Branching Fractions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math>Leptons to Three Charged Hadrons

Abstract

From electron-positron collision data collected with the CLEO detector operating at Cornell Electron Storage Ring near $\sqrt{s}=10.6\text{ }\text{ }\mathrm{G}\mathrm{e}\mathrm{V}$, improved measurements of the branching fractions for $\ensuremath{\tau}$ decays into three explicitly identified hadrons and a neutrino are presented as $\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}})=(9.13\ifmmode\pm\else\textpm\fi{}0.05\ifmmode\pm\else\textpm\fi{}0.46)%$, $\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}})=(3.84\ifmmode\pm\else\textpm\fi{}0.14\ifmmode\pm\else\textpm\fi{}0.38)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, $\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}})=(1.55\ifmmode\pm\else\textpm\fi{}0.06\ifmmode\pm\else\textpm\fi{}0.09)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, and $\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}})&lt;3.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ at 90% C.L., where the uncertainties are statistical and systematic, respectively.