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

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.

Comments: 32 pages, 5 figures, journal version