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arXiv:2410.18022

An improved Bell-CHSH observable for gauge boson pairs

R. P. Grabarczyk

Published Oct 23, 2024• 1 citation
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Abstract

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 $pp \rightarrow ZZ$ 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 $W$ boson and gluon in the $pp \rightarrow W^{\pm} (g\rightarrow b\bar{b})$ process.

DOI
10.48550/arxiv.2410.18022

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Higgs boson decays produce pairs of W bosons in a maximally entangled state, the spins of which can be expected to violate Bell inequalities. We show that the spin density matrix of the W± pair may be reconstructed experimentally from the directions of the charged lepton decay products, and from it the expectation values of various Bell operators determined. Numerical simulations of H→WW⁎ decays indicate that violation of a generalised CHSH inequality is unlikely to be measurable, however the CGLMP inequality is near-maximally violated. Experimental Bell tests could be performed at a variety of colliders and in different production channels. If reconstruction effects and backgrounds can be controlled then statistically significant violations could be observable even with datasets comparable to those already collected at the LHC.
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→WW∗H\rightarrow W W^*H→WW∗ H → W W ∗ and H→ZZ∗H\rightarrow Z Z^*H→ZZ∗ H → Z Z ∗ , in which W∗W^*W∗ W ∗ and Z∗Z^*Z∗ Z ∗ 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→ZZ∗H\rightarrow Z Z^*H→ZZ∗ H → Z Z ∗ 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 π/2\pi /2π/2 π / 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−e^+e^-e+e− 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.
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New observables for testing Bell inequalities in WWW boson pair production
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