CMSTOP23001 ; CERNEP2024137  
Observation of quantum entanglement in top quark pair production in protonproton collisions at $ \sqrt{s}= $ 13 TeV  
CMS Collaboration  
6 June 2024  
Rep. Prog. Phys. 87 (2024) 117801  
Abstract: Entanglement is an intrinsic property of quantum mechanics and is predicted to be exhibited in the particles produced at the Large Hadron Collider. A measurement of the extent of entanglement in top quarkantiquark ($ \mathrm{t} \bar{\mathrm{t}} $) events produced in protonproton collisions at a centerofmass energy of 13 TeV is performed with the data recorded by the CMS experiment at the CERN LHC in 2016, and corresponding to an integrated luminosity of 36.3 fb$ ^{1} $. The events are selected based on the presence of two leptons with opposite charges and high transverse momentum. An entanglementsensitive observable $ D $ is derived from the top quark spindependent parts of the $ \mathrm{t} \bar{\mathrm{t}} $ production density matrix and measured in the region of the $ \mathrm{t} \bar{\mathrm{t}} $ production threshold. Values of $ D {<} $1/3 are evidence of entanglement and $ D $ is observed (expected) to be $$0.480$ ^{+0.026}_{0.029} $ ($$0.467$ ^{+0.026}_{0.029} $) at the parton level. With an observed significance of 5.1 standard deviations with respect to the nonentangled hypothesis, this provides observation of quantum mechanical entanglement within $ \mathrm{t} \bar{\mathrm{t}} $ pairs in this phase space. This measurement provides a new probe of quantum mechanics at the highest energies ever produced.  
Links: eprint arXiv:2406.03976 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; 
Figures  
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Figure 1:
Representative leading order QCD Feynman diagrams for the $ \mathrm{t} \bar{\mathrm{t}} $ production through $ \mathrm{g}\mathrm{g} $ fusion (left) and quarkantiquark annihilation (right). 
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Figure 2:
Predicted values of $ (1+\Delta)/ $ 3 obtained from $ \mathrm{t} \bar{\mathrm{t}} $ MC simulation, without accounting for detector effects, are shown on the left as a function of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ and the cosine of the top quark scattering angle $ \Theta $. The value of $ (1+\Delta)/ $ 3 also determined by a $ \mathrm{t} \bar{\mathrm{t}} $ MC simulation as a function of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ and $ \beta_z({\mathrm{t}\bar{\mathrm{t}}} ) $ is shown on the right. In both figures the black solid lines represent the $ D=1/ $ 3 boundary for entanglement, while the black dashed line indicates the selected phase space in this analysis. The minimum value on the $ z $ axis of1 corresponds to the boundary $ \mathrm{tr}[C]= $ 3, a maximally entangled state. Top quarks with no spin correlations correspond to a value of $ D= $ 0 and $ \Delta= $ 1 ($ C=\mathbf{0} $). 
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Figure 2a:
Predicted values of $ (1+\Delta)/ $ 3 obtained from $ \mathrm{t} \bar{\mathrm{t}} $ MC simulation, without accounting for detector effects, are shown on the left as a function of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ and the cosine of the top quark scattering angle $ \Theta $. The value of $ (1+\Delta)/ $ 3 also determined by a $ \mathrm{t} \bar{\mathrm{t}} $ MC simulation as a function of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ and $ \beta_z({\mathrm{t}\bar{\mathrm{t}}} ) $ is shown on the right. In both figures the black solid lines represent the $ D=1/ $ 3 boundary for entanglement, while the black dashed line indicates the selected phase space in this analysis. The minimum value on the $ z $ axis of1 corresponds to the boundary $ \mathrm{tr}[C]= $ 3, a maximally entangled state. Top quarks with no spin correlations correspond to a value of $ D= $ 0 and $ \Delta= $ 1 ($ C=\mathbf{0} $). 
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Figure 2b:
Predicted values of $ (1+\Delta)/ $ 3 obtained from $ \mathrm{t} \bar{\mathrm{t}} $ MC simulation, without accounting for detector effects, are shown on the left as a function of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ and the cosine of the top quark scattering angle $ \Theta $. The value of $ (1+\Delta)/ $ 3 also determined by a $ \mathrm{t} \bar{\mathrm{t}} $ MC simulation as a function of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ and $ \beta_z({\mathrm{t}\bar{\mathrm{t}}} ) $ is shown on the right. In both figures the black solid lines represent the $ D=1/ $ 3 boundary for entanglement, while the black dashed line indicates the selected phase space in this analysis. The minimum value on the $ z $ axis of1 corresponds to the boundary $ \mathrm{tr}[C]= $ 3, a maximally entangled state. Top quarks with no spin correlations correspond to a value of $ D= $ 0 and $ \Delta= $ 1 ($ C=\mathbf{0} $). 
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Figure 3:
Reconstructionlevel $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ (upper left), $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ (upper right), and $ \cos\varphi $ (lower) distributions of the combined signal model (POWHEGv2$+$PYTHIA8${+}\eta$t, labeled PH$+$P8${+}\eta$t) in the full phase space comparing the modeling of the data by MC simulation when not including $\eta$t contributions (purple dotted line in the upper panel under each plot), or no $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ reweighting is applied (gray dashed line in the upper panel), or neither of those (red dasheddotted line in upper panel). The lower panel under each plot compares the data to POWHEGv2$+$HERWIG++ (blue dashed line, labeled PH$+$HPP${+}\eta$t), to MG5_MC@NLOFxFx$+$PYTHIA8 (purple dasheddotted line), and finally to the nominal MC including $\eta$t contributions and $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ reweighting (orange solid line, labeled PH$+$P8${+}\eta$t). The hashed uncertainty bands correspond to the prefit systematic uncertainties and includes the statistical uncertainty of the data as well. The label ``$ p_{\mathrm{T}} $ rew.'' in the legend refers to the $ p_{\mathrm{T}} $ reweighting procedure (detailed in Section 7) used to reweight the $ \mathrm{t} \bar{\mathrm{t}} $ sample to NNLO in QCD. 
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Figure 3a:
Reconstructionlevel $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ (upper left), $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ (upper right), and $ \cos\varphi $ (lower) distributions of the combined signal model (POWHEGv2$+$PYTHIA8${+}\eta$t, labeled PH$+$P8${+}\eta$t) in the full phase space comparing the modeling of the data by MC simulation when not including $\eta$t contributions (purple dotted line in the upper panel under each plot), or no $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ reweighting is applied (gray dashed line in the upper panel), or neither of those (red dasheddotted line in upper panel). The lower panel under each plot compares the data to POWHEGv2$+$HERWIG++ (blue dashed line, labeled PH$+$HPP${+}\eta$t), to MG5_MC@NLOFxFx$+$PYTHIA8 (purple dasheddotted line), and finally to the nominal MC including $\eta$t contributions and $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ reweighting (orange solid line, labeled PH$+$P8${+}\eta$t). The hashed uncertainty bands correspond to the prefit systematic uncertainties and includes the statistical uncertainty of the data as well. The label ``$ p_{\mathrm{T}} $ rew.'' in the legend refers to the $ p_{\mathrm{T}} $ reweighting procedure (detailed in Section 7) used to reweight the $ \mathrm{t} \bar{\mathrm{t}} $ sample to NNLO in QCD. 
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Figure 3b:
Reconstructionlevel $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ (upper left), $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ (upper right), and $ \cos\varphi $ (lower) distributions of the combined signal model (POWHEGv2$+$PYTHIA8${+}\eta$t, labeled PH$+$P8${+}\eta$t) in the full phase space comparing the modeling of the data by MC simulation when not including $\eta$t contributions (purple dotted line in the upper panel under each plot), or no $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ reweighting is applied (gray dashed line in the upper panel), or neither of those (red dasheddotted line in upper panel). The lower panel under each plot compares the data to POWHEGv2$+$HERWIG++ (blue dashed line, labeled PH$+$HPP${+}\eta$t), to MG5_MC@NLOFxFx$+$PYTHIA8 (purple dasheddotted line), and finally to the nominal MC including $\eta$t contributions and $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ reweighting (orange solid line, labeled PH$+$P8${+}\eta$t). The hashed uncertainty bands correspond to the prefit systematic uncertainties and includes the statistical uncertainty of the data as well. The label ``$ p_{\mathrm{T}} $ rew.'' in the legend refers to the $ p_{\mathrm{T}} $ reweighting procedure (detailed in Section 7) used to reweight the $ \mathrm{t} \bar{\mathrm{t}} $ sample to NNLO in QCD. 
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Figure 3c:
Reconstructionlevel $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ (upper left), $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ (upper right), and $ \cos\varphi $ (lower) distributions of the combined signal model (POWHEGv2$+$PYTHIA8${+}\eta$t, labeled PH$+$P8${+}\eta$t) in the full phase space comparing the modeling of the data by MC simulation when not including $\eta$t contributions (purple dotted line in the upper panel under each plot), or no $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ reweighting is applied (gray dashed line in the upper panel), or neither of those (red dasheddotted line in upper panel). The lower panel under each plot compares the data to POWHEGv2$+$HERWIG++ (blue dashed line, labeled PH$+$HPP${+}\eta$t), to MG5_MC@NLOFxFx$+$PYTHIA8 (purple dasheddotted line), and finally to the nominal MC including $\eta$t contributions and $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ reweighting (orange solid line, labeled PH$+$P8${+}\eta$t). The hashed uncertainty bands correspond to the prefit systematic uncertainties and includes the statistical uncertainty of the data as well. The label ``$ p_{\mathrm{T}} $ rew.'' in the legend refers to the $ p_{\mathrm{T}} $ reweighting procedure (detailed in Section 7) used to reweight the $ \mathrm{t} \bar{\mathrm{t}} $ sample to NNLO in QCD. 
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Figure 4:
Reconstructionlevel distributions of $ \cos\varphi $ (left) and $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ (right) requiring 345 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 400 GeV and $ \beta_z({\mathrm{t}\bar{\mathrm{t}}} ) < $ 0.9. The lower panels on each figure show the same model comparison done in Fig. 3. The hashed uncertainty bands correspond to the prefit systematic uncertainties and includes the statistical uncertainty of the data as well. The label ``$ p_{\mathrm{T}} $ rew.'' in the legend refers to the $ p_{\mathrm{T}} $ reweighting procedure (detailed in Section 7) used to reweight the $ \mathrm{t} \bar{\mathrm{t}} $ sample to NNLO in QCD. 
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Figure 4a:
Reconstructionlevel distributions of $ \cos\varphi $ (left) and $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ (right) requiring 345 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 400 GeV and $ \beta_z({\mathrm{t}\bar{\mathrm{t}}} ) < $ 0.9. The lower panels on each figure show the same model comparison done in Fig. 3. The hashed uncertainty bands correspond to the prefit systematic uncertainties and includes the statistical uncertainty of the data as well. The label ``$ p_{\mathrm{T}} $ rew.'' in the legend refers to the $ p_{\mathrm{T}} $ reweighting procedure (detailed in Section 7) used to reweight the $ \mathrm{t} \bar{\mathrm{t}} $ sample to NNLO in QCD. 
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Figure 4b:
Reconstructionlevel distributions of $ \cos\varphi $ (left) and $ p_{\mathrm{T}}(\mathrm{t}/\bar{\mathrm{t}}) $ (right) requiring 345 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 400 GeV and $ \beta_z({\mathrm{t}\bar{\mathrm{t}}} ) < $ 0.9. The lower panels on each figure show the same model comparison done in Fig. 3. The hashed uncertainty bands correspond to the prefit systematic uncertainties and includes the statistical uncertainty of the data as well. The label ``$ p_{\mathrm{T}} $ rew.'' in the legend refers to the $ p_{\mathrm{T}} $ reweighting procedure (detailed in Section 7) used to reweight the $ \mathrm{t} \bar{\mathrm{t}} $ sample to NNLO in QCD. 
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Figure 5:
Reconstructionlevel distribution of the combined $ {\mathrm{t}\bar{\mathrm{t}}} {+} {\eta}$t signal model in mixtures of the noSC combined signal sample. Template variations as a function of $ \cos\varphi $ requiring an $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ of 345 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 400 GeV and $ \beta_z({\mathrm{t}\bar{\mathrm{t}}} ) < $ 0.9 are shown. The $ \mathrm{t} \bar{\mathrm{t}} $ noSC and SC mixtures ranging from $ 100% $ to $ +100% $ noSC are shown on the left. The $\eta$t noSC and SC mixtures ranging from zero noSC to $ +100% $ noSC are shown on the right. 
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Figure 5a:
Reconstructionlevel distribution of the combined $ {\mathrm{t}\bar{\mathrm{t}}} {+} {\eta}$t signal model in mixtures of the noSC combined signal sample. Template variations as a function of $ \cos\varphi $ requiring an $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ of 345 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 400 GeV and $ \beta_z({\mathrm{t}\bar{\mathrm{t}}} ) < $ 0.9 are shown. The $ \mathrm{t} \bar{\mathrm{t}} $ noSC and SC mixtures ranging from $ 100% $ to $ +100% $ noSC are shown on the left. The $\eta$t noSC and SC mixtures ranging from zero noSC to $ +100% $ noSC are shown on the right. 
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Figure 5b:
Reconstructionlevel distribution of the combined $ {\mathrm{t}\bar{\mathrm{t}}} {+} {\eta}$t signal model in mixtures of the noSC combined signal sample. Template variations as a function of $ \cos\varphi $ requiring an $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ of 345 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 400 GeV and $ \beta_z({\mathrm{t}\bar{\mathrm{t}}} ) < $ 0.9 are shown. The $ \mathrm{t} \bar{\mathrm{t}} $ noSC and SC mixtures ranging from $ 100% $ to $ +100% $ noSC are shown on the left. The $\eta$t noSC and SC mixtures ranging from zero noSC to $ +100% $ noSC are shown on the right. 
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Figure 6:
The postfit detectorlevel distribution of $ \cos\varphi $ requiring 345 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 400 GeV, $ \beta_z({\mathrm{t}\bar{\mathrm{t}}} ) < $ 0.9, and including $\eta$t in the fit, is shown on the left. The hashed band corresponds to the postfit uncertainty and includes the statistical uncertainty of the data added in quadrature. The nominal combined signal model, POWHEGv2$+$PYTHIA8${+}\eta$t, is labeled as PH$+$P8${+}\eta$t. The fitted noSC and SC mixture template for the combined signal model in the $ \cos\varphi $ distribution is shown on the right. 
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Figure 6a:
The postfit detectorlevel distribution of $ \cos\varphi $ requiring 345 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 400 GeV, $ \beta_z({\mathrm{t}\bar{\mathrm{t}}} ) < $ 0.9, and including $\eta$t in the fit, is shown on the left. The hashed band corresponds to the postfit uncertainty and includes the statistical uncertainty of the data added in quadrature. The nominal combined signal model, POWHEGv2$+$PYTHIA8${+}\eta$t, is labeled as PH$+$P8${+}\eta$t. The fitted noSC and SC mixture template for the combined signal model in the $ \cos\varphi $ distribution is shown on the right. 
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Figure 6b:
The postfit detectorlevel distribution of $ \cos\varphi $ requiring 345 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 400 GeV, $ \beta_z({\mathrm{t}\bar{\mathrm{t}}} ) < $ 0.9, and including $\eta$t in the fit, is shown on the left. The hashed band corresponds to the postfit uncertainty and includes the statistical uncertainty of the data added in quadrature. The nominal combined signal model, POWHEGv2$+$PYTHIA8${+}\eta$t, is labeled as PH$+$P8${+}\eta$t. The fitted noSC and SC mixture template for the combined signal model in the $ \cos\varphi $ distribution is shown on the right. 
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Figure 7:
Result of the scan of the quantity $ 2\Delta\ln L $ from a profile likelihood fit as a function of the parameter of interest $ D $, when including (left) or excluding (right) the $\eta$t contribution. Both results are at parton level and the relevant phase space is indicated in the figures itself. The region where the $ \mathrm{t} \bar{\mathrm{t}} $ pairs become separable and not entangled ($ D > 1/ $ 3) is indicated by the shaded area. 
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Figure 7a:
Result of the scan of the quantity $ 2\Delta\ln L $ from a profile likelihood fit as a function of the parameter of interest $ D $, when including (left) or excluding (right) the $\eta$t contribution. Both results are at parton level and the relevant phase space is indicated in the figures itself. The region where the $ \mathrm{t} \bar{\mathrm{t}} $ pairs become separable and not entangled ($ D > 1/ $ 3) is indicated by the shaded area. 
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Figure 7b:
Result of the scan of the quantity $ 2\Delta\ln L $ from a profile likelihood fit as a function of the parameter of interest $ D $, when including (left) or excluding (right) the $\eta$t contribution. Both results are at parton level and the relevant phase space is indicated in the figures itself. The region where the $ \mathrm{t} \bar{\mathrm{t}} $ pairs become separable and not entangled ($ D > 1/ $ 3) is indicated by the shaded area. 
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Figure 9:
Summary of the measurement of the entanglement proxy $ D $ in data (black filled or open point) compared with MC predictions including (solid line) or not including (dashed line) contributions from the $\eta$t state. The legend denotes MC predictions without the $\eta$t state with a slash through $\eta$t. Inner error bars represent the statistical uncertainty, while the outer error bars represent the total uncertainty for data. The statistical uncertainty in the MC predictions is denoted by the light shaded region and the total uncertainty, including scale and PDF uncertainties, is represented by the darker shaded region. The boundary for entanglement is indicated by the shaded region at $ D=1/ $ 3. 
Tables  
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Table 1:
The expected number of events from signal and background contributions after event selection, compared with the number observed in data. The `` $ \mathrm{t} \bar{\mathrm{t}} $ other'' category includes misidentified semileptonic and fully hadronic decays, and hadronic decays of tau leptons of the $ \mathrm{t} \bar{\mathrm{t}} $ pairs. The uncertainties include only the MC statistical uncertainties. The ``Only $\eta$t '' contribution is not added to the total MC prediction since it is included in the combined ($ {\mathrm{t}\bar{\mathrm{t}}} {+} {\eta}$t) signal contribution. 
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Table 2:
An overview of the systematic uncertainties and their impact on the yields and shape of the $ \cos\varphi $ distribution. The uncertainties are categorized by their type where ``norm.'' refers to normalization uncertainties modeled with a lognormal prior and ``shape'' refers to shape uncertainties. The impact on the yields and shape of the $ \cos\varphi $ distribution is given in percent where the difference in the shape of the $ \cos\varphi $ distribution is determined from the forwardbackward asymmetry. The JES systematics are split as in Ref. [70] with the addition of ``JES: Relative Balance'' accounting for the difference in modeling of missing transverse momentum. 
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Table 3:
The number of predicted and observed events in the selected phase space, before the fit to the data (prefit) and with their best fit normalizations (postfit). The uncertainties in the prefit and postfit yields reflect total uncertanties but do not include correlations. The ``Only $\eta$t '' contribution is not added to the total MC prediction since it is included in the combined signal contribution. 
Summary 
Entanglement is an intrinsic property of quantum mechanics and its measurement utilizes elementary particles to test quantum mechanics. Recently, the ATLAS Collaboration reported the first observation of entanglement in the top quarkantiquark ($ \mathrm{t} \bar{\mathrm{t}} $) system [21] wih a result indicating slight deviation from MC simulation. The measurement of the entanglement of $ \mathrm{t} \bar{\mathrm{t}} $ pairs performed with CMS data exploits the spin correlation variable $ D $, which at the $ \mathrm{t} \bar{\mathrm{t}} $ production threshold, and in absence of BSM contributions, provides access to the full spin correlation information. This result contrasts with the ATLAS Collaboration's findings in several key ways. We directly measure entanglement at the parton level, whereas ATLAS reports their observable at the particle level. Additionally, our analysis is the first to consider nonrelativistic boundstate effects in the production threshold by including the ground state of toponium, $\eta$t, which were not included in the ATLAS result. Unlike ATLAS, the CMS result is derived from a binned likelihood fit to extract the entanglement proxy, rather than using a calibration curve. The $ D $ variable represents an entanglement proxy, where less than $ 1/ $ 3 signals the presence of entanglement. This proxy is measured using events containing two oppositely charged electrons or muons produced in pp collisions at a centerofmass energy of 13 TeV. The modeling of the data is improved when including the additional predicted contribution of the ground state of toponium, $\eta$t, and is utilized in a combined signal model of $ {\mathrm{t}\bar{\mathrm{t}}} {+} {\eta}$t in the measurement. The extent to which $ \mathrm{t} \bar{\mathrm{t}} $ pairs are entangled is measured by means of a binned profile likelihood fit of the parameter of interest $ D $ directly from the distribution of $ \cos\varphi $, where $ \varphi $ is the angle between the two charged decay leptons in their respective parent top quark rest frames. In the most sensitive kinematic phase space of the relative velocity between the lab and $ \mathrm{t} \bar{\mathrm{t}} $ reference frames $ \beta_z({\mathrm{t}\bar{\mathrm{t}}} ) < $ 0.9, and of the invariant mass of the top quark pair 345 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 400 GeV, the fit of the $ \cos\varphi $ distribution yields an observed value of $ D=$0.480$^{+0.026}_{0.029} $ and an expected value of $ D=$0.467$ ^{+0.026}_{0.029} $ including the predicted $\eta$t state. This result has an observed (expected) significance of 5.1 (4.7) $ \sigma $, corresponding to the observation of top quark entanglement. The measured value of $ D $ is in good agreement with the MC modeling in this phase space when including the expected $\eta$t bound state contribution. 
References  
1  S. J. Freedman and J. F. Clauser  Experimental test of local hiddenvariable theories  PRL 28 (1972) 938  
2  A. Aspect, J. Dalibard, and G. Roger  Experimental test of Bell's inequalities using timevarying analyzers  PRL 49 (1982) 1804  
3  A. Vaziri, G. Weihs, and A. Zeilinger  Experimental twophoton, threedimensional entanglement for quantum communication  PRL 89 (2002) 240401  
4  A. Aspect, P. Grangier, and G. Roger  Experimental realization of EinsteinPodolskyRosenBohm gedankenexperiment: A new violation of Bell's inequalities  PRL 49 (1982) 91  
5  B. Hensen et al.  Loopholefree Bell inequality violation using electron spins separated by 1.3 kilometres  Nature 526 (2015) 682  1508.05949 
6  M. Giustina et al.  Significantloopholefree test of Bell's theorem with entangled photons  PRL 115 (2015) 250401  1511.03190 
7  W. Pfaff et al.  Demonstration of entanglementbymeasurement of solidstate qubits  Nature Phys. 9 (2012) 29  
8  J. S. Bell  On the EinsteinPodolskyRosen paradox  Phys. Phys. Fiz. 1 (1964) 195  
9  M. A. Rowe et al.  Experimental violation of a Bell's inequality with efficient detection  Nature 409 (2001) 791  
10  M. Ansmann et al.  Violation of Bell's inequality in Josephson phase qubits  Nature 461 (2009) 504  
11  A. Einstein, B. Podolsky, and N. Rosen  Can quantummechanical description of physical reality be considered complete?  PR 47 (1935) 777  
12  A. J. Barr, P. Caban, and J. Rembieli \'n ski  Belltype inequalities for systems of relativistic vector bosons  Quantum 7 (2023) 1070  2204.11063 
13  A. J. Barr  Testing Bell inequalities in Higgs boson decays  PLB 825 (2022) 136866  2106.01377 
14  J. A. AguilarSaavedra  Laboratoryframe tests of quantum entanglement in $ {\mathrm{H}\to\mathrm{W}\mathrm{W}} $  PRD 107 (2023) 076016  2209.14033 
15  J. A. AguilarSaavedra, A. Bernal, J. A. Casas, and J. M. Moreno  Testing entanglement and Bell inequalities in $ {\mathrm{H}\to\mathrm{Z}\mathrm{Z}} $  PRD 107 (2023) 016012  2209.13441 
16  M. M. Altakach et al.  Quantum information and $ {CP} $ measurement in $ {\mathrm{H}\to\tau^{+}\tau^{}} $ at future lepton colliders  PRD 107 (2023) 093002  2211.10513 
17  K. Cheng, T. Han, and M. Low  Optimizing fictitious states for Bell inequality violation in bipartite qubit systems  2311.09166  
18  T. Han, M. Low, and T. A. Wu  Quantum entanglement and Bell inequality violation in semileptonic top decays  2310.17696  
19  Z. Dong, D. Gon ç alves, K. Kong, and A. Navarro  When the machine chimes the Bell: Entanglement and Bell inequalities with boosted $ \mathrm{t} \overline{\mathrm{t}} $  2305.07075  
20  M. Varma and O. K. Baker  Quantum entanglement in top quark pair production  Nucl. Phys. A 1042 (2024) 122795  2306.07788 
21  A. J. Barr et al.  Quantum entanglement and Bell inequality violation at colliders  Prog. Part. Nucl. Phys. 139 (2024) 104134  2402.07972 
22  M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola  Bell inequalities and quantum entanglement in weak gauge boson production at the LHC and future colliders  EPJC 83 (2023) 823  2302.00683 
23  K. Cheng, T. Han, and M. Low  Optimizing entanglement and Bell inequality violation in top antitop events  2407.01672  
24  S. A. Abel, M. Dittmar, and H. Dreiner  Testing locality at colliders via Bell's inequality?  PLB 280 (1992) 304  
25  M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola  Bell inequality is violated \\ in $ {\mathrm{B}^0} {\rightarrow} \mathrm{J}/\psi $\HepParticleResonanceFull$ \mathrm{K} $\ast8920 decays  PRD 109 (2024) L031104  2305.04982 
26  ATLAS Collaboration  Observation of quantum entanglement in topquark pairs using the ATLAS detector  Submitted to Nature, 2023  2311.07288 
27  Y. Afik and J. R. M. de Nova  Entanglement and quantum tomography with top quarks at the LHC  Eur. Phys. J. Plus 136 (2021) 907  2003.02280 
28  M. Fabbrichesi, R. Floreanini, and G. Panizzo  Testing Bell inequalities at the LHC with topquark pairs  PRL 127 (2021) 161801  2102.11883 
29  C. Severi, C. Degli Esposti Boschi, F. Maltoni, and M. Sioli  Quantum tops at the LHC: from entanglement to Bell inequalities  EPJC 82 (2022) 285  2110.10112 
30  R. Iengo  Sommerfeld enhancement: general results from field theory diagrams  JHEP 05 (2009) 024  
31  R. Mammen Abraham and D. Gon ç alves  Boosting new physics searches in $ {{\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z}} $ and $ {\mathrm{t}\mathrm{Z}\mathrm{j}} $ production with angular moments  EPJC 83 (2023) 965  2208.05986 
32  D. Gon ç alves, J. H. Kim, K. Kong, and Y. Wu  Direct Higgstop $ {CP} $phase measurement with $ {{\mathrm{t}\overline{\mathrm{t}}} \mathrm{h}} $ at the 14 TeV LHC and 100 TeV FCC  JHEP 01 (2022) 158  2108.01083 
33  R. Aoude, E. Madge, F. Maltoni, and L. Mantani  Quantum SMEFT tomography: Top quark pair production at the LHC  PRD 106 (2022) 055007  2203.05619 
34  H. Baer et al.  Top squarks from the landscape at high luminosity LHC  PRD 108 (2023) 075027  2307.08067 
35  C. Severi and E. Vryonidou  Quantum entanglement and top spin correlations in SMEFT at higher orders  JHEP 01 (2023) 148  2210.09330 
36  M. Fabbrichesi, R. Floreanini, and E. Gabrielli  Constraining new physics in entangled twoqubit systems: topquark, taulepton and photon pairs  EPJC 83 (2023) 162  2208.11723 
37  F. Maltoni, C. Severi, S. Tentori, and E. Vryonidou  Quantum detection of new physics in topquark pair production at the LHC  JHEP 03 (2024) 099  2401.08751 
38  F. Maltoni, C. Severi, S. Tentori, and E. Vryonidou  Quantum tops at circular lepton colliders  2404.08049  
39  Particle Data Group , R. L. Workman et al.  Review of particle physics  Prog. Theor. Exp. Phys. 2022 (2022) 083C01  
40  G. Mahlon and S. J. Parke  Spin correlation effects in top quark pair production at the LHC  PRD 81 (2010) 074024  1001.3422 
41  CMS Collaboration  Measurement of the top quark polarization and $ \mathrm{t} \overline{\mathrm{t}} $ spin correlations using dilepton final states in protonproton collisions at $ \sqrt{s}= $ 13 TeV  PRD 100 (2019) 072002  CMSTOP18006 1907.03729 
42  M. Czakon and A. Mitov  top++: a program for the calculation of the toppair crosssection at hadron colliders  Comput. Phys. Commun. 185 (2014) 2930  1112.5675 
43  M. Czakon and A. Mitov  NNLO corrections to toppair production at hadron colliders: the allfermionic scattering channels  JHEP 12 (2012) 054  1207.0236 
44  M. Czakon and A. Mitov  NNLO corrections to top pair production at hadron colliders: the quarkgluon reaction  JHEP 01 (2013) 080  1210.6832 
45  M. Czakon, P. Fiedler, and A. Mitov  Total topquark pairproduction cross section at hadron colliders through $ \mathcal{O}({\alpha_\mathrm{S}}^4) $  PRL 110 (2013) 252004  1303.6254 
46  B. Fuks, K. Hagiwara, K. Ma, and Y.J. Zheng  Signatures of toponium formation in LHC run 2 data  PRD 104 (2021) 034023  2102.11281 
47  N. Brambilla, A. Pineda, J. Soto, and A. Vairo  Potential NRQCD: an effective theory for heavy quarkonium  NPB 566 (2000) 275  hepph/9907240 
48  CMS Collaboration  Differential cross section measurements for the production of top quark pairs and of additional jets using dilepton events from $ {\mathrm{p}\mathrm{p}} $ collisions at $ \sqrt{s}= $ 13 TeV  Submitted to JHEP, 2024  CMSTOP20006 2402.08486 
49  CMS Collaboration  Measurements of $ \mathrm{t} \overline{\mathrm{t}} $ differential cross sections in protonproton collisions at $ \sqrt{s}= $ 13 TeV using events containing two leptons  JHEP 02 (2019) 149  CMSTOP17014 1811.06625 
50  CMS Collaboration  Measurement of differential cross sections for top quark pair production using the lepton+jets final state in protonproton collisions at 13 TeV  PRD 95 (2017) 092001  CMSTOP16008 1610.04191 
51  ATLAS Collaboration  Measurements of $ \mathrm{t} \overline{\mathrm{t}} $ differential crosssections of highly boosted top quarks decaying to allhadronic final states in $ {\mathrm{p}\mathrm{p}} $ collisions at $ \sqrt{s}= $ 13 TeV using the ATLAS detector  PRD 98 (2018) 012003  1801.02052 
52  ATLAS Collaboration  Measurement of the $ \mathrm{t} \overline{\mathrm{t}} $ production crosssection in the lepton+jets channel at $ \sqrt{s}= $ 13 TeV with the ATLAS experiment  PLB 810 (2020) 135797  2006.13076 
53  Y. Kiyo et al.  Topquark pair production near threshold at LHC  EPJC 60 (2009) 375  0812.0919 
54  W.L. Ju et al.  Top quark pair production near threshold: single/double distributions and mass determination  JHEP 06 (2020) 158  2004.03088 
55  Y. Sumino and H. Yokoya  Boundstate effects on kinematical distributions of top quarks at hadron colliders  JHEP 09 (2010) 034  1007.0075 
56  V. S. Fadin, V. A. Khoze, and T. Sjöstrand  On the threshold behaviour of heavy top production  Z. Phys. C 48 (1990) 613  
57  M. Beneke et al.  Nexttoleading power endpoint factorization and resummation for offdiagonal `gluon' thrust  JHEP 07 (2022) 144  2205.04479 
58  G. Mahlon and S. J. Parke  Angular correlations in top quark pair production and decay at hadron colliders  PRD 53 (1996) 4886  hepph/9512264 
59  W. Bernreuther, D. Heisler, and Z.G. Si  A set of top quark spin correlation and polarization observables for the LHC: Standard model predictions and new physics contributions  JHEP 12 (2015) 026  1508.05271 
60  A. Brandenburg, Z. G. Si, and P. Uwer  QCDcorrected spin analysing power of jets in decays of polarized top quarks  PLB 539 (2002) 235  hepph/0205023 
61  CDF Collaboration  Measurement of $ \mathrm{t} \overline{\mathrm{t}} $ spin correlation in $ {\mathrm{p}\overline{\mathrm{p}}} $ collisions using the CDF II detector at the Tevatron  PRD 83 (2011) 031104  1012.3093 
62  A. Peres  Separability criterion for density matrices  PRL 77 (1996) 1413  quantph/9604005 
63  M. Horodecki, P. Horodecki, and R. Horodecki  On the necessary and sufficient conditions for separability of mixed quantum states  Phys. Lett. A 223 (1996) 1  quantph/9605038 
64  M. Baumgart and B. Tweedie  A new twist on top quark spin correlations  JHEP 03 (2013) 117  1212.4888 
65  R. Horodecki, P. Horodecki, and M. Horodecki  Violating Bell inequality by mixed spin1/2 states: necessary and sufficient condition  Phys. Lett. A 200 (1995) 340  
66  J. A. AguilarSaavedra and J. A. Casas  Improved tests of entanglement and Bell inequalities with LHC tops  EPJC 82 (2022) 666  2205.00542 
67  CMS Collaboration  Projection of the top quark spin correlation measurement and search for top squark pair production at the HLLHC  CMS Physics Analysis Summary, 2022 CMSPASFTR18034 
CMSPASFTR18034 
68  CMS Collaboration  The CMS statistical analysis and combination tool: combine  Submitted to Comput. Softw. Big Sci, 2024  CMSCAT23001 2404.06614 
69  W. Verkerke and D. Kirkby  The RooFit toolkit for data modeling  in Proc. 13th International Conference on Computing in High Energy and Nuclear Physics (CHEP ): La Jolla CA, 2003 [eConf C0303241 MOLT007] 
physics/0306116 
70  L. Moneta et al.  The RooStats project  in Proc. 13th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT ): Jaipur, India, 2010 [PoS (ACAT) 057] 
1009.1003 
71  CMS Collaboration  The CMS trigger system  JINST 12 (2017) P01020  CMSTRG12001 1609.02366 
72  CMS Collaboration  The CMS experiment at the CERN LHC  JINST 3 (2008) S08004  
73  CMS Collaboration  Development of the CMS detector for the CERN LHC Run 3  JINST 19 (2024) P05064  CMSPRF21001 2309.05466 
74  CMS Collaboration  Particleflow reconstruction and global event description with the CMS detector  JINST 12 (2017) P10003  CMSPRF14001 1706.04965 
75  M. Cacciari, G. P. Salam, and G. Soyez  The anti$ k_{\mathrm{T}} $ jet clustering algorithm  JHEP 04 (2008) 063  0802.1189 
76  M. Cacciari, G. P. Salam, and G. Soyez  FASTJET user manual  EPJC 72 (2012) 1896  1111.6097 
77  CMS Collaboration  Pileup mitigation at CMS in 13 TeV data  JINST 15 (2020) P09018  CMSJME18001 2003.00503 
78  CMS Collaboration  Jet energy scale and resolution in the CMS experiment in $ {\mathrm{p}\mathrm{p}} $ collisions at 8 TeV  JINST 12 (2017) P02014  CMSJME13004 1607.03663 
79  CMS Collaboration  Performance of missing transverse momentum reconstruction in protonproton collisions at $ \sqrt{s}= $ 13 TeV using the CMS detector  JINST 14 (2019) P07004  CMSJME17001 1903.06078 
80  CMS Collaboration  Performance of electron reconstruction and selection with the CMS detector in protonproton collisions at $ \sqrt{s}= $ 8 TeV  JINST 10 (2015) P06005  CMSEGM13001 1502.02701 
81  CMS Collaboration  Electron and photon reconstruction and identification with the CMS experiment at the CERN LHC  JINST 16 (2021) P05014  CMSEGM17001 2012.06888 
82  CMS Collaboration  ECAL 2016 refined calibration and \mboxRun 2 summary plots  CMS Detector Performance Note CMSDP2020021, 2020 CDS 

83  CMS Collaboration  Performance of the CMS muon detector and muon reconstruction with protonproton collisions at $ \sqrt{s}= $ 13 TeV  JINST 13 (2018) P06015  CMSMUO16001 1804.04528 
84  S. Frixione, G. Ridolfi, and P. Nason  A positiveweight nexttoleadingorder Monte Carlo for heavy flavour hadroproduction  JHEP 09 (2007) 126  0707.3088 
85  P. Nason  A new method for combining NLO QCD with shower Monte Carlo algorithms  JHEP 11 (2004) 040  hepph/0409146 
86  S. Frixione, P. Nason, and C. Oleari  Matching NLO QCD computations with parton shower simulations: the POWHEG method  JHEP 11 (2007) 070  0709.2092 
87  S. Alioli, P. Nason, C. Oleari, and E. Re  A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG box  JHEP 06 (2010) 043  1002.2581 
88  J. Alwall et al.  The automated computation of treelevel and nexttoleading order differential cross sections, and their matching to parton shower simulations  JHEP 07 (2014) 079  1405.0301 
89  P. Artoisenet, R. Frederix, O. Mattelaer, and R. Rietkerk  Automatic spinentangled decays of heavy resonances in Monte Carlo simulations  JHEP 03 (2013) 015  1212.3460 
90  R. Frederix and S. Frixione  Merging meets matching in MC@NLO  JHEP 12 (2012) 061  1209.6215 
91  NNPDF Collaboration  Parton distributions for the LHC run II  JHEP 04 (2015) 040  1410.8849 
92  M. Czakon, D. Heymes, and A. Mitov  fastNLO tables for NNLO topquark pair differential distributions  1704.08551  
93  M. Czakon, D. Heymes, and A. Mitov  Highprecision differential predictions for topquark pairs at the LHC  PRL 116 (2016) 082003  1511.00549 
94  M. Czakon, D. Heymes, and A. Mitov  Dynamical scales for multiTeV toppair production at the LHC  JHEP 04 (2017) 071  1606.03350 
95  CMS Collaboration  Measurement of the top quark Yukawa coupling from $ \mathrm{t} \overline{\mathrm{t}} $ kinematic distributions in the dilepton final state in protonproton collisions at $ \sqrt{s}= $ 13 TeV  PRD 102 (2020) 092013  CMSTOP19008 2009.07123 
96  T. Sjöstrand et al.  An introduction to PYTHIA8.2  Comput. Phys. Commun. 191 (2015) 159  1410.3012 
97  CMS Collaboration  Investigations of the impact of the parton shower tuning in PYTHIA8 in the modelling of $ \mathrm{t} \overline{\mathrm{t}} $ at $ \sqrt{s}= $ 8 and 13 TeV  CMS Physics Analysis Summary, 2016 CMSPASTOP16021 
CMSPASTOP16021 
98  CMS Collaboration  Event generator tunes obtained from underlying event and multiparton scattering measurements  EPJC 76 (2016) 155  CMSGEN14001 1512.00815 
99  M. Bähr et al.  HERWIG++ physics and manual  EPJC 58 (2008) 639  0803.0883 
100  S. Gieseke, C. Röhr, and A. Siodmok  Colour reconnections in HERWIG++  EPJC 72 (2012) 2225  1206.0041 
101  GEANT4 Collaboration  GEANT 4a simulation toolkit  NIM A 506 (2003) 250  
102  CMS Collaboration  Identification of heavyflavour jets with the CMS detector in $ {\mathrm{p}\mathrm{p}} $ collisions at 13 TeV  JINST 13 (2018) P05011  CMSBTV16002 1712.07158 
103  CMS Collaboration  Measurement of the $ \mathrm{t} \overline{\mathrm{t}} $ production cross section in the dilepton channel in $ {\mathrm{p}\mathrm{p}} $ collisions at $ \sqrt{s}= $ 7 TeV  JHEP 11 (2012) 067  CMSTOP11005 1208.2671 
104  CMS Collaboration  Measurement of the differential cross section for top quark pair production in $ {\mathrm{p}\mathrm{p}} $ collisions at $ \sqrt{s} = $ 8 TeV  EPJC 75 (2015) 542  CMSTOP12028 1505.04480 
105  CMS Collaboration  Measurement of the top quark pair production cross section in protonproton collisions at $ \sqrt{s}= $ 13 TeV  PRL 116 (2016) 052002  CMSTOP15003 1510.05302 
106  CMS Collaboration  Measurement of the DrellYan cross section in $ {\mathrm{p}\mathrm{p}} $ collisions at $ \sqrt{s}= $ 7 TeV  JHEP 10 (2011) 007  CMSEWK10007 1108.0566 
107  CMS Collaboration  Measurement of the inelastic protonproton cross section at $ \sqrt{s}= $ 13 TeV  JHEP 07 (2018) 161  CMSFSQ15005 1802.02613 
108  CMS Collaboration  Precision luminosity measurement in protonproton collisions at $ \sqrt{s}= $ 13 TeV in 2015 and 2016 at CMS  EPJC 81 (2021) 800  CMSLUM17003 2104.01927 
109  CMS Collaboration  Extraction and validation of a new set of CMS PYTHIA8 tunes from underlyingevent measurements  EPJC 80 (2020) 4  CMSGEN17001 1903.12179 
110  J. R. Christiansen and P. Z. Skands  String formation beyond leading colour  JHEP 08 (2015) 003  1505.01681 
111  S. Argyropoulos and T. Sjöstrand  Effects of color reconnection on $ \mathrm{t} \overline{\mathrm{t}} $ final states at the LHC  JHEP 11 (2014) 043  1407.6653 
112  M. G. Bowler  $ {e^+e^} $ production of heavy quarks in the string model  Z. Phys. C 11 (1981) 169  
113  B. Andersson, G. Gustafson, G. Ingelman, and T. Sjöstrand  Parton fragmentation and string dynamics  Physics Reports 97 (1983) 31  
114  CMS Collaboration  Measurement of the shape of the b quark fragmentation function using charmed mesons produced inside b jets from $ \mathrm{t} \overline{\mathrm{t}} $ pair decays  CMS Physics Analysis Summary, 2021 CMSPASTOP18012 
CMSPASTOP18012 
115  CMS Collaboration  Review of top quark mass measurements in CMS  Submitted to Phys. Rept., 2024  CMSTOP23003 2403.01313 
116  A. Martin  Toponium physics  in Quarks, Leptons, and Their Constituents, A. Zichichi, ed., Springer, 1988 link 

117  CMS Collaboration  HEPData record for this analysis  link 
Compact Muon Solenoid LHC, CERN 