to the data, using external PDFs, the two parameters are determined with high accuracy and rather weak correlation between them, however, the extracted $\alpha_S$ values depend on the PDF set. In a simultaneous fit of $\alpha_S$, $m_{\mathrm{t}}^{\text{pole}}$, and PDFs, the inclusion of the new multi-differential $\mathrm{t\bar{t}}$ measurements has a significant impact on the extracted gluon PDF at large values of $x$, where $x$ is the fraction of the proton momentum carried by a parton, and at the same time allows an accurate determination of $\alpha_S$ and $m_{\mathrm{t}}^{\text{pole}}$. |
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