Measurement of Michel Parameters ($\bar{\eta }$, $\xi \kappa$) in the radiative leptonic decay of tau at Belle

Abstract

We present the first measurement of the Michel parameters $\bar{\eta }$ and $\xi \kappa$ in the radiative leptonic decay of the $\tau$ lepton using 703 f${\mathrm{b}}^{-1}$ of data collected with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. The Michel parameters are measured by an unbinned maximum likelihood fit to the kinematic information of $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}\to ({\pi }^{+}{\pi }^0\bar{\nu })(l^{-}\nu \bar{\nu }\gamma )$ $(l=e$ or $\mu )$. The preliminary values of the measured Michel parameters are $\bar{\eta }=-2.0\pm 1.5\pm 0.8$ and $\xi \kappa =0.6\pm 0.4\pm 0.2$, where the first error is statistical and the second is systematic.