Measurements of polarization and spin correlation and observation of entanglement in top quark pairs using lepton+jets events from proton-proton collisions at $\sqrt{s}$ = 13 TeV

The CMS collaboration
CMS-TOP-23-007, 2024.

Abstract
Measurements of the polarization and spin correlation in top quark pairs ($\mathrm{t\bar{t}}$) are presented using events with a single electron or muon and jets in the final state. The measurements are based on proton-proton collision data from the LHC at $\sqrt{s}$ = 13 TeV collected by the CMS experiment, corresponding to an integrated luminosity of 138 fb$^{-1}$. All coefficients of the polarization vectors and the spin correlation matrix are extracted simultaneously by performing a binned likelihood fit to the data. The measurement is performed inclusively and in bins of additional observables, such as the mass of the $\mathrm{t\bar{t}}$ system and the top quark scattering angle in the $\mathrm{t\bar{t}}$ rest frame. The measured polarization and spin correlation are in agreement with the standard model. From the measured spin correlation, conclusions on the $\mathrm{t\bar{t}}$ spin entanglement are drawn by applying the Peres-Horodecki criterion. The standard model predicts entangled spins for $\mathrm{t\bar{t}}$ states at the production threshold and at high masses of the $\mathrm{t\bar{t}}$ system. Entanglement is observed for the first time in events at high $\mathrm{t\bar{t}}$ mass, where a large fraction of the $\mathrm{t\bar{t}}$ decays are space-like separated, with an expected and observed significance of above 5 standard deviations.

  • Results for full matrix inclusive from m(tt)

    Figure 17, upper panel

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    Results for full matrix measurement inclusive from $m(t\bar{t})$

  • Covariance for full matrix inclusive from m(tt)

    Figure 23, supplementary material

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    Covariance for full matrix measurement inclusive from $m(t\bar{t})$

  • Results for full matrix fine bins from m(tt)

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    Results for full matrix measurement all bins from $m(t\bar{t})$ fit

  • Covariance for full matrix fine bins from m(tt)

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    Covariance for full matrix measurement all bins from $m(t\bar{t})$ fit

  • Results for full matrix inclusive from p_T(t)

    Figure 17, lower panel

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    Results for full matrix measurement inclusive from $p_{T}(t)$

  • Covariance for full matrix inclusive from p_T(t)

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    Covariance for full matrix measurement inclusive from $p_{T}(t)$

  • Results for full matrix fine bins from p_T(t)

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    Results for full matrix measurement all bins from $p_{T}(t)$ fit

  • Covariance for full matrix fine bins from p_T(t)

    10.17182/hepdata.153301.v1/t8

    Covariance for full matrix measurement all bins from $p_{T}(t)$ fit

  • Results for full matrix m(tt) differential

    Figures 19-20

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    Results for full matrix measurement differential in $m(t\bar{t})$

  • Covariance for full matrix m(tt) differential

    10.17182/hepdata.153301.v1/t10

    Covariance for full matrix measurement differential in $m(t\bar{t})$

  • Results for full matrix m(tt) differential for cos<0.4

    Figures 25-26

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    Results for full matrix measurement differential in $m(t\bar{t})$ for $|cos(\theta)| < 0.4$

  • Covariance for full matrix m(tt) differential for cos<0.4

    10.17182/hepdata.153301.v1/t12

    Covariance for full matrix measurement differential in $m(t\bar{t})$ for $|cos(\theta)| < 0.4$

  • Results for full matrix p_T(t) differential

    Figures 21-22

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    Results for full matrix measurement differential in $p_{T}(t)$

  • Covariance for full matrix p_T(t) differential

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    Covariance for full matrix measurement differential in $p_{T}(t)$

  • Results for D inclusive from m(tt)

    Figure 19

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    Results for $D$ measurement inclusive from $m(t\bar{t})$

  • Covariance for D inclusive from m(tt)

    Example location

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    Covariance for $D$ measurement inclusive from $m(t\bar{t})$

  • Results for D inclusive from p_T(t)

    Figure 19

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    Results for $D$ measurement inclusive from $p_{T}(t)$

  • Covariance for D inclusive from p_T(t)

    Example location

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    Covariance for $D$ measurement inclusive from $p_{T}(t)$

  • Results for Dtilde inclusive from m(tt)

    Figure 19

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    Results for $\tilde{D}$ measurement inclusive in $m(t\bar{t})$

  • Covariance for Dtilde inclusive from m(tt)

    Example location

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    Covariance for $\tilde{D}$ measurement inclusive in $m(t\bar{t})$

  • Results for Dtilde inclusive from p_T(t)

    Figure 19

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    Results for $\tilde{D}$ measurement inclusive in $p_{T}(t)$

  • Covariance for Dtilde inclusive from p_T(t)

    Example location

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    Covariance for $\tilde{D}$ measurement inclusive in $p_{T}(t)$

  • Results for D in fine bins from m(tt)

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    Results for $D$ measurement all bins from from $m(t\bar{t})$ fit

  • Covariance for D in fine bins from m(tt)

    Example location

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    Covariance for $D$ measurement all bins from from $m(t\bar{t})$ fit

  • Results for D in fine bins from p_T(t)

    10.17182/hepdata.153301.v1/t25

    Results for $D$ measurement all bins from from $p_{T}(t)$ fit

  • Covariance for D in fine bins from p_T(t)

    Example location

    10.17182/hepdata.153301.v1/t26

    Covariance for $D$ measurement all bins from from $p_{T}(t)$ fit

  • Results for Dtilde in fine bins from m(tt)

    10.17182/hepdata.153301.v1/t27

    Results for $\tilde{D}$ measurement all bins from from $m(t\bar{t})$ fit

  • Covariance for Dtilde in fine bins from m(tt)

    Example location

    10.17182/hepdata.153301.v1/t28

    Covariance for $\tilde{D}$ measurement all bins from from $m(t\bar{t})$ fit

  • Results for Dtilde in fine bins from p_T(t)

    10.17182/hepdata.153301.v1/t29

    Results for $\tilde{D}$ measurement all bins from from $p_{T}(t)$ fit

  • Covariance for Dtilde in fine bins from p_T(t)

    Example location

    10.17182/hepdata.153301.v1/t30

    Covariance for $\tilde{D}$ measurement all bins from from $p_{T}(t)$ fit

  • Results for D differential in m(tt)

    Figure 23, upper left panel

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    Results for $D$ measurement differential in $m(t\bar{t})$

  • Covariance for D differential in m(tt)

    Example location

    10.17182/hepdata.153301.v1/t32

    Covariance for $D$ measurement differential in $m(t\bar{t})$

  • Results for Dtilde differential in m(tt)

    Figure 23, lower left panel

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    Results for $\tilde{D}$ measurement differential in $m(t\bar{t})$

  • Covariance for Dtilde differential in m(tt)

    Example location

    10.17182/hepdata.153301.v1/t34

    Covariance for $\tilde{D}$ measurement differential in $m(t\bar{t})$

  • Results for Dtilde m(tt) differential for cos<0.4

    Figure 27

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    Results for $\tilde{D}$ measurement differential in $m(t\bar{t})$ for $|cos(\theta)| < 0.4$

  • Covariance for Dtilde m(tt) differential for cos<0.4

    Example location

    10.17182/hepdata.153301.v1/t36

    Covariance for $\tilde{D}$ measurement differential in $m(t\bar{t})$ for $|cos(\theta)| < 0.4$

  • Results for D differential in p_T(t)

    Figure 23, upper right panel

    10.17182/hepdata.153301.v1/t37

    Results for $D$ measurement differential in $p_{T}(t)$

  • Covariance for D differential in p_T(t)

    Example location

    10.17182/hepdata.153301.v1/t38

    Covariance for $D$ measurement differential in $p_{T}(t)$

  • Results for Dtilde differential in p_T(t)

    Figure 23, lower right panel

    10.17182/hepdata.153301.v1/t39

    Results for $\tilde{D}$ measurement differential in $p_{T}(t)$

  • Covariance for Dtilde differential in p_T(t)

    Example location

    10.17182/hepdata.153301.v1/t40

    Covariance for $\tilde{D}$ measurement differential in $p_{T}(t)$

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