Physical review. D/Physical review. D.

Tripartite entanglement in H → Z Z , W W decays

J. A. Aguilar–Saavedra

Published Jun 21, 2024• 24 citations

Abstract

The decays of the Higgs boson produce a state in which the spins of the decay products and the orbital angular momentum ( L ) are highly entangled. We obtain the tripartite density operator, as well as reduced operators, for the decay into two weak bosons. For H → Z Z in the four-lepton final state we also estimate the statistical sensitivity at the Large Hadron Collider and future upgrades, using a binned method to reconstruct the density operators from distributions. With the expected Run 3 data, establishing genuine tripartite entanglement would be possible beyond the 5 σ level. The violation of Bell inequalities involving the spins of the two weak bosons could also be established beyond the 5 σ level. Published by the American Physical Society 2024

DOI: 10.1103/physrevd.109.113004

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Physical review. D/Physical review. D.

Tripartite entanglement in H → Z Z , W W decays

J. A. Aguilar–Saavedra

Published Jun 21, 2024• 24 citations

Publisher

Abstract

DOI: 10.1103/physrevd.109.113004

Related papers

Tripartite entanglement in $H \to ZZ,WW$ decaysTripartite entanglement in $H \to ZZ,WW$ decays

J. A. Aguilar–Saavedra

The decays of the Higgs boson produce a state in which the spins of the decay products and the orbital angular momentum ( $L$ ) are highly entangled. We obtain the tripartite density operator, as well as reduced operators, for the decay into two weak bosons. For $H \to ZZ$ in the four-lepton final state we also estimate the statistical sensitivity at the Large Hadron Collider and future upgrades, using a binned method to reconstruct the density operators from distributions. With the expected Run 3 data, establishing genuine tripartite entanglement would be possible beyond the $5σ$ level. The violation of Bell inequalities involving the spins of the two weak bosons could also be established beyond the $5σ$ level.The decays of the Higgs boson produce a state in which the spins of the decay products and the orbital angular momentum ($L$) are highly entangled. We obtain the tripartite density operator, as well as reduced operators, for the decay into two weak bosons. For $H \to ZZ$ in the four-lepton final state we also estimate the statistical sensitivity at the Large Hadron Collider and future upgrades, using a binned method to reconstruct the density operators from distributions. With the expected Run 3 data, establishing genuine tripartite entanglement would be possible beyond the $5σ$ level. The violation of Bell inequalities involving the spins of the two weak bosons could also be established beyond the $5σ$ level.

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Tripartite entanglement in

H \to ZZ,WW

decays

The decays of the Higgs boson produce a state in which the spins of the decay products and the orbital angular momentum (

L

) are highly entangled. We obtain the tripartite density operator, as well as reduced operators, for the decay into two weak bosons. For

H \to ZZ

in the four-lepton final state we also estimate the statistical sensitivity at the Large Hadron Collider and future upgrades, using a binned method to reconstruct the density operators from distributions. With the expected Run 3 data, establishing genuine tripartite entanglement would be possible beyond the

5σ

level. The violation of Bell inequalities involving the spins of the two weak bosons could also be established beyond the

5σ

level.

Momentum entanglement at colliders: the

H \to WW,ZZ

case

We address momentum entanglement in Higgs decays to weak boson pairs,

H \to WW,ZZ

, by discretising momentum space. The momenta of the two weak bosons are entangled, as well as the degrees of freedom in momentum and spin spaces. For

H \to ZZ

in the four-lepton final state, we also estimate the statistical sensitivity of entanglement measures at the Large Hadron Collider and future upgrades. The discretisation method introduced here is broadly applicable, offering a framework for studies of momentum entanglement at the energy frontier.

H\rightarrow W W^*

H → W W ∗ and

H\rightarrow Z Z^*

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\rightarrow Z Z^*

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

\pi /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.