Ascertaining higher-order quantum correlations in high energy physics

TL;DR

This work extends quantum nonlocality tests beyond first-order moments by introducing a cumulant-based framework for entangled hyperon–antihyperon pairs produced in charmonium decays. It formulates a generalized CH inequality and derives third-order skewness and fourth-order central-moment bounds, analyzing their violations in χ_{c0}/η_c → ΛΛ̄ and J/ψ → YȲ channels while accounting for timelike background. The results show robust third-order nonlocality signals in χ_{c0} decays and broader higher-order sensitivity in J/ψ channels, with the fourth-order moment hinting at contextuality-like behavior. Dynamical insights reveal that interference between electric and magnetic form factors governs entanglement strength, linking QCD dynamics to observable higher-order quantum correlations and enabling feasible tests at BESIII and Belle II.

Abstract

Nonlocality is a peculiar nature of quanta and it stands as an important quantum resource in application. Yet mere linear property of it, viz. the first order in moment, has been explored through various inequalities. Noticing the vast higher-order regime unexplored, in this study we investigate the higher-order quantum correlations in entangled hyperon-antihyperon system, which may be generated massively in charmonium decays. A new type of Clauser-Horne inequality for statistical cumulants and central moments is formulated. We find that a significant violation of the third-order constraint, indicating the existence of higher-order correlation, exists in hyperon-antihyperon system and can be observed in high energy physics experiments, like BESIII and Belle II. Notably, the violation manifests more in higher energy systems of the $Λ\barΛ$ pair against the kinematic contamination of timelike events.

Figures (6)

• Figure 1: Violation of the modified CH inequality \ref{['eq:modifiedCH']} for the process $\chi_{c0}/\eta_c \to \Lambda\bar{\Lambda}$. The solid blue curve represents the quantum mechanical prediction for the spin-singlet state. The horizontal brown dot-dashed and dashed lines correspond to the upper and lower bounds in \ref{['eq:modifiedCH']} for $\chi_{c0}$, while the orange dot-dashed and dashed lines correspond to $\eta_c$. The black dashed line symbolizes the classical lower bound ($-\alpha_\Lambda^2$) in \ref{['lemma:CH']}.
• Figure 2: Violation of the third-order cumulant criteria from \ref{['theorem:CHcumulant']} and \ref{['corollary:hyperonCHcumulant']} for the processes $\chi_{c0}/\eta_c \to \Lambda\bar{\Lambda}$. The solid blue curve represent the quantum prediction for the spin-singlet state in $\chi_{c0}/\eta_c$ decay. The horizontal orange and brown dot-dashed line symbolize the upper bounds in \ref{['corollary:hyperonCHcumulant']} for $\eta_c$ and $\chi_{c0}$ channels, respectively. The black dashed line indicates the classical upper bound defined in \ref{['theorem:CHcumulant']}.
• Figure 3: Maximum value of $\langle\mathcal{B}_{\mathrm{CH}}\rangle$ versus scattering angle $\theta$ for $\Lambda\bar{\Lambda}$ (blue solid) and $\Sigma^+\bar{\Sigma}^-$ (brown solid) in $J/\psi$ decays. The classical upper bound ($0$) in \ref{['eq:CHhyperon']} is marked by the black line, while the modified upper bounds defined in \ref{['eq:modifiedCH']} are shown as dashed lines. Although the quantum predictions violate the former bound, they remain within the modified bounds across the entire range in terms of scattering angle.
• Figure 4: Third-order cumulant $\kappa_3(\mathcal{B}_{\text{CH}})$ versus scattering angle $\vartheta$ for entangled $\Sigma^+\bar{\Sigma}^-$ and $\Lambda\bar{\Lambda}$ pairs produced in $J/\psi$ decays. The solid blue and brown curves represent the quantum predictions for $\Lambda\bar{\Lambda}$ and $\Sigma^+\bar{\Sigma}^-$, respectively. The horizontal dot-dashed lines indicate the modified upper bounds from \ref{['corollary:hyperonCHcumulant']}, while the dashed lines represent the upper bounds defined in \ref{['theorem:CHcumulant']} for $\Lambda\bar{\Lambda}$ (orange) and $\Sigma^+\bar{\Sigma}^-$ (brown).
• Figure 5: Fourth-order central moment $\mu_4$ versus scanning angle $\phi$ for chi-c0/eta-c to Lambda Lambda-bar decays. The quantum prediction is shown as a solid blue curve. The classical bound from \ref{['eq:idealfourthCentrbound']} is indicated by the black dashed line, while the timelike-modified bounds from \ref{['eq:modifiedfourthCentrbound']} for chi-c0 and eta-c are depicted by dot-dashed lines. Shaded regions highlight the violations of these classical limits.

Theorems & Definitions (5)

• Proposition 1
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4