Excluding local hidden variables in Λ Λ production: the incompatibility with angular-momentum conservation and CPT invariance

2026/01/22 by Junle Pei, Lina Wu, Li‐Na Wu +2
Physics and Astronomy · Computer Science · #Quantum Chromodynamics and Particle Interactions #Quantum Information and Cryptography #Particle physics theoretical and experimental studies

paper · pdf · doi:10.1007/jhep07(2026)154

Abstract

A bstract We analyze spin entanglement in Λ Λ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> <mml:mover> <mml:mi>Λ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> pairs produced in the decays of spin-zero particles, contrasting predictions from quantum field theory (QFT) with those of local hidden-variable theories (LHVTs). Using the self-analyzing weak decays Λ → pπ − and Λ→ pπ⁺ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>Λ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>→</mml:mo> <mml:mover> <mml:mi>p</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:math> , we derive the joint angular distributions within QFT. Our key findings are: for scalar production h→ Λ Λ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>h</mml:mi> <mml:mo>→</mml:mo> <mml:mi>Λ</mml:mi> <mml:mover> <mml:mi>Λ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> , no LHVT respecting locality and angular-momentum conservation can reproduce the QFT distribution. For pseudoscalar production a→ Λ Λ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>a</mml:mi> <mml:mo>→</mml:mo> <mml:mi>Λ</mml:mi> <mml:mover> <mml:mi>Λ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> , a CPT-symmetric LHVT is excluded by positivity constraints given the measured analyzing powers; however, if CPT symmetry is relaxed, an explicit LHVT construction — with uniform hidden-variable measure and response functions satisfying b₁c₁=3α_Λα_Λ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>b</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:msub> <mml:mi>c</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>Λ</mml:mi> </mml:msub> <mml:msub> <mml:mi>α</mml:mi> <mml:mover> <mml:mi>Λ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:msub> </mml:math> — can match the QFT result. For the most general spin-zero decay s→ Λ Λ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>s</mml:mi> <mml:mo>→</mml:mo> <mml:mi>Λ</mml:mi> <mml:mover> <mml:mi>Λ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> with arbitrary scalar-pseudoscalar mixing, we, under CPT invariance, identify the regions of parameter space where the QFT joint angular distribution does or does not admit an LHVT realization. These distinct signatures provide clear, experimentally testable criteria to discriminate between QFT and LHVT in Λ Λ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> <mml:mover> <mml:mi>Λ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> systems across different production mechanisms.

Citations

• Observation of quantum entanglement in top quark pair production in proton–proton collisions at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>13</mml:mn></mml:mrow></mml:math> TeV
• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?

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