Momentum Entanglement in High-Energy Colliders: Beyond Spin-Based Bell Tests

Current collider Bell tests (e.g., Ruzi et al., Wu et al., Fabbrichesi et al. in "Conflict" sources) focus exclusively on spin entanglement of particles like Z bosons or top quarks. However, quantum field theory predicts entanglement in all degrees of freedom. We'll pioneer the study of momentum entanglement by analyzing angular and energy correlations in particle pairs (e.g., H→ZZ→4ℓ or tt̄ events). This is fundamentally different because momentum entanglement is less explored but could be more robust against decoherence. We'll develop new Bell-like inequalities tailored to continuous momentum variables, inspired by the CGLMP inequality used in spin tests. This challenges the current paradigm by showing that Bell violations aren't limited to spin but permeate all quantum correlations. If momentum entanglement is detected, it would provide a new window into quantum field theory and could lead to more sensitive tests of the Standard Model.

References:

1. Testing Bell inequalities and probing quantum entanglement at a muon collider. Alim Ruzi, Youpeng Wu, Ran Ding, Sitian Qian, A. Levin, Qiang Li (2024). Journal of High Energy Physics.
2. Testing Bell inequalities and probing quantum entanglement at CEPC. Youpeng Wu, Ruobing Jiang, Alim Ruzi, Yong-Boo Ban, Xueqing Yan, Qiang Li (2024). Physical Review D.
3. Bell inequalities and quantum entanglement in weak gauge boson production at the LHC and future colliders. M. Fabbrichesi, R. Floreanini, E. Gabrielli, L. Marzola (2023). The European Physical Journal C.