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

TL;DR

This paper develops a high-precision theoretical framework for analyzing spin correlations in $ ext{Lambda}ar{ ext{Lambda}}$ pairs from $e^+e^-$ collisions, enabling Bell inequality tests and insights into quantum entanglement in particle physics.

Contribution

It introduces the first resummation of large logarithms for spin correlations in $ ext{Lambda}ar{ ext{Lambda}}$ production, with next-to-next-to-leading accuracy, linking experimental measurements to quantum entanglement tests.

Findings

Resummation of large logarithms improves prediction accuracy.

Establishes a direct link between $C_{TT}$ and Bell inequality testing.

Provides a method to quantify quantum decoherence in hadronization.

Abstract

We present a comprehensive theoretical study of spin correlations in $\Lambda\bar{\Lambda}$ 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.