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International Conference on High Energy Physics (ICHEP)

New observables for testing Bell inequalities in $W$ boson pair production

Hao Zhang, Qi Bi, Qing-Hong Cao, Kun Cheng

Published Dec 17, 2024• 1 citation
Publisher

Abstract

We show that testing Bell inequalities in $W^\pm$ pair systems by measuring their angular correlation suffers from the ambiguity in kinetical reconstruction of the di-lepton decay mode. We further propose a new set of Bell observables based on the measurement of the linear polarization of the $W$ bosons that can be used in the semi-leptonic decay mode of $W^\pm$ pair, and we analyze the prospects of testing the violation of Bell inequalities at $e^+ e^-$ colliders.

DOI
10.22323/1.476.0342

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New observables for testing Bell inequalities in WWW boson pair production
We show that testing Bell inequalities in W±W^\pmW± pair systems by measuring their angular correlation suffers from the ambiguity in kinetical reconstruction of the di-lepton decay mode. We further propose a new set of Bell observables based on the measurement of the linear polarization of the WWW bosons that can be used in the semi-leptonic decay mode of W±W^\pmW± pair, and we analyze the prospects of testing the violation of Bell inequalities at e+e−e^+ e^-e+e− colliders.
We show that testing Bell inequalities in W± pair systems by measuring their angular correlation suffers from the ambiguity in kinetical reconstruction of the dilepton decay mode. We further propose a new set of Bell observables based on the measurement of the linear polarization of the W bosons that can be used in the semileptonic decay mode of W± pair, and we analyze the prospects of testing the violation of Bell inequalities at e+e− colliders. Published by the American Physical Society 2024
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.
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.
We explore the phenomenology of quantum entanglement at collider experiments by computing the polarization density matrix of processes yielding two massive gauge bosons. After reviewing the formalism, we detail observables suitable to test the presence of entanglement and quantum correlations in the di-boson system. The implied violation of Bell inequalities can be observed with future data at the LHC in the decays of the Higgs boson to ZZZ boson pairs.
Spin correlations between particles produced at colliders provide valuable insights for quantum information studies. While traditional studies of quantum information at colliders are typically limited to massive particles with perturbative decay, we propose an innovative method to explore the Bell inequality in massless quark pair systems by analyzing the azimuthal correlations in π^{+}π^{-} dihadron pair production at lepton colliders. Revisiting the Belle data, we have shown the potential to detect Bell inequality violation of light quarks by introducing an additional angular cut, achieving a significance of 2.5σ even in the worst-case scenario of 100% correlated systematic uncertainties in each bin. The significance substantially exceeds 5σ when considering uncorrelated systematic uncertainties. Our approach opens avenues for exploring spin quantum information with nonperturbative processes as spin analyzer and leverages existing data for quantum information research.
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→ZZpp \rightarrow ZZpp→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 WWW boson and gluon in the pp→W±(g→bbˉ)pp \rightarrow W^{\pm} (g\rightarrow b\bar{b})pp→W±(g→bbˉ) process.