Exclusive branching fraction measurements of semileptonic tau decays into three charged hadrons, ${\tau }^{-}\to \varphi {\pi }^{-}{\nu }_{\tau }$ and ${\tau }^{-}\to \varphi K^{-}{\nu }_{\tau }$

Abstract

Using a data sample corresponding to an integrated luminosity of 342 $f{b}^{-1}$ collected with the BABAR detector at the SLAC PEP-II electron-positron storage ring operating at a center-of-mass energy near 10.58 GeV, we measure $\mathcal{B}({\tau }^{-}\to {\pi }^{-}{\pi }^{-}{\pi }^{+}{\nu }_{\tau })=(8.83\pm 0.01\pm 0.13)$, $\mathcal{B}({\tau }^{-}\to K^{-}{\pi }^{-}{\pi }^{+}{\nu }_{\tau })=(0.273\pm 0.002\pm 0.009)$, $\mathcal{B}({\tau }^{-}\to K^{-}{\pi }^{-}{K}^{+}{\nu }_{\tau })=(0.1346\pm 0.0010\pm 0.0036)$ and $\mathcal{B}({\tau }^{-}\to K^{-}{K}^{-}{K}^{+}{\nu }_{\tau })=(1.58\pm 0.13\pm 0.12)\times 10^{-5}$, where the uncertainties are statistical and systematic, respectively. Events where the ${\pi }^{+}{\pi }^{-}$ pair is consistent with coming from a $K_S^0$ are excluded. These are significant improvements over previous measurements, with the $\mathcal{B}({\tau }^{-}\to K^{-}{K}^{-}{K}^{+}{\nu }_{\tau })$ result being the first resonant plus non-resonant measurement of this mode. We also report a first measurement of $\mathcal{B}({\tau }^{-}\to \varphi {\pi }^{-}{\nu }_{\tau })=(3.42\pm 0.55\pm 0.25)\times 10^{-5}$ and a new measurement of $\mathcal{B}({\tau }^{-}\to \varphi K^{-}{\nu }_{\tau })=(3.39\pm 0.20\pm 0.28)\times 10^{-5}$.

7 pages, 2 postscript figures, 3 tables, published in Physical Review Letters 100, 011801 (2008)

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