CMSTOP23001 ; CERNEP2024137  
Observation of quantum entanglement in top quark pair production in protonproton collisions at $ \sqrt{s}= $ 13 TeV  
CMS Collaboration  
6 June 2024  
Submitted to Reports on Progress in Physics  
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 ; 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. 
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