Search for the Electric Dipole Moment and anomalous magnetic moment of the tau lepton at tau factories

Precise measurement of the Electric Dipole Moment (EDM) and anomalous magnetic moment ($g$-2) of particles are important tests of Beyond Standard Model (BSM) physics. It is generally believed that the tau lepton couples more strongly to BSM due to its large mass, and can be searched for at collider experiments. A new method to approximately reconstruct the neutrinos from the hadronic decays of $\tau^-\tau^+$ pairs produced at $e^-e^+$ tau factories is proposed. With all final state particle momenta available, observables based on matrix elements and sensitive to BSM are calculated. It is estimated that with 50 ab$^{-1}$ of data to be delivered by the $Belle$-II experiment, a tau EDM search with a 1-$\sigma$ level precision of $|d_\tau^{NP}|<2.04\times 10^{-19}$ e$\cdot$cm, and $g$-2 search with $|a_\tau^{NP}|<1.75\times 10^{-5}$ ($1.5\%$ of the SM prediction), can be expected when systematics are not considered. The new precision can effectively constrain BSM models with heavy mirror neutrinos. It can also constrain models containing a light scalar with mass at $O$(1 GeV), which can explain the current muon $g$-2 anomaly as well. The method in this work offers a new opportunity to search for BSM at current and future tau factories with high precision.