Quantum information and CP measurement in $H\to \ddot{I}{„}^{+}\ddot{I}{„}^{-}$ at future lepton colliders

Abstract

We introduce a methodology and investigate the feasibility of measuring quantum properties of tau lepton pairs in the $H\to \ddot{I}{„}^{+}\ddot{I}{„}^{-}$ 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 $H\ddot{I}„\ddot{I}„$ 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.

14 pages, 2 figures, Version published in PRD