Quantum Entanglement is Quantum: ZZ Production at the LHC

TL;DR

The paper develops and applies a quantum-tomography framework to test entanglement in diboson systems at the LHC by reconstructing the $ZZ$ density matrix from angular observables. It analyzes LO and NLO QCD/EW corrections for $pp\to e^+e^-\mu^+\mu^-$ and $h\to e^+e^-\mu^+\mu^-$, highlighting how radiative effects modify entanglement signals and the validity of a two-qutrit description. NLO QCD preserves the two-qutrit structure but typically weakens entanglement, with jet-binning able to recover part of the LO behavior, while NLO EW introduces non-factorizable contributions that can undermine the density-matrix framework, especially in Higgs decays where singly-resonant effects are pronounced. The results emphasize the necessity of including higher-order corrections to the weak mixing angle and other radiative effects to reliably interpret quantum observables at colliders.

Abstract

Polarization and spin correlations in diboson systems serve as powerful tools for precision tests and searches for new physics. Recently, interpreting these observables through the lens of quantum information, for instance by examining whether the diboson systems exhibit entanglement, has introduced a compelling new dimension to these studies. We analyze the angular coefficients in the processes $pp\to e^+e^-μ^+μ^-$ and $h\to e^+e^-μ^+μ^-$, incorporating higher-order QCD and electroweak corrections. Guided by the fundamental properties of the spin density matrix, we assess the stability of the two-qutrit interpretation under radiative effects. For the $pp \to e^+e^-μ^+μ^-$ process, NLO QCD corrections preserve the two-qutrit structure but weaken entanglement indicators, an effect that can be partially mitigated by jet binning. In contrast, electroweak corrections introduce non-factorizable contributions that modify the quantum properties of the system. While these effects can be largely depleted by selecting events with a double-resonant $ZZ$ structure, such a kinematic handle is not available for Higgs decays. In the $h \to e^+e^-μ^+μ^-$ channel, singly-resonant NLO electroweak corrections substantially distort the angular coefficients, challenging the description of these events as a two-qutrit system.

Figures (14)

• Figure 1: Sample of representative Feynman diagrams for $pp \rightarrow 4\ell$ at leading order.
• Figure 2: Smallest eigenvalue for the reconstructed diboson density matrix evaluated using the LO $pp\to e^+e^-\mu^+\mu^-$ (black) and $pp\to ZZ\to e^+e^-\mu^+\mu^-$ (red) samples with inclusive results in $m_{4\ell}$ as a function of the lowest reconstructed mass for the same-flavor and opposite-sign dilepton, $m_{Z_2}>m_{Z_2}^\text{min}$. The color band represents the statistical error.
• Figure 3: Lower $\mathscr{C}_{\mathrm{LB}}$ (left) and upper $\mathscr{C}_{\mathrm{UB}}$ (right) bounds of the concurrence for $pp\rightarrow e^- e^+ \mu^- \mu^+$ (black) and $pp\rightarrow ZZ\to e^- e^+ \mu^- \mu^+$ (red) at LO as a function of the $\cos\theta_\text{CM}$ with invariant mass selection $81~\text{GeV}<m_{\ell^{+}\ell^{-}}<101$ GeV. The color bands represent the statistical uncertainties.
• Figure 4: Lower $\mathscr{C}_{\mathrm{LB}}$ (left) and upper $\mathscr{C}_{\mathrm{UB}}$ (right) bounds of the concurrence for the diboson system at LO are shown as functions of the four-lepton invariant mass $m_{4\ell}$ and $|\cos\theta_\text{CM}|$. A narrow invariant mass window, $81~\text{GeV}<m_{\ell^{+}\ell^{-}}<101$ GeV, is imposed to isolate the $ZZ$ system.
• Figure 5: Sample of representative Feynman diagrams for $pp \rightarrow 4\ell$ contributing to the next-to-leading order QCD corrections. Diagrams illustrating real radiation are presented in the top panel (a), while those depicting virtual corrections are shown in the bottom panel (b).