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| CMS-PAS-TOP-22-004 ATLAS-CONF-2026-001 | ||
| Combination of ATLAS and CMS measurements of the azimuthal spin correlation variable in dilepton $ \mathrm{t\bar{t}} $ events at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 2026-01-15 | ||
| Abstract: This document presents a combination of measurements sensitive to $ \mathrm{t\bar{t}} $ spin correlations. Measurements were performed by ATLAS and CMS in the dilepton channel, using 36 fb$ ^{-1} $ of 13 TeV proton-proton data. The observable studied is the azimuthal opening angle in the laboratory frame between the two leptons in the final state: $ \Delta\phi_{\ell\ell} $. The differential distribution of $ \Delta\phi_{\ell\ell} $ has been unfolded to parton level, which removes all detector effects in the individual measurements. Comparisons are made to Monte Carlo predictions based on next-to-leading-order QCD calculations, focusing on the common POWHEG+PYTHIA 8 simulation developed by the two experiments. This model shows a shape difference between the measurement and the prediction. Higher perturbative precision is provided by fixed-order predictions at next-to-next-to-leading order in the strong coupling constant, or at next-to-leading order including weak corrections. These predictions show better agreement with the combined $ \Delta\phi_{\ell\ell} $ measurement. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Results of the ATLAS and CMS $ \Delta\phi_{\ell\ell} $ combination. The combined distribution is shown together with the original measurements by the ATLAS and CMS experiments, the POWHEG+PYTHIA8 Common MC prediction [50] and the NNLO QCD prediction from Ref. [29]. The grey shaded area indicates the scale uncertainty in the NNLO prediction and the hatched area corresponds to the combined scale and statistical uncertainties on the MC prediction. The lower panel of the figure shows the ratio of all measurements and predictions with respect to the NNLO prediction. The data are shown with open circles for ATLAS, open diamonds for CMS and closed circles for the combined measurement. The top panel shows the total uncertainties on the data, while the bottom panel shows the contribution of the statistical uncertainty within the total uncertainty. |
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Figure 2:
Correlation matrix of the bins of the combined ATLAS and CMS $ \Delta\phi_{\ell\ell} $ distribution. |
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Figure 3:
Results of the ATLAS and CMS $ \Delta\phi_{\ell\ell} $ combination, shown together with the POWHEG+PYTHIA8 Common MC prediction [50], the NNLO QCD prediction from Ref. [29] and the expanded NLO QCD+Weak prediction from Refs. [30,31,19]. The grey shaded area indicates the scale uncertainty in the NNLO prediction and the hatched areas correspond to the combined scale and statistical uncertainties in the MC and NLO predictions. The lower panel of the figure shows the ratio of the measurements and predictions with respect to the NNLO prediction. The data are shown with closed circles for the combined measurement. The top panel shows the total uncertainties on the data, while the bottom panel shows the contribution of the statistical uncertainty within the total uncertainty. |
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Figure 4:
Comparison of the Common MC POWHEG+PYTHIA8 sample [50], the NNLO QCD prediction [29] and the expanded NLO QCD+Weak prediction [30,31,19] to the combined ATLAS and CMS data. The ratio is calculated relative to the Common MC prediction. |
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Figure 5:
Comparison of the uncertainties of the individual ATLAS or CMS measurements to those on the combined measurement. The green band corresponds to the variation in the combined uncertainty for a range of different correlation assumptions. |
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Figure 6:
Comparison of the Common MC POWHEG+PYTHIA8 sample [50], the expanded NLO QCD+Weak prediction [30,31,19] and several versions of the fixed-order NLO and NNLO QCD predictions [29] to the combined ATLAS and CMS data. The ratio is calculated relative to the Common MC prediction. The renormalisation $ \mu_{\textrm{R}} $ and factorisation $ \mu_{\textrm{F}} $ scales are shown in parentheses. The $ \mu_{\textrm{R/F}}=m_t $ predictions in (b) and (c) are interpolated from 10 bins to 6 bins. |
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Figure 6-a:
Comparison of the Common MC POWHEG+PYTHIA8 sample [50], the expanded NLO QCD+Weak prediction [30,31,19] and several versions of the fixed-order NLO and NNLO QCD predictions [29] to the combined ATLAS and CMS data. The ratio is calculated relative to the Common MC prediction. The renormalisation $ \mu_{\textrm{R}} $ and factorisation $ \mu_{\textrm{F}} $ scales are shown in parentheses. The $ \mu_{\textrm{R/F}}=m_t $ predictions in (b) and (c) are interpolated from 10 bins to 6 bins. |
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Figure 6-b:
Comparison of the Common MC POWHEG+PYTHIA8 sample [50], the expanded NLO QCD+Weak prediction [30,31,19] and several versions of the fixed-order NLO and NNLO QCD predictions [29] to the combined ATLAS and CMS data. The ratio is calculated relative to the Common MC prediction. The renormalisation $ \mu_{\textrm{R}} $ and factorisation $ \mu_{\textrm{F}} $ scales are shown in parentheses. The $ \mu_{\textrm{R/F}}=m_t $ predictions in (b) and (c) are interpolated from 10 bins to 6 bins. |
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Figure 6-c:
Comparison of the Common MC POWHEG+PYTHIA8 sample [50], the expanded NLO QCD+Weak prediction [30,31,19] and several versions of the fixed-order NLO and NNLO QCD predictions [29] to the combined ATLAS and CMS data. The ratio is calculated relative to the Common MC prediction. The renormalisation $ \mu_{\textrm{R}} $ and factorisation $ \mu_{\textrm{F}} $ scales are shown in parentheses. The $ \mu_{\textrm{R/F}}=m_t $ predictions in (b) and (c) are interpolated from 10 bins to 6 bins. |
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Figure 6-d:
Comparison of the Common MC POWHEG+PYTHIA8 sample [50], the expanded NLO QCD+Weak prediction [30,31,19] and several versions of the fixed-order NLO and NNLO QCD predictions [29] to the combined ATLAS and CMS data. The ratio is calculated relative to the Common MC prediction. The renormalisation $ \mu_{\textrm{R}} $ and factorisation $ \mu_{\textrm{F}} $ scales are shown in parentheses. The $ \mu_{\textrm{R/F}}=m_t $ predictions in (b) and (c) are interpolated from 10 bins to 6 bins. |
| Tables | |
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Table 1:
Assumed correlations between the ATLAS and CMS systematic uncertainties. Full details of the uncertainties are given in Refs. [none-none-none,none-none-none-none]. Any uncertainties not included in the table are considered to be uncorrelated. The ``Variations'' column indicates the range of variations considered for the modelling and jet uncertainties, while the ``Reduced correlation'' column shows the assumptions made when each correlation is reduced by one step (typically 25%). The exact names of the jet-related uncertainties are listed, for completeness. |
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Table 2:
Assumed correlations between alternative combinations of the ATLAS and CMS systematic uncertainties. Full details of the uncertainties are given in Refs. [none-none-none,none-none-none-none]. The ``Variations'' column indicates the range of variations considered for the modelling and jet uncertainties. The exact names of the jet-related uncertainties are listed, for completeness. |
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Table 3:
Fractional uncertainties (statistical and systematic) on the normalised differential cross-section as a function of $ \Delta\phi_{\ell\ell} $ from the ATLAS and CMS combination. The uncertainties are compared between the nominal correlation assumptions, the case where all uncertainties are treated as uncorrelated between ATLAS and CMS, and the maximum uncertainty from alternative correlation assumptions considered in Tables 1 and 2, respectively. |
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Table 4:
Normalised differential cross-section as a function of $ \Delta\phi_{\ell\ell} $ from ATLAS and CMS individually, and for their combination. The two uncertainties in each measurement are the statistical and systematic uncertainty contributions, respectively. The statistical uncertainty includes both the data statistical uncertainty and the contribution from MC statistics. |
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Table 5:
$ \chi^2 $ values per degree of freedom (DOF) and $ \chi^2 $ probabilities for compatibility between data and predictions, using the full covariance matrix for the ATLAS and CMS combined dataset. The `Measurement' uncertainties refer to those derived from the $\textit{Convino}$ combination, while the `Total' uncertainty also includes statistical and scale uncertainties in the theoretical predictions. The QCD scales ($ \mu_{\textrm{R}}, \mu_{\textrm{F}} $) used in the fixed-order predictions and in the POWHEG ME are also listed. |
| Summary |
| A combination of the normalised $ \Delta\phi_{\ell\ell} $ distributions measured by the ATLAS and CMS experiments has been performed, and is presented in this note. The uncertainties in the combined distributions are reduced compared to the original measurements. The data are compared to predictions from the POWHEG matrix element generator, interfaced to the PYTHIA8 parton shower, focusing on a common MC sample developed by the two experiments. The common NLO MC prediction is in tension with the combined data, showing clear differences in shape. The discrepancy remains when a $ \chi^2 $ compatibility value is evaluated from the full covariance of the measurements, even when theoretical uncertainties estimated from MC scale variations are taken into account, leading to a $ \chi^2 $ probability of 2% for the MC\@. In contrast, the fixed-order theoretical predictions including higher-order corrections agree better with the data, with $ \chi^2 $ probabilities of 17% for NNLO QCD and 55% for NLO QCD+Weak predictions. |
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