Precise measurement of CP violating $\tau$ EDM through $e^{+}{e}^{-}\to {\gamma }^{\ast },\psi (2s)\to {\tau }^{+}{\tau }^{-}$

Abstract

A nonzero electric dipole moment of a tauon, $d_{\tau }$, signals CP violation and provides an important probe for new physics. We study methods to measure $d_{\tau }$ at low energy $e^{+}{e}^{-}$ colliders through the processes $e^{+}{e}^{-}\to {\gamma }^{\ast },\psi (2S)\to {\tau }^{+}{\tau }^{-}$ with ${\tau }^{\pm }$ decays into a charged hadron and a tau neutrino. We point out that, with measuring energies of the charged hadron, Im$(d_{\tau })$ can be measured. On the other hand, selecting events of $\tau$ decays after traveling more than the detector resolution distance, Re$(d_{\tau })$ can also be determined. We find that the precision at Super Tau-Charm Facility (STCF) running at the center energy of $m_{\psi (2S)}$ for 10 year data accumulation, the precision of Im$(d_{\tau })$ and Re$(d_{\tau })$ are found to be 1.8 and 11 in unit of $10^{-18}e\text{cm}$, respectively. The sensitivity for $d_{\tau }$ measurement precision at the STCF can be reached its optimum at a central energy of $6.3\text{GeV}$, achieving a precision of $0.7$ for Im$(d_{\tau })$ and $2.8$ for Re$(d_{\tau })$ in unit of $10^{-18}e\text{cm}$.

Comments: 8 pages, 2 figures