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| CMS-TOP-25-016 ; CERN-EP-2025-287 | ||
| Characterization of the quantum state of top quark pairs produced in proton-proton collisions at $ \sqrt{s}= $ 13 TeV using the beam and helicity bases | ||
| CMS Collaboration | ||
| 19 December 2025 | ||
| Submitted to Phys. Rev. D | ||
| Abstract: Measurements of the spin correlation coefficients in the beam basis are presented for top quark-antiquark ($ \mathrm{t} \overline{\mathrm{t}} $) systems produced in proton-proton collisions at $ \sqrt{s}= $ 13 TeV collected by the CMS experiment in 2016-2018, and corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The $ \mathrm{t} \overline{\mathrm{t}} $ system is reconstructed from final states containing an electron or muon, and jets. Together with the previously reported results in the helicity basis, these measurements are used to decompose the system into the Bell and spin eigenstates in various kinematic regions. The spin correlation coefficients are also used to evaluate properties of the $ \mathrm{t} \overline{\mathrm{t}} $ quantum state, such as the purity, von Neumann entropy, and entanglement. All results are consistent with standard model predictions. | ||
| Links: e-print arXiv:2512.17557 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Results of the spin correlation coefficients in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ vs. $ |\cos(\theta)| $ (left) and $ p_{\mathrm{T}}(\mathrm{t}) $ vs. $ |\cos(\theta)| $ (right) in the beam basis. The measurements (markers) are shown with the statistical (inner error bars) and total (outer error bars) uncertainties and compared to the predictions from POWHEG + HERWIG, MINNLO+ PYTHIA, and POWHEG + PYTHIA. The POWHEG + PYTHIA prediction is displayed with the ME scale and PDF uncertainties. |
png pdf |
Figure 1-a:
Results of the spin correlation coefficients in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ vs. $ |\cos(\theta)| $ (left) and $ p_{\mathrm{T}}(\mathrm{t}) $ vs. $ |\cos(\theta)| $ (right) in the beam basis. The measurements (markers) are shown with the statistical (inner error bars) and total (outer error bars) uncertainties and compared to the predictions from POWHEG + HERWIG, MINNLO+ PYTHIA, and POWHEG + PYTHIA. The POWHEG + PYTHIA prediction is displayed with the ME scale and PDF uncertainties. |
png pdf |
Figure 1-b:
Results of the spin correlation coefficients in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ vs. $ |\cos(\theta)| $ (left) and $ p_{\mathrm{T}}(\mathrm{t}) $ vs. $ |\cos(\theta)| $ (right) in the beam basis. The measurements (markers) are shown with the statistical (inner error bars) and total (outer error bars) uncertainties and compared to the predictions from POWHEG + HERWIG, MINNLO+ PYTHIA, and POWHEG + PYTHIA. The POWHEG + PYTHIA prediction is displayed with the ME scale and PDF uncertainties. |
png pdf |
Figure 2:
Results of the state decomposition in terms of the Bell and spin states in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ vs. $ |\cos(\theta)| $ in the helicity (left) and beam (right) basis. The measurements (markers) are shown with the statistical (inner error bars) and total (outer error bars) uncertainty and compared to the predictions from POWHEG + PYTHIA, and POWHEG + PYTHIA +{\HepParticle$ \eta \mathrm{t} $. The POWHEG + PYTHIA prediction is displayed with the ME scale and PDF uncertainties. |
png pdf |
Figure 2-a:
Results of the state decomposition in terms of the Bell and spin states in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ vs. $ |\cos(\theta)| $ in the helicity (left) and beam (right) basis. The measurements (markers) are shown with the statistical (inner error bars) and total (outer error bars) uncertainty and compared to the predictions from POWHEG + PYTHIA, and POWHEG + PYTHIA +{\HepParticle$ \eta \mathrm{t} $. The POWHEG + PYTHIA prediction is displayed with the ME scale and PDF uncertainties. |
png pdf |
Figure 2-b:
Results of the state decomposition in terms of the Bell and spin states in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ vs. $ |\cos(\theta)| $ in the helicity (left) and beam (right) basis. The measurements (markers) are shown with the statistical (inner error bars) and total (outer error bars) uncertainty and compared to the predictions from POWHEG + PYTHIA, and POWHEG + PYTHIA +{\HepParticle$ \eta \mathrm{t} $. The POWHEG + PYTHIA prediction is displayed with the ME scale and PDF uncertainties. |
png pdf |
Figure 3:
Results of the purity $ \gamma(\rho) $ (upper) and entropy $ S(\rho) $ (lower) measurements in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ vs. $ |\cos(\theta)| $ in the helicity (left) and beam (right) basis. The measurements (markers) are shown with the statistical (inner error bars) and total (outer error bars) uncertainty and compared to the predictions from POWHEG + PYTHIA, shown with the ME scale and PDF uncertainties. |
png pdf |
Figure 3-a:
Results of the purity $ \gamma(\rho) $ (upper) and entropy $ S(\rho) $ (lower) measurements in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ vs. $ |\cos(\theta)| $ in the helicity (left) and beam (right) basis. The measurements (markers) are shown with the statistical (inner error bars) and total (outer error bars) uncertainty and compared to the predictions from POWHEG + PYTHIA, shown with the ME scale and PDF uncertainties. |
png pdf |
Figure 3-b:
Results of the purity $ \gamma(\rho) $ (upper) and entropy $ S(\rho) $ (lower) measurements in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ vs. $ |\cos(\theta)| $ in the helicity (left) and beam (right) basis. The measurements (markers) are shown with the statistical (inner error bars) and total (outer error bars) uncertainty and compared to the predictions from POWHEG + PYTHIA, shown with the ME scale and PDF uncertainties. |
png pdf |
Figure 3-c:
Results of the purity $ \gamma(\rho) $ (upper) and entropy $ S(\rho) $ (lower) measurements in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ vs. $ |\cos(\theta)| $ in the helicity (left) and beam (right) basis. The measurements (markers) are shown with the statistical (inner error bars) and total (outer error bars) uncertainty and compared to the predictions from POWHEG + PYTHIA, shown with the ME scale and PDF uncertainties. |
png pdf |
Figure 3-d:
Results of the purity $ \gamma(\rho) $ (upper) and entropy $ S(\rho) $ (lower) measurements in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ vs. $ |\cos(\theta)| $ in the helicity (left) and beam (right) basis. The measurements (markers) are shown with the statistical (inner error bars) and total (outer error bars) uncertainty and compared to the predictions from POWHEG + PYTHIA, shown with the ME scale and PDF uncertainties. |
png pdf |
Figure 4:
Results of the entanglement marker $ \Delta_{\mathrm{E}} $ measurements in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ vs. $ |\cos(\theta)| $ in the helicity (left) and beam (right) basis. The measurements (markers) are shown with the statistical (inner error bars) and total (outer error bars) uncertainty and compared to the predictions from POWHEG + PYTHIA, shown with the ME scale and PDF uncertainties. The dashed green line represents the lower bound for entangled states. |
png pdf |
Figure 4-a:
Results of the entanglement marker $ \Delta_{\mathrm{E}} $ measurements in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ vs. $ |\cos(\theta)| $ in the helicity (left) and beam (right) basis. The measurements (markers) are shown with the statistical (inner error bars) and total (outer error bars) uncertainty and compared to the predictions from POWHEG + PYTHIA, shown with the ME scale and PDF uncertainties. The dashed green line represents the lower bound for entangled states. |
png pdf |
Figure 4-b:
Results of the entanglement marker $ \Delta_{\mathrm{E}} $ measurements in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ vs. $ |\cos(\theta)| $ in the helicity (left) and beam (right) basis. The measurements (markers) are shown with the statistical (inner error bars) and total (outer error bars) uncertainty and compared to the predictions from POWHEG + PYTHIA, shown with the ME scale and PDF uncertainties. The dashed green line represents the lower bound for entangled states. |
| Summary |
| In summary, the spin correlation measurements of the top quark-antiquark ($ \mathrm{t} \overline{\mathrm{t}} $) system from Ref. [8] are extended to include results in the beam basis for the first time. This is done with bins in two dimensions, comprising the top quark scattering angle and either the invariant mass of the $ \mathrm{t} \overline{\mathrm{t}} $ system or the transverse momentum of the top quark, using proton-proton collisions at $ \sqrt{s}= $ 13 TeV recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The density matrix is decomposed into eigenstates, which are identified as Bell states in the helicity basis and spin states in the beam basis. We also present the first experimental results for the purity, von Neumann entropy, and entanglement of the $ \mathrm{t} \overline{\mathrm{t}} $ system in both bases. All the measurements are consistent with standard model expectations. |
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