Search for CP violation effects in the $h\to \tau\tau$ decay with $e^+e^-$ colliders.

A new method is proposed to reconstruct the neutrinos in the $e^+e^-\to Zh$ process followed by the $h\to\tau\tau$ decay. With the help of a refined Higgs momentum reconstruction from the recoiling system and the impact parameters, high precision in the determination of the momentum of neutrinos can be achieved. The prospect of measuring the Higgs CP mixing angle with the $h\to\tau\tau$ decay at future $e^+e^-$ colliders is studied with the new method. The analysis is based on a detailed detector simulation of the signal and backgrounds. The fully reconstructed neutrinos and also other visible products from the tau decay are used to build matrix element (ME) based CP observables. With 5 $ab^{-1}$ of data at $E_{\text{CM}}=250$ GeV, a precision of $2.9^\circ$ can be achieved for the CP mixing angle with three main one-prong decay modes of the taus. The precision is found to be about 35\% better than the other methods.