Looking into the quantum entanglement in $H\to ZZ^\star$ at LHC within SMEFT framework

TL;DR

This paper investigates quantum entanglement in the Higgs decay to Z bosons at the LHC within the SMEFT framework, analyzing angular asymmetries and density matrices to identify entanglement and CP properties.

Contribution

It introduces a method to reconstruct the density matrix of the $ZZ^ op$ system using angular asymmetries, addressing negativity issues, and explores entanglement as a probe of anomalous couplings.

Findings

$ZZ^ op$ system is entangled for all anomalous couplings.

Symmetrized density matrix helps mitigate negativity issues.

Entanglement shows distinct behavior for CP-even and odd couplings.

Abstract

We study $H\to ZZ^\star$ production process in final four lepton states at $13$ TeV LHC in SMEFT framework. The anomalous $HZZ$ couplings are parameterized with dimension-6 $SU(2)_L\times U(1)_Y$ gauge invariant operators. We compute the eight polarizations of each $Z$ boson and $64$ spin-correlations as asymmetries in angular functions of final decayed leptons in the rest frame of the $Z$ boson. These asymmetries are further used to construct the joint density matrix (DM) for $ZZ^\star$ system. However, such DM suffers from negative probability and eigenvalues. To alleviate the negativity issues, we reconstruct the DM using asymmetries of symmetrized angular functions owing to the indistinguishability of two $Z$ bosons. The symmetrized DM is further employed to compute lower bound for concurrence as a witness of entanglement measurable at the collider experiments. The $ZZ^\star$ system is found to be in an entangled state for all values of the anomalous couplings. Notably, while the lower bound exhibits poorer sensitivity to anomalous couplings compared to asymmetries, it demonstrates distinct behavior for CP-even and odd couplings.