Spin correlations and Bell nonlocality in $Λ\barΛ$ pair production from $e^+e^-$ collisions with a thrust cut

TL;DR

This work develops a state-of-the-art theoretical framework for spin correlations in $e^+e^- o ext{Λ}ar{ ext{Λ}}X$ with a thrust cut, employing soft-collinear effective theory to achieve NNLL resummation and introducing polarized fragmenting jet functions. By combining SCET factorization, RG evolution, and the density-matrix formalism, the authors provide robust predictions for the longitudinal and transverse spin correlations $C_{LL}$ and $C_{TT}$, and map $C_{TT}$ onto a testable CHSH-Bell parameter to quantify decoherence from fragmentation. They explore the impact of polarized fragmentation functions through multiple models, revealing that $C_{LL}$ is sensitive to flavor structure while $C_{TT}$ provides a direct handle on entanglement survival, albeit with significant decoherence from QCD dynamics. A key novelty is the direct link between high-energy spin observables and quantum-information concepts, offering a quantitative framework to study quantum decoherence in hadronization with practical implications for Belle II and future facilities. Overall, the work delivers a rigorous, predictive toolkit for precision QCD spin phenomenology and opens avenues to probe fundamental quantum aspects of the strong interaction.

Abstract

We present a comprehensive theoretical study of spin correlations in $Λ\barΛ$ production from $e^+e^-$ annihilation, providing the theoretical predictions for the Belle II experiment. Using soft-collinear effective theory, we perform the first resummation of large logarithms for the longitudinal ($C_{LL}$) and transverse ($C_{TT}$) spin correlations for events with a cut on the thrust variable. Our calculation achieves next-to-next-to-leading logarithmic accuracy and incorporates the determination of polarized fragmenting jet functions. This framework provides robust predictions with significantly reduced theoretical uncertainties compared to fixed-order parton model approaches. Furthermore, we establish a direct mapping between the experimentally accessible spin correlation, $C_{TT}$, and a testable CHSH-Bell inequality. This result reframes $C_{TT}$ as a quantitative probe of quantum decoherence, providing a novel tool to measure the degree of parton-level entanglement that survives the fragmentation and hadronization process.

Figures (7)

• Figure 1: Kinematic configuration for $e^+e^- \to \Lambda\bar{\Lambda} X$. The transverse spin vectors $\boldsymbol{S}_T^{\Lambda}$ and $\boldsymbol{S}_T^{\bar{\Lambda}}$ have azimuthal angles $\phi_{S_1}$ and $\phi_{S_2}$ in the lab frame. The electron-positron collision axis is oriented at an angle $\theta$ relative to the $z$-axis.
• Figure 2: Resummed cross sections for $\Lambda\bar{\Lambda}$ production integrated up to $\tau_{\text{cut}}=0.2$, showing the unpolarized (a, d), longitudinally polarized (b, e), and transversely polarized (c, f) components. The left panels show results for $Q=10.58$ GeV, while the right panels are for $Q=100$ GeV. The wider, blue bands correspond to the NLL prediction, and the narrower, red bands represent the NNLL result. The black line represents the parton model (p.m.) result. The bands indicate the theoretical uncertainty from scale variations.
• Figure 4: The hadronic Bell variable $\mathcal{B}^{\Lambda \bar{\Lambda}}_+$ as a function of $z_{1,2}$. Panels (a) and (c) show contour plots of the theoretical upper limit from positivity bounds at $Q=10.58$ GeV and $100$ GeV, respectively, with $\theta=\pi/2$. The dashed line indicates the CHSH-Bell inequality violation threshold, $\mathcal{B}^{\Lambda \bar{\Lambda}}_+=\sqrt{2}$. Panels (b) and (d) display $\mathcal{B}_+^{\Lambda\bar{\Lambda}}$ as a function of $z_2$ at fixed $z_1=0.5$ and $Q=10.58$ GeV for the three FF scenarios. These panels compare the three FF models: Scenario 1 (magenta solid), Scenario 2 (teal dashed), and Scenario 3 (dark blue dotted). Panel (b) is evaluated at the partonic violation threshold ($\theta=\theta_0$ and $\mathcal{B}_+^{q\bar{q}}=\sqrt{2}$), while panel (d) is at the point of maximal partonic entanglement ($\theta=\pi/2$ and $\mathcal{B}_+^{q\bar{q}}=2$).
• Figure 5: Feynman diagram contributing to the one-loop FJF in the light-cone gauge.
• Figure : Longitudinal spin correlation $C_{LL}$