Resonance structure of ${\tau }^{-}\to K^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau }$ decays

Using a sample of 4.7 ${\mathrm{fb}}^{-1}$ integrated luminosity accumulated with the CLEO II detector at the Cornell Electron Storage Ring (CESR), we investigate the mass spectrum and resonant structure in ${\tau }^{-}\to K^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau }$ decays. We measure the relative fractions of $K_1\mathrm{}\left(1270\right)\mathrm{}$ and $K_1\mathrm{}\left(1400\right)\mathrm{}$ resonances in these decays, as well as the $K_1$ masses and widths. Our fitted $K_1$ resonances are somewhat broader than previous hadroproduction measurements, and in agreement with recent CERN LEP results from tau decay. The larger central value of our measured width supports models which attribute the small ${\tau }^{-}\to K^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau }$ branching fraction to larger $K_1$ widths than are presently tabulated. We also determine the $K_a{-K}_b$ mixing angle ${\theta }_K.$