Measurement of the tau Michel parameters $\bar{\eta}$ and $\xi\kappa$ in the radiative leptonic decay $\tau^- \rightarrow \ell^- \nu_{\tau} \bar{\nu}_{\ell}\gamma$

TL;DR

This paper reports the first measurement of the tau lepton's Michel parameters $ar{ exteta}$ and $\xi extkappa$ in radiative leptonic decay, using Belle data, providing results consistent with the Standard Model and constraining weak interaction couplings.

Contribution

First measurement of the tau Michel parameters $ar{ exteta}$ and $\xi extkappa$ in radiative leptonic decay using Belle data and unbinned maximum likelihood analysis.

Findings

Measured $ar{ exteta} = -1.3 \, extpm \, 1.5 \, ext{(stat)} \, extpm \, 0.8 \, ext{(syst)}$

Measured $\xi extkappa = 0.5 \, extpm \, 0.4 \, ext{(stat)} \, extpm \, 0.2 \, ext{(syst)}$

Results are consistent with Standard Model predictions.

Abstract

We present a measurement of the Michel parameters of the $\tau$ lepton, $\bar{\eta}$ and $\xi\kappa$, in the radiative leptonic decay $\tau^- \rightarrow \ell^- \nu_{\tau} \bar{\nu}_{\ell} \gamma$ using 711~f$\mathrm{b}^{-1}$ of collision data collected with the Belle detector at the KEKB $e^+e^-$ collider. The Michel parameters are measured in an unbinned maximum likelihood fit to the kinematic distribution of $e^+e^-\rightarrow\tau^+\tau^-\rightarrow (\pi^+\pi^0 \bar{\nu}_\tau)(\ell^-\nu_{\tau}\bar{\nu}_{\ell}\gamma)$ $(\ell=e$ or $\mu)$. The measured values of the Michel parameters are $\bar{\eta} = -1.3 \pm 1.5 \pm 0.8$ and $\xi\kappa = 0.5 \pm 0.4 \pm 0.2$, where the first error is statistical and the second is systematic. This is the first measurement of these parameters. These results are consistent with the Standard Model predictions within their uncertainties and constrain the coupling constants of the generalized weak interaction.