A bstract A muon collider represents a promising candidate for the next generation of particle physics experiments after the expected end of LHC operations in the early 2040s. Rare or hard-to-detect processes at the LHC, such as the production of multiple gauge bosons, become accessible at a TeV muon collider. We present here the prospects of detecting quantum entanglement and the violation of Bell inequalities in H → ZZ → 4 ℓ events at a potential future muon collider. We show that the spin density matrix of the Z boson pairs can be reconstructed using the kinematics of the charged leptons from the Z boson decays. Once the density matrix is determined, it is straightforward to obtain the expectation values of various Bell operators and test the quantum entanglement between the Z boson pair. Through a detailed study based on Monte-Carlo simulation, we show that the generalized CGLMP inequality can be maximally violated, and testing Bell inequalities could be established with high significance.
We study quantum entanglement and test violation of Bell-type inequality at the Circular Electron Positron Collider (CEPC), which is one of the most attractive future collides. It is a promising particle collider designed to search new physics, make Standard Model (SM) precision measurements, and serving as a Higgs factory. Our study is based on a fast simulation of the Z boson pair production from Higgs boson decay at s = 250 GeV . The detector effects are also included in the simulation. The spin density matrix of the joint Z Z system is parametrized using irreducible tensor operators and reconstructed from the spherical coordinates of the decay leptons. To test Bell inequalities, we construct observable quantities for the H → Z Z * process in CEPC by using the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality, whose value is determined from the density matrix of the Z boson pairs. The sensitivity of the Bell inequality violation is observed with more than 1 σ and the presence of the quantum entanglement is probed with more than 2 σ confidence level.
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 → W W ∗ and
H→ZZ∗ H → Z Z ∗ , in which
W∗ W ∗ and
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 → 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 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 - 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.
We explore the potential to study quantum entanglement through Bell-type inequalities in Higgs boson decays at a future muon collider. Our analysis focuses on the channel
μ+μ−→ννˉh→ννˉZZ∗, with one
Z decaying to charged leptons and the other decaying hadronically into jets. We study the violation of the CGLMP inequality using the optimal Bell operator for the bipartite qutrit system from
h→ZZ∗. The entanglement measure
I3 is constructed from spin-correlated angular observables of the
Z decay products. An unfolding method on the angular variables is applied to correct for hadronization and detector effects, recovering the advantage of the hadronic mode with higher event yield and reduced uncertainty. The study is performed at 1, 3, and 10 TeV centre-of-mass energies, assuming 10 ab
−1 integrated luminosity for each case. At 1 TeV, we use a boosted decision tree for signal isolation, while at higher energies, simple cut-based analyses are sufficient. We find clear Bell inequality violation with the expected values
I3=2.625±0.012,
2.623±0.004, and
2.582±0.010 for the 1, 3, and 10 TeV machines, respectively. Overall, a strong level of entanglement close to the maximum achievable value of 2.9149 for a two-qutrit system can be measured with very small uncertainties due to the large event yield in the hadronic mode.
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
Z boson pairs.
Abstract Recent studies have shown that observing entangled particle states at a particle collider, such as the Large Hadron Collider (LHC), and testing the violation of Bell inequality in them can open up new research areas for studying high energy physics. We examine the presence of quantum entanglement in the process at leading order. We apply a generally recognized method, quantum state tomography, to reconstruct the spin density matrix of the joint ZZ system, through which all the relevant observables can be obtained. The angular distribution of the final leptons is obtained from simulated events using a Monte-Carlo program, which is used to reconstruct the spin density matrix. A non-zero value of the lower bound of the concurrence is measured with the simulated data. The numerical analysis shows that, with the luminosity corresponding to LHC Run 2+3, entanglement can be probed at the 2 level and up to the 3.75 level for High-Luminosity LHC data (3ab -1 ), revealing the possibility of finding quantum entanglement in real collider experiments.