A study of three-prong tau decays with charged kaons

Abstract.

From an analysis of the ionisation energy loss of charged particles selected from a sample of 147926 ${\rm e}^+{\rm e}^- \!\!\rightarrow\! \tau^+\tau^-$ candidates recorded in the OPAL detector at ${\rm e}^+{\rm e}^-$ centre-of-mass energies near the ${\rm Z}^0$ resonance, we determine the branching ratios: \begin{eqnarray*} {\rm Br}(\tau^-\rightarrow \,\nu_\tau\,{\rm K}^-\pi^-\pi^+ (\pi^0)) & = & 0.343\pm0.073\pm0.031 \;\% \nonumber \\[1mm] {\rm Br}(\tau^-\rightarrow \,\nu_\tau\,{\rm K}^-\pi^-{\rm K}^+ (\pi^0)) & = & 0.159\pm0.053\pm0.020 \;\% , \nonumber \end{eqnarray*} where the $(\pi^0)$ notation refers to decay modes with or without an accompanying $\pi^0$. The \[\tau^- \rightarrow \nu_\tau{\rm K}^-\pi^- \pi^+ (\pi^0)\] final states occurring through $\tau^- \rightarrow \nu_\tau{\rm K}^-{\rm K}^0_{\rm S} (\pi^0)$ are treated as background in this analysis. We also examine the resonant structure of $\tau^- \!\!\rightarrow\!\! \,\nu_\tau\,{\rm K}^-\pi^-\pi^+$ candidates. Under the assumption that the resonant structure is dominated by the K$_1$ resonances, we determine: \begin{eqnarray*} R & = & {{{\rm Br}(\tau^-\rightarrow \,\nu_\tau\,{\rm K}_1(1270))}\over { {\rm Br}(\tau^-\rightarrow \,\nu_\tau\,{\rm K}_1(1400)) + {\rm Br}(\tau^-\rightarrow \,\nu_\tau\,{\rm K}_1(1270))} } = 0.71 \pm 0.16 \pm 0.11 . \nonumber \end{eqnarray*} In all results, the first uncertainties are statistical and the second are systematic.