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

TL;DR

This paper proposes methods to precisely measure the tau lepton's electric dipole moment at low energy electron-positron colliders, providing potential insights into CP violation and new physics beyond the Standard Model.

Contribution

It introduces novel measurement techniques for both the real and imaginary parts of the tau EDM using tau decay energies and decay length, with detailed sensitivity estimates at the STCF.

Findings

Im$(d_\tau)$ can be measured via charged hadron energy measurements.

Re$(d_\tau)$ can be determined by decay length after traveling beyond detector resolution.

Projected sensitivities at STCF reach $0.7$ and $2.8 \times 10^{-18} e\,\text{cm}$ for Im$(d_\tau)$ and Re$(d_\tau)$ respectively.

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 $e^+e^- \to \gamma^*, \psi(2S) \to \tau^+\tau^-$ 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}$.