Quantum information and CP measurement in $H \to \tau^+ \tau^-$ at future lepton colliders

TL;DR

This paper proposes a method to measure quantum properties like entanglement and Bell inequality violations in tau lepton pairs from Higgs decays at future lepton colliders, enabling tests of quantum correlations and CP violation.

Contribution

It introduces a novel likelihood-based reconstruction method that accounts for energy resolution effects, allowing accurate quantum property measurements and model-independent CP violation tests.

Findings

Quantum correlations can be measured with precise tau rest frame reconstruction.

The likelihood method effectively corrects for energy mismeasurements.

CP phase can be constrained to within 7.9° at ILC and 5.4° at FCC-ee.

Abstract

We introduce a methodology and investigate the feasibility of measuring quantum properties of tau lepton pairs in the $H \to \tau^+ \tau^-$ decay at future lepton colliders. In particular, observation of entanglement, steerability and violation of Bell inequalities are examined for the ILC and FCC-ee. We find that detecting quantum correlation crucially relies on precise reconstruction of the tau lepton rest frame and a simple kinematics reconstruction does not suffice due to the finite energy resolution of the colliding beams and detectors. To correct for energy mismeasurements, a log-likelihood method is developed that incorporates the information of impact parameters of tau lepton decays. We demonstrate that an accurate measurement of quantum properties is possible with this method. As a by-product, we show that a novel model-independent test of CP violation can be performed and the CP-phase of $H \tau \tau$ interaction can be constrained with an accuracy comparable to dedicated analyses, i.e., up to $7.9^{\circ}$ and $5.4^{\circ}$ at ILC and FCC-ee, respectively.