Radiative<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math>production and decay

We have studied the muon decay channel of the $\ensuremath{\tau}$ lepton with the presence of a photon in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation data at ${E}_{\mathrm{c}.\mathrm{m}.}=29$ GeV from the Mark II detector. Included in this study is the first direct measurement of radiative $\ensuremath{\tau}$ decay. We find the ratio of the measured $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ branching fraction to the expected value from QED to be 1.03\ifmmode\pm\else\textpm\fi{}0.42.