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arXiv:2605.13250

Determining the Spin-Analyzing Powers via Invariants of the Spin Correlation Matrices and Probing the Bell Non-Locality at the Lepton Colliders

Dianwei Wang, X. Q. Hao, Liwei Liu, Lina Wu, Tianjun Li

Published May 13, 2026• 0 citations
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Abstract

We consider the two-fermion $F_a F_b$ productions and decays via one mediator exchange at the $e^+e^-$ collider. With the assumption that the spin is defined via the Lorentz symmetry, or considering the implicit symmetry in the spin density matrix, we prove that the trace ${\rm Tr} [C]$ of the spin correlation matrix $C$ is an invariant quantity, and is invariant under basis rotations. Thus, for the exchanges of one mediator such as scalar and gauge boson, we can determine the product of the spin-analyzing powers for $F_a F_b$ via ${\rm Tr} [C]$, and reconstruct the spin correlation matrix. With the CHSH-Horodecki criterion, we can probe the Bell non-locality, and evade the no-go theorem. To be concrete, we study the Bell non-locality for the $Λ\bar Λ$ productions and decays at the BESIII experiment. In addition, the invariant ${\rm Tr} [C]$ is a new physics observable to probe the new physics beyond the Standard Model (SM) and study the SM precision measurements. Moreover, for the scalar exchanges, we discuss the general invariants of the spin correlation matrices and the related phenomenological consequences.

DOI
10.48550/arxiv.2605.13250

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A bstract We investigate the quantum properties of heavy-fermion pairs, such as tt‾ t\overline{t} tt t t ¯ or τ + τ − , produced in lepton-lepton collisions with polarised beams. Focusing on spin correlations, entanglement, Bell-inequality violation, and quantum-information-theoretic measures such as purity and magic, we analyse how beam polarisation shapes the structure of the spin-density matrix. We derive analytic expressions for a wide range of helicity configurations, including both Standard Model contributions and generic new physics effects parametrised by scalar, vector, and tensor four-fermion operators within an effective field theory framework. We show that beam polarisation unlocks a substantially richer set of spin configurations and significantly enhances sensitivity to non-standard interactions. As a phenomenological application, we study tt‾ t\overline{t} tt t t ¯ production at a future linear collider and demonstrate that quantum observables provide a comprehensive and complementary probe of top-quark interactions and stronger constraints on the scale of new physics.
For particles decaying without parity violation, it is impossible to reconstruct the full spin-density matrix from the velocities of their decay products. In this work, we consider Bell inequalities based on squares of spin operators. The corresponding Bell operators probe only the part of the density matrix that can be reconstructed from any gauge boson decay or splitting to fermions, which is accessible regardless of whether parity is violated. We find that our new choice of Bell operator has promising properties regarding states seen at colliders. In particular, it substantially outperforms the inequality previously used for the pp→ZZpp \rightarrow ZZpp→ZZ process at the LHC in terms of the phase space volume in which it is violated. We also conduct the first investigation of Bell violation in a system involving gauge bosons mediating different interactions, namely the WWW boson and gluon in the pp→W±(g→bbˉ)pp \rightarrow W^{\pm} (g\rightarrow b\bar{b})pp→W±(g→bbˉ) process.
It has been argued more than 30 years ago that it is not possible to test locality at colliders, due to the inability to directly measure non-commutating observables such as spin components in current collider experiments. Recently, there has been a lot of phenomenological and experimental activity around testing locality via Bell-type experiments or entanglement versus non-entanglement in a collider environment. These results seem to evade the earlier no-go theorem by indirectly measuring spin correlations via their relation to angular correlations between momenta. We perform a careful study of the feasibility of such an approach. We scrutinize the relationship between spin and angular correlations in both quantum mechanics and local hidden variable theories. Our conclusion is that it is currently not possible to perform a logically coherent set of experimental measurements at colliders that would allow one to test locality or entanglement versus non-entanglement. This reaffirms the earlier no-go theorem. We stress that the no-go theorem does not apply to measurements of observables inspired from entanglement and Quantum Information Theory to test the Standard Model of particle physics.