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| CMS-PAS-TOP-23-001 | ||
| Probing entanglement in top quark production with the CMS detector | ||
| CMS Collaboration | ||
| 27 March 2024 | ||
| Abstract: Entanglement is an intrinsic property of quantum mechanics and its measurement probes the current understanding of the underlying quantum nature of elementary particles at a fundamental level. A measurement of the extent of entanglement in top quark-antiquark ($ \mathrm{t\bar{t}} $) events produced in proton-proton collisions at a center-of-mass energy of 13 TeV is performed on the data recorded by the CMS experiment at the CERN LHC in 2016, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The events are selected based on the presence of two oppositely charged high transverse momentum leptons. An entanglement-sensitive observable $ D $ is derived from the top quark spin-dependent parts of the $ \mathrm{t\bar{t}} $ production density matrix. Values of $ D $ smaller than $ -$1/3 are evidence of entanglement and, within a particular phase space, $ D $ is measured to be $-$0.478 $ ^{+0.025}_{-0.027} $. With an expected (observed) significance of 5.1 (5.7) standard deviations, this provides observation for quantum mechanical entanglement within $ \mathrm{t\bar{t}} $ pairs in this phase space. This measurement provides a new quantum probe of the inner workings of the standard model at the highest energy ever tested. | ||
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Links:
CDS record (PDF) ;
Physics Briefing ;
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These preliminary results are superseded in this paper, Submitted to ROPP. The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1:
Subfigure (a) shows the Feynman diagram for the leading order QCD gluon-gluon fusion process and (b) shows the quark-antiquark fusion process for top quark pair production. |
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Figure 2:
Predicted values of $ -(1 + \Delta)/ 3 $ (see Eq. (4)) obtained from calculations of the $ \mathrm{t} \overline{\mathrm{t}} $ production cross section [7], without accounting for detector effects, are shown as a function of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ and the top quark scattering angle $ \Theta $ for the gluon-gluon fusion production. The black solid lines represent the $ D= -1/ 3$ boundary for entanglement while the black dashed line corresponds to $ m({\mathrm{t}\overline{\mathrm{t}}} )= $ 400 GeV. The minimum value on the z axis corresponds to the boundary below which $ \Delta = tr[\mathbf{C}] - 1$. Top quarks with no spin correlations correspond to a value of 0. |
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Figure 3:
Reconstruction-level $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ (left) and $ p_{\mathrm{T}}(\mathrm{t}/\overline{\mathrm{t}}) $ (right) distributions of the combined signal model in the full phase space comparing the modeling of the data by MC when not including $ \eta_{\mathrm{t}} $ (red line in upper ratio pad), no $ p_{\mathrm{T}}(\mathrm{t}/\overline{\mathrm{t}}) $ reweighting is applied (blue line in upper ratio pad), or neither of those (pink line in upper ratio pad). The lower ratio pad compares the data to POWHEGV2+HERWIG (pink line in lower ratio pad), to MG5_AMC@NLO (FXFX)+PYTHIA8 (blue line in lower ratio pad), and finally to the nominal MC including $ \eta_{\mathrm{t}} $ and $ p_{\mathrm{T}}(\mathrm{t}/\overline{\mathrm{t}}) $ reweighting (green line in lower ratio pad). |
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Figure 3-a:
Reconstruction-level $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ (left) and $ p_{\mathrm{T}}(\mathrm{t}/\overline{\mathrm{t}}) $ (right) distributions of the combined signal model in the full phase space comparing the modeling of the data by MC when not including $ \eta_{\mathrm{t}} $ (red line in upper ratio pad), no $ p_{\mathrm{T}}(\mathrm{t}/\overline{\mathrm{t}}) $ reweighting is applied (blue line in upper ratio pad), or neither of those (pink line in upper ratio pad). The lower ratio pad compares the data to POWHEGV2+HERWIG (pink line in lower ratio pad), to MG5_AMC@NLO (FXFX)+PYTHIA8 (blue line in lower ratio pad), and finally to the nominal MC including $ \eta_{\mathrm{t}} $ and $ p_{\mathrm{T}}(\mathrm{t}/\overline{\mathrm{t}}) $ reweighting (green line in lower ratio pad). |
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Figure 3-b:
Reconstruction-level $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ (left) and $ p_{\mathrm{T}}(\mathrm{t}/\overline{\mathrm{t}}) $ (right) distributions of the combined signal model in the full phase space comparing the modeling of the data by MC when not including $ \eta_{\mathrm{t}} $ (red line in upper ratio pad), no $ p_{\mathrm{T}}(\mathrm{t}/\overline{\mathrm{t}}) $ reweighting is applied (blue line in upper ratio pad), or neither of those (pink line in upper ratio pad). The lower ratio pad compares the data to POWHEGV2+HERWIG (pink line in lower ratio pad), to MG5_AMC@NLO (FXFX)+PYTHIA8 (blue line in lower ratio pad), and finally to the nominal MC including $ \eta_{\mathrm{t}} $ and $ p_{\mathrm{T}}(\mathrm{t}/\overline{\mathrm{t}}) $ reweighting (green line in lower ratio pad). |
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Figure 4:
Reconstruction-level distribution (left) of $ \cos \varphi $ with 345 $ < m({\mathrm{t}\overline{\mathrm{t}}} ) < $ 400 GeV and 0.0 $ < \beta < $ 0.9. On the right, the $ p_{\mathrm{T}}(\mathrm{t}/\overline{\mathrm{t}}) $ distributions is shown with the same model comparison as was done in Fig. 3. |
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Figure 4-a:
Reconstruction-level distribution (left) of $ \cos \varphi $ with 345 $ < m({\mathrm{t}\overline{\mathrm{t}}} ) < $ 400 GeV and 0.0 $ < \beta < $ 0.9. On the right, the $ p_{\mathrm{T}}(\mathrm{t}/\overline{\mathrm{t}}) $ distributions is shown with the same model comparison as was done in Fig. 3. |
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Figure 4-b:
Reconstruction-level distribution (left) of $ \cos \varphi $ with 345 $ < m({\mathrm{t}\overline{\mathrm{t}}} ) < $ 400 GeV and 0.0 $ < \beta < $ 0.9. On the right, the $ p_{\mathrm{T}}(\mathrm{t}/\overline{\mathrm{t}}) $ distributions is shown with the same model comparison as was done in Fig. 3. |
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Figure 5:
Reconstruction-level distribution (top) of the combined $ \mathrm{t} \overline{\mathrm{t}} $ + $ \eta_{\mathrm{t}} $ signal model in mixtures of the noSC combined signal sample, more details in the text. Template variations are shown as a function of $ \cos \varphi $ in the phase space of 345 $ < m({\mathrm{t}\overline{\mathrm{t}}} ) < $ 400 GeV and 0.0 $ < \beta < $ 0.9 for a $+$50% mixture of SC and noSC (bottom left) and a $-$50% mixture (bottom right). |
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Figure 5-a:
Reconstruction-level distribution (top) of the combined $ \mathrm{t} \overline{\mathrm{t}} $ + $ \eta_{\mathrm{t}} $ signal model in mixtures of the noSC combined signal sample, more details in the text. Template variations are shown as a function of $ \cos \varphi $ in the phase space of 345 $ < m({\mathrm{t}\overline{\mathrm{t}}} ) < $ 400 GeV and 0.0 $ < \beta < $ 0.9 for a $+$50% mixture of SC and noSC (bottom left) and a $-$50% mixture (bottom right). |
png pdf |
Figure 5-b:
Reconstruction-level distribution (top) of the combined $ \mathrm{t} \overline{\mathrm{t}} $ + $ \eta_{\mathrm{t}} $ signal model in mixtures of the noSC combined signal sample, more details in the text. Template variations are shown as a function of $ \cos \varphi $ in the phase space of 345 $ < m({\mathrm{t}\overline{\mathrm{t}}} ) < $ 400 GeV and 0.0 $ < \beta < $ 0.9 for a $+$50% mixture of SC and noSC (bottom left) and a $-$50% mixture (bottom right). |
png pdf |
Figure 5-c:
Reconstruction-level distribution (top) of the combined $ \mathrm{t} \overline{\mathrm{t}} $ + $ \eta_{\mathrm{t}} $ signal model in mixtures of the noSC combined signal sample, more details in the text. Template variations are shown as a function of $ \cos \varphi $ in the phase space of 345 $ < m({\mathrm{t}\overline{\mathrm{t}}} ) < $ 400 GeV and 0.0 $ < \beta < $ 0.9 for a $+$50% mixture of SC and noSC (bottom left) and a $-$50% mixture (bottom right). |
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Figure 6:
Postfit detector level distribution of $ \cos \varphi \otimes m({\mathrm{t}\overline{\mathrm{t}}} ) $ for 345 $ < m({\mathrm{t}\overline{\mathrm{t}}} ) < $ 400 GeV and 0.0 $ < \beta < $ 0.9. |
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Figure 7:
Result of the scan of the quantity $ -2\ln L $ resulting from a maximum likelihood fit as a function of the parameter of interest, $ D $. The region where entanglement is not implied ($ D > -1/ $ 3) is indicated by the pink shading. |
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Figure 8:
Summary of the measurement of the entanglement proxy $ D $ compared with the SM expectations including (filled) or not including (open) contributions from the hypothetical toponium state. |
| Tables | |
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Table 1:
The number of observed and predicted events categorized into signal and background contributions. All selection requirements are applied, i.e., the final event yield includes all requirements. Finally, we also apply an electroweak correction to the MC signal samples of $ \mathrm{t} \overline{\mathrm{t}} $ and $ \eta_{\mathrm{t}} $. The uncertainties reflect those originating from the limited MC sample size. The ``Only $ \eta_{\mathrm{t}} $" contribution is not added to the total MC prediction since it is included in the combined signal contribution. |
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Table 2:
The number of predicted and observed events in the finally selected phase space, before the fit to the data (pre-fit) and with their best fit normalizations (post-fit). The uncertainties in the pre-fit yields originate from limited MC statistics, while for the uncertainties of post-fit yields total uncertainties including systematic ones are provided (but without correlations). Please note that the ``Only $ \eta_{\mathrm{t}} $" contribution is not added to the total MC prediction since it is included in the combined signal contribution. |
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Table 3:
Breakdown into leading ten systematic uncertainties in the entanglement proxy $ D $ at the postfit level. |
| Summary |
| A measurement of the entanglement of top quark pairs $ \mathrm{t} \overline{\mathrm{t}} $ utilizing the spin correlation variable $ D $ is presented. This entanglement proxy is measured using events containing two oppositely charged leptons (including semileptonic decays of $ \tau $ leptons) produced in proton-proton collisions at a center-of-mass energy of 13 TeV. The extent to which top quarks are entangled is measured by means of a binned profile likelihood fit of the parameter of interest $ D $ from the distribution of $ \cos\varphi $ in the most sensitive kinematic phase space of 345 $ < m({\mathrm{t}\overline{\mathrm{t}}} ) < $ 400 GeV and 0.0 $ < \beta < $ 0.9. The value of the entanglement proxy $ D $ itself is measured by a negative log-likelihood scan of the parameter of interest $ D $ and yields an expected value of $ D = -$0.465 $ ^{+0.025}_{-0.028} $ and an observed value of $ D = -$0.478 $ ^{+0.025}_{-0.027} $. This result has an expected (observed) significance of 5.1 (5.7) standard deviations, corresponding to the observation of top quark entanglement. This measurement with CMS data of the quantum mechanics phenomena of entanglement present in top quark events provides a new and fundamental probe to beyond the standard model contributions and represents a first step towards quantum tomography and coherence in top quark events. |
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