{"paper":{"title":"Determining the Spin-Analyzing Powers via Invariants of the Spin Correlation Matrices and Probing the Bell Non-Locality at the Lepton Colliders","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The trace of the spin correlation matrix is invariant under basis rotations in two-fermion production at lepton colliders.","cross_cats":["hep-ex","hep-th"],"primary_cat":"hep-ph","authors_text":"Dianwei Wang, Lina Wu, Liwei Liu, Tianjun Li, Xiqing Hao","submitted_at":"2026-05-13T09:34:03Z","abstract_excerpt":"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. Wi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that the trace 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 Fa Fb via Tr [C], and reconstruct the spin correlation matrix.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"With the assumption that the spin is defined via the Lorentz symmetry, or considering the implicit symmetry in the spin density matrix.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Tr[C] is an invariant of the spin correlation matrix that determines the product of spin-analyzing powers for fermion pairs from single-mediator exchange at lepton colliders and enables Bell non-locality probes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The trace of the spin correlation matrix is invariant under basis rotations in two-fermion production at lepton colliders.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"584079ce01d2f6be006037b0d82b17df0ddef9e62296a6aa50a642c473d2e87b"},"source":{"id":"2605.13250","kind":"arxiv","version":1},"verdict":{"id":"a330ef75-6d61-497f-a123-257d494e4815","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:22:50.048856Z","strongest_claim":"We prove that the trace 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 Fa Fb via Tr [C], and reconstruct the spin correlation matrix.","one_line_summary":"Tr[C] is an invariant of the spin correlation matrix that determines the product of spin-analyzing powers for fermion pairs from single-mediator exchange at lepton colliders and enables Bell non-locality probes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"With the assumption that the spin is defined via the Lorentz symmetry, or considering the implicit symmetry in the spin density matrix.","pith_extraction_headline":"The trace of the spin correlation matrix is invariant under basis rotations in two-fermion production at lepton colliders."},"references":{"count":140,"sample":[{"doi":"","year":null,"title":"A LHVT with a set of local hidden variables","work_id":"e6102668-fdb7-474d-b7f8-0c0cc6cdbce4","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Special relativity and Poincar´ e-invariance hold","work_id":"8ff60308-afc9-40f5-a3cd-f435707d175e","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"The decays ofF a andF b are independent of each other. 3","work_id":"6401c16c-d254-4750-91b0-22a62c00a1fc","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"And thus the spins play the role of hidden variables","work_id":"1f7ed765-960e-4eea-9cf3-678ceaa10c44","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"With these assumptions, we can obtain the same rela- tions as given in Eq","work_id":"f4d8d7bc-1219-4a01-9738-8ab435d53116","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":140,"snapshot_sha256":"6a2b39637e1c5452b1d7050ce8e642b54dca9b67f4899201822e59355ffd3afa","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}