Local vs. nonlocal entanglement in top-quark pairs at the LHC

Abstract

We show that the entanglement observed in top-antitop quark spin states at the LHC is local in the energy region close to the production threshold. In contrast, nonlocal entanglement is observed in the central boosted region defined by a top-quark pair invariant mass $m_{t\bar t} > 800$ GeV and scattering angles $Θ$ satisfying $|\cos Θ|<0.2$. This makes top-quark pairs a unique laboratory for studying the interplay between entanglement and Bell locality. The locality of entanglement near the production threshold is further supported by a recent CMS analysis, which reports a significance of more than $5σ$. We also demonstrate that there exists a kinematic region where the spin states of the top-antitop quark are separable, yet they exhibit non-zero discord and magic.

Figures (5)

• Figure 1: Parton luminosities $L^{gg} (\tau)$ and $L^{q\bar{q}} (\tau)$ in the range of invariant mass of interest. At threshold the ratio $L^{gg} (\tau)/L^{q\bar{q}} (\tau)$ is about 9.
• Figure 2: The behavior of the concurrence, $\mathscr{C}[\rho]$, and of the Horodecki parameter $\mathfrak{m}_{12}[\operatorname{C}]$ over the considered kinematic space. The white, dashed line marks the $\mathfrak{m}_{12}[\operatorname{C}]=1$ contour, above which the condition for Bell nonlocality is satisfied. The hatched areas denote two of the bins used by the CMS collaboration in their data analysis CMS:2024zkc.
• Figure 3: Enlarged view of concurrence $\mathscr{C}[\rho]$ and $\mathfrak{m}_{12}[\operatorname{C}]$ parameter in the threshold bin defined by the invariant mass $340 < m_{t\bar{t}} < 400$. The white, dashed lines mark the Horodecki condition for Bell nonlocality, in the lower panel, and a vanishing concurrence in the upper one.
• Figure 4: Concurrence $\mathscr{C}[\rho]$ and discord $\mathcal{D}[\rho]$ in the intermediate bin $400 < m_{t\bar{t}}<600$ GeV. The reddish region between the white dashed-lines, in the concurrence plot on top, contains separable states for which the concurrence (and the negativity) vanish. On the other hand, the plot below shows non-vanishing values of the discord in the same kinematic region.
• Figure 5: Magic $\mathscr{M}[\rho]$ of the top-quark pairs produced at the LHC in the intermediate region $400 < m_{t\bar{t}}<600$ GeV.