https://doi.org/10.1140/epjc/s10052-023-11935-8
Regular Article - Theoretical Physics
Bell inequalities and quantum entanglement in weak gauge boson production at the LHC and future colliders
1
Physics Department, University of Trieste, Strada Costiera 11, 34151, Trieste, Italy
2
INFN, Sezione di Trieste, Via Valerio 2, 34127, Trieste, Italy
3
NICPB, Ravala 10, 10143, Tallinn, Estonia
Received:
12
June
2023
Accepted:
18
August
2023
Published online:
15
September
2023
Quantum entanglement of weak interaction gauge bosons produced at colliders can be explored by computing the corresponding polarization density matrix. To this end, we consider the Higgs boson decays 
and 
, in which 
and 
are off-shell states, and the WW, WZ and ZZ di-boson production in proton collisions. The polarization density matrix of the di-boson state is determined by the amplitude of the production process and can be experimentally reconstructed from the angular distribution of the momenta of the final states into which the gauge bosons decay. We show that a suitable instance of the Bell inequality is violated in to a degree that can be tested at the LHC with future data. The same Bell inequality is violated in the production of WW and ZZ boson pairs for invariant masses above 900 GeV and scattering angles close to 
in the center of mass frame. LHC data in this case are not sufficient to establish the violation of the Bell inequality. We also analyze the prospects for detecting Bell inequality violations in di-boson final states at future 
and muon colliders. A further observable that provides a lower bound on the amount of polarization entanglement in the di-boson system is computed for each of the examined processes. The analytic expressions for the polarization density matrices are presented in full in an Appendix. We also provide the unitary matrices required in the optimization procedure necessary in testing the Bell inequalities.
© The Author(s) 2023
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Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.
