Bell inequalities and quantum entanglement in weak gauge bosons production at the LHC and future colliders

Abstract

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 $H\to W{W}^{\ast }$ and $H\to Z{Z}^{\ast }$, in which $W^{\ast }$ and $Z^{\ast }$ 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 $H\to Z{Z}^{\ast }$ 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 $\pi /2$ 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 $e^{+}{e}^{-}$ 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.

59 pages, 20 figures, same as published version

References in corpus (12)

• The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations
• The PDF4LHC21 combination of global PDF fits for the LHC Run III
• Vector boson fusion at multi-TeV muon colliders
• Quantum information with top quarks in QCD
• Improved tests of entanglement and Bell inequalities with LHC tops
• Testing entanglement and Bell inequalities in $H\to ZZ$
• NLO QCD corrections to WW+jet production at hadron colliders
• Constraining new physics in entangled two-qubit systems: top-quark, tau-lepton and photon pairs
• Quantum state tomography, entanglement detection and Bell violation prospects in weak decays of massive particles
• NNLO QCD+NLO EW with MATRIX+OpenLoops: precise predictions for vector-boson pair production
• Quantum information and CP measurement in $H\to {\tau }^{+}{\tau }^{-}$ at future lepton colliders
• Quantum entanglement and top spin correlations in SMEFT at higher orders

Cited by in corpus (27)

• Observation of quantum entanglement in top quark pair production in proton-proton collisions at $\sqrt{s}$ = 13 TeV
• Entanglement and Bell inequalities violation in $H\to ZZ$ with anomalous coupling
• Quantum anomaly detection in the latent space of proton collision events at the LHC
• Entanglement in flavored scalar scattering
• Quantum Information meets High-Energy Physics: Input to the update of the European Strategy for Particle Physics
• New observables for testing Bell inequalities in $W$ boson pair production
• Optimizing Entanglement and Bell Inequality Violation in Top Anti-Top Events
• From angular coefficients to quantum observables: a phenomenological appraisal in di-boson systems
• Three-body Entanglement in Particle Decays
• Quantum properties of $H\to V{V}^{\ast }$: precise predictions in the SM and sensitivity to new physics
• Polarized ZZ pairs in gluon fusion and vector boson fusion at the LHC
• Entanglement and Bell inequality violation in vector diboson systems produced in decays of spin-0 particles
• Imprints of screened dark energy on nonlocal quantum correlations
• Spin correlations and Bell nonlocality in $\Lambda \bar{\Lambda }$ pair production from $e^{+}{e}^{-}$ collisions with a thrust cut
• Quantum Entanglement is Quantum: ZZ Production at the LHC
• Higher-Order Corrections to Quantum Observables in $h\to W{W}^{\ast }$
• Polarized-boson pairs at NLO in the SMEFT
• BRST invariant formulation of the Bell-CHSH inequality in gauge field theories
• Entanglement features in scattering mediated by heavy particles
• Qubit entanglement from forward scattering
• Universality of entanglement in gluon dynamics
• Testing spooky action between free-traveling electron-positron pairs
• Quantum state tomography with muons
• Particle Collisions & Quantum Entanglement in High-Energy Collisions
• Nonviolation of the CHSH inequality under local spin-1 measurements on two spin qutrits
• Colliders are not Testing Locality via Bell's Inequality nor Providing an Unconditional Proof of Entanglement
• Parameter Inference from Final-State Entanglement in Higgs Decays