Measurement of the τ Michel parameters $\bar{\eta}$ and $\xi\kappa$ in the radiative leptonic decay $\tau^- \rightarrow \ell^- \nu_{\tau} \bar{\nu}_{\ell}\gamma$
2018
We present a measurement of the
Michel parametersof 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 parametersare 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 parametersare $\bar{\eta} = -1.3 \pm 1.5 \pm 0.8$ 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.
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