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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

The CMS collaboration
Hayrapetyan, Aram , Makarenko, Vladimir , Tumasyan, Armen , Adam, Wolfgang , Benato, Lisa , Bergauer, Thomas , Dragicevic, Marko , Hussain, Priya Sajid , Jeitler, Manfred , Krammer, Natascha
CMS-TOP-25-016, 2025.
https://doi.org/10.17182/hepdata.166080.v1

Abstract
Measurements of the spin correlation coefficients in the beam basis are presented for top quark-antiquark ($\mathrm{t\bar{t}}$) 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 $\mathrm{t\bar{t}}$ 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 $\mathrm{t\bar{t}}$ quantum state, such as the purity, von Neumann entropy, and entanglement. All results are consistent with standard model predictions.

  • Measured spin correlation coeffs - beam basis - m(ttbar)

    Figure 1, left

    10.17182/hepdata.166080.v1/t1

    Measured spin correlation coefficients in beam basis for $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Covariance for spin correlation coeffs - beam basis - m(ttbar)

    10.17182/hepdata.166080.v1/t2

    Covariance for spin correlation coefficients in beam basis for $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Measured spin correlation coeffs - beam basis - pT(t)

    Figure 1, right

    10.17182/hepdata.166080.v1/t3

    Measured spin correlation coefficients in beam basis for $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Covariance for spin correlation coeffs - beam basis - pT(t)

    10.17182/hepdata.166080.v1/t4

    Covariance for spin correlation coefficients in beam basis for $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for Phi+ - helicity basis - m(ttbar)

    Figure 2, left, first panel

    10.17182/hepdata.166080.v1/t5

    Results for Eigenstate decomposition for $|\Phi^{+} \rangle$ in Helicity basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for Phi- - helicity basis - m(ttbar)

    Figure 2, left, second panel

    10.17182/hepdata.166080.v1/t6

    Results for Eigenstate decomposition for $|\Phi^{-} \rangle$ in Helicity basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for Psi+ - helicity basis - m(ttbar)

    Figure 2, left, third panel

    10.17182/hepdata.166080.v1/t7

    Results for Eigenstate decomposition for $|\Psi^{+} \rangle$ in Helicity basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for Psi- - helicity basis - m(ttbar)

    Figure 2, left, fourth panel

    10.17182/hepdata.166080.v1/t8

    Results for Eigenstate decomposition for $|\Psi^{-} \rangle$ in Helicity basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for up-up - beam basis - m(ttbar)

    Figure 2, right, first panel

    10.17182/hepdata.166080.v1/t9

    Results for Eigenstate decomposition for $|\uparrow \uparrow \rangle$ in Beam basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for down-down - beam basis - m(ttbar)

    Figure 2, right, second panel

    10.17182/hepdata.166080.v1/t10

    Results for Eigenstate decomposition for $|\downarrow \downarrow \rangle$ in Beam basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for Psi+ - beam basis - m(ttbar)

    Figure 2, right, third panel

    10.17182/hepdata.166080.v1/t11

    Results for Eigenstate decomposition for $|\Psi^{+} \rangle$ in Beam basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for Psi- - beam basis - m(ttbar)

    Figure 2, right, fourth panel

    10.17182/hepdata.166080.v1/t12

    Results for Eigenstate decomposition for $|\Psi^{-} \rangle$ in Beam basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Purity - helicity basis - m(ttbar)

    Figure 3, upper left

    10.17182/hepdata.166080.v1/t13

    Results for Purity in Helicity basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Purity - beam basis - m(ttbar)

    Figure 3, upper right

    10.17182/hepdata.166080.v1/t14

    Results for Purity in Beam basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Entropy - helicity basis - m(ttbar)

    Figure 3, lower left

    10.17182/hepdata.166080.v1/t15

    Results for Entropy in Helicity basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Entropy - beam basis - m(ttbar)

    Figure 3, lower right

    10.17182/hepdata.166080.v1/t16

    Results for Entropy in Beam basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Entanglement - helicity basis - m(ttbar)

    Figure 4, left

    10.17182/hepdata.166080.v1/t17

    Results for Entanglement in Helicity basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Entanglement - beam basis - m(ttbar)

    Figure 4, right

    10.17182/hepdata.166080.v1/t18

    Results for Entanglement in Beam basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for Phi+ - helicity basis - pT(t)

    10.17182/hepdata.166080.v1/t19

    Results for Eigenstate decomposition for $|\Phi^{+} \rangle$ in Helicity basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for Phi- - helicity basis - pT(t)

    10.17182/hepdata.166080.v1/t20

    Results for Eigenstate decomposition for $|\Phi^{-} \rangle$ in Helicity basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for Psi+ - helicity basis - pT(t)

    10.17182/hepdata.166080.v1/t21

    Results for Eigenstate decomposition for $|\Psi^{+} \rangle$ in Helicity basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for Psi- - helicity basis - pT(t)

    10.17182/hepdata.166080.v1/t22

    Results for Eigenstate decomposition for $|\Psi^{-} \rangle$ in Helicity basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for up-up - beam basis - pT(t)

    10.17182/hepdata.166080.v1/t23

    Results for Eigenstate decomposition for $|\uparrow \uparrow \rangle$ in Beam basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for down-down - beam basis - pT(t)

    10.17182/hepdata.166080.v1/t24

    Results for Eigenstate decomposition for $|\downarrow \downarrow \rangle$ in Beam basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for Psi+ - beam basis - pT(t)

    10.17182/hepdata.166080.v1/t25

    Results for Eigenstate decomposition for $|\Psi^{+} \rangle$ in Beam basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Eigenstate decomp for Psi- - beam basis - pT(t)

    10.17182/hepdata.166080.v1/t26

    Results for Eigenstate decomposition for $|\Psi^{-} \rangle$ in Beam basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Purity - helicity basis - pT(t)

    10.17182/hepdata.166080.v1/t27

    Results for Purity in Helicity basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Purity - beam basis - pT(t)

    10.17182/hepdata.166080.v1/t28

    Results for Purity in Beam basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Entropy - helicity basis - pT(t)

    10.17182/hepdata.166080.v1/t29

    Results for Entropy in Helicity basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Entropy - beam basis - pT(t)

    10.17182/hepdata.166080.v1/t30

    Results for Entropy in Beam basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Entanglement - helicity basis - pT(t)

    10.17182/hepdata.166080.v1/t31

    Results for Entanglement in Helicity basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

  • Entanglement - beam basis - pT(t)

    10.17182/hepdata.166080.v1/t32

    Results for Entanglement in Beam basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

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