Study of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math>Decays to Four-Hadron Final States with Kaons

Abstract

The rare $\ensuremath{\tau}$ lepton decays to four explicitly identified hadrons have been studied with the CLEO detector at the Cornell Electron Storage Ring using $(7.56\ifmmode\pm\else\textpm\fi{}0.15)\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data collected near $\sqrt{s}=10.58\text{ }\text{ }\mathrm{GeV}$. The first statistically significant measurements of $\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\nu}}_{\ensuremath{\tau}},\mathrm{\text{excluding}}{K}^{0})=(7.4\ifmmode\pm\else\textpm\fi{}0.8\ifmmode\pm\else\textpm\fi{}1.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ and $\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\nu}}_{\ensuremath{\tau}})=(5.5\ifmmode\pm\else\textpm\fi{}1.4\ifmmode\pm\else\textpm\fi{}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ are presented, including the first observation of the decay ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}\ensuremath{\omega}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ with branching fraction, $(4.1\ifmmode\pm\else\textpm\fi{}0.6\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. We publish the first upper limit for $\mathcal{B}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\nu}}_{\ensuremath{\tau}})&lt;4.8(6.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ at 90% (95%) confidence level. We measure for the first time the invariant mass distributions, which together with the branching fraction measurements are important ingredients that can be used to extract the standard model parameters, the strange quark mass, and the Cabibbo-Kobayashi-Maskawa element ${V}_{us}$.