Probing the electromagnetic dipole moment of the $\tau$ lepton in the $e^+e^- \to \gamma^*/Z \to \tau^+ \tau^-$ reaction

TL;DR

This paper investigates how to precisely measure the electromagnetic dipole moments of the tau lepton using high-energy collider data, proposing optimal observables and analyzing sensitivities at different collider energies.

Contribution

It introduces an analysis of optimal observables for extracting tau lepton dipole moments with high precision at various collider energies, including the Z pole and below.

Findings

Sensitivity to Im$d_{ au}$ and Re$d_{ au}$ can reach 10^{-21} ecm at CEPC

Sensitivity at Belle-II is around 10^{-20} ecm

Precision for tau anomalous magnetic moments can reach 10^{-5} at Belle-II

Abstract

High-precision measurements of the lepton's electromagnetic dipole moments provide a powerful probe for testing the Standard Model. A non-zero value of the $\tau$ lepton's electric(weak) dipole moment ($d_{\tau}^{\gamma}$, $d_{\tau}^{Z}$) would serve as a smoking gun of the new physics. On the one hand, current and future high energy colliders offer an ideal environment for such measurements. On the other hand, it is essential to investigate the optimal measurement method for extracting not only $d_{\tau}^{\gamma}$ and $d_{\tau}^{Z}$, but also the anomalous magnetic dipole moment ($a_{\tau}$). In this work, we analyze the precision of observables, particularly optimal observables, for determining these physics quantities through the process $e^+e^- \to \gamma^*/Z \to \tau^+ \tau^-$ with $\tau$ leptons undergoing (semi-)leptonic and hadronic decays at the centre-of-mass energies at the Z pole mass and significantly below $m_Z$. By considering the full kinematic information of the decay products, we find that the sensitivities to Im$d_{\tau}$ and Re$d_{\tau}$ can reach $10^{-21}$ $ecm$ at CEPC $\sqrt s = m_Z$, compared to $10^{-20}$ $ecm$ at Belle-II $\Upsilon(4S)$ resonance and $10^{-17}$ $ecm$ at BEPCII $\psi(2S)$ resonance. For $a_{\tau}$, we find that Im$a_{\tau}$ and Re$a_{\tau}$ with a precision of $10^{-5}$ at Belle-II $\sqrt s=10.58$ GeV can be attained.