Study of 3-prong hadronic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math>decays with charged kaons

Using a sample of 4.7 ${\mathrm{fb}}^{\ensuremath{-}1}$ integrated luminosity accumulated with the CLEO-II detector at the Cornell Electron Storage Ring (CESR), we have measured the ratios of the branching fractions $\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{h}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}})/\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{h}^{\ensuremath{-}}{h}^{+}{h}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}})=(5.16\ifmmode\pm\else\textpm\fi{}0.20\ifmmode\pm\else\textpm\fi{}0.50)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2},$ $\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{h}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\nu}}_{\ensuremath{\tau}})/\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{h}^{\ensuremath{-}}{h}^{+}{h}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\nu}}_{\ensuremath{\tau}})=(2.54\ifmmode\pm\else\textpm\fi{}0.44\ifmmode\pm\else\textpm\fi{}0.39)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2},$ $\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}})/\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{h}^{\ensuremath{-}}{h}^{+}{h}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}})=(1.52\ifmmode\pm\else\textpm\fi{}0.14\ifmmode\pm\else\textpm\fi{}0.29)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$, and the upper limit $\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\nu}}_{\ensuremath{\tau}})/\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{h}^{\ensuremath{-}}{h}^{+}{h}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\nu}}_{\ensuremath{\tau}})&lt;0.0154$ at 95% C.L. Coupled with additional experimental information, we use our results to extract information on the structure of three-prong tau decays to charged kaons.