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Unfolding quantum entanglement from $h\to ZZ^*\to jj\ell\ell$ at a muon collider

Songshaptak De, Atri Dey, Tousik Samui

TL;DR

The paper investigates measuring quantum entanglement in Higgs decays via Bell-type inequalities at a future muon collider, focusing on the channel $\\mu^+\\mu^-\\to\\nu\\bar{\\nu} h\\to\\nu\\bar{\\nu} ZZ^*$ and the CGLMP inequality for a bipartite qutrit system. It constructs the entanglement observable $\\mathcal{I}_3$ from spin-correlated angular observables of the $Z$ decays and uses an unfolding procedure to correct hadronization and detector effects in the hadronic final state, enabling a high-precision measurement. The analysis, performed at $\\sqrt{s}=1,3,10$ TeV with $\\mathcal{L}=10\\,\\mathrm{ab}^{-1}$, reports Bell-inequality violations around $\\mathcal{I}_3\\approx2.58$–$2.63$ with sub-0.02 uncertainties, demonstrating strong entanglement near the maximal two-qutrit value $2.9149$ when unfolded. The work highlights the feasibility of accessing quantum correlations in Higgs decays at lepton colliders, advocates extending to fully hadronic channels, and suggests improvements in unfolding and alternative entanglement measures for future high-energy collider studies.

Abstract

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 $μ^+ μ^- \to ν\barν h \to ν\barν ZZ^*$, 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 $h \to ZZ^*$. The entanglement measure $\mathcal{I}_3$ 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 $\mathcal{I}_3 = 2.625 \pm 0.012$, $2.623 \pm 0.004$, and $2.582 \pm 0.010$ 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.

Unfolding quantum entanglement from $h\to ZZ^*\to jj\ell\ell$ at a muon collider

TL;DR

The paper investigates measuring quantum entanglement in Higgs decays via Bell-type inequalities at a future muon collider, focusing on the channel and the CGLMP inequality for a bipartite qutrit system. It constructs the entanglement observable from spin-correlated angular observables of the decays and uses an unfolding procedure to correct hadronization and detector effects in the hadronic final state, enabling a high-precision measurement. The analysis, performed at TeV with , reports Bell-inequality violations around – with sub-0.02 uncertainties, demonstrating strong entanglement near the maximal two-qutrit value when unfolded. The work highlights the feasibility of accessing quantum correlations in Higgs decays at lepton colliders, advocates extending to fully hadronic channels, and suggests improvements in unfolding and alternative entanglement measures for future high-energy collider studies.

Abstract

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 , with one 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 . The entanglement measure is constructed from spin-correlated angular observables of the 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 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 , , and 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.

Paper Structure

This paper contains 15 sections, 26 equations, 8 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Density Matrix and Bell Nonlocality
  4. Spin Density Matrix for $h\to ZZ^*$ System
  5. Angular Distributions and Density Matrix Reconstruction from the $Z$ Bosons Decay
  6. Monte Carlo Event Samples and Angular Variables Construction
  7. Event Generation
  8. Computation of $A_{LM}$ and $C_{LM, L'M'}$ Coefficients
  9. Unfolding Angular Variables
  10. Results
  11. Selection of Signal Region for 1 TeV Machine
  12. Boosted Decision Tree Analysis for 1 TeV Collider.
  13. Signal Region Selection for 3 and 10 TeV Machine
  14. Estimation of $\mathcal{I}_3$
  15. Summary and Outlook

Figures (8)

  • Figure 1: Definition of reference frames. In the Higgs CM frame, the direction of the on-shell $Z$ boson defines the positive $z$-axis (left). The same coordinate system is employed to describe the angular distributions of the final-state fermion and anti-fermion pairs in their respective $Z$ rest frames (right).
  • Figure 2: Comparison of parton-level (filled), detector-level (dashed), and unfolded (solid red) normalized distributions for spherical harmonic coefficients at $\sqrt{s} = 1~\text{TeV}$.
  • Figure 3: Comparison of parton-level (filled), detector-level (dashed), and unfolded (solid red) normalized distributions for spherical harmonic coefficients at $\sqrt{s} = 3~\text{TeV}$.
  • Figure 4: Comparison of parton-level (filled), detector-level (dashed), and unfolded (solid red) normalized distributions for spherical harmonic coefficients at $\sqrt{s} = 10~\text{TeV}$.
  • Figure 5: Normalized distributions of (a) $M_{jj\ell\ell}$ and (b) the missing transverse energy $E_{T}^{\text{miss}}$ for signal and background processes at $\sqrt{s} = 1~\text{TeV}$.
  • ...and 3 more figures