Testing Bell inequality through $h\to\tau\tau$ at CEPC

The decay of Higgs boson into two spin-1/2 particles provides an ideal system to reveal quantum entanglement and Bell-nonlocality. Future $e^+e^-$ colliders can improve the measurement accuracy of the spin correlation of tau lepton pairs from Higgs boson decay. We show the testability of Bell inequality through $h\to \tau\tau$ at Circular Electron Positron Collider (CEPC). Two realistic methods of testing Bell inequality are investigated, i.e., T\"{o}rnqvist's method and Clauser-Home-Shimony-Holt (CHSH) inequality. In the simulation, we take into account the detector effects of CEPC including uncertainties for tracks and jets from $Z$ boson in the production of $e^+e^-\to Zh$. Necessary reconstruction approaches are described to measure quantum entanglement between $\tau^+$ and $\tau^-$. Finally, we show the sensitivity of CEPC to the Bell inequality violation for the two methods.