Exclusive branching fraction measurements of semileptonic tau decays into three charged hadrons, $τ^- \to ϕπ^- ν_τ$ and $τ^- \to ϕK^- ν_τ$
Using a data sample corresponding to an integrated luminosity of 342 $fb^{-1}$ 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 ${\cal{B}} (τ^- \to π^- π^- π^+ ν_τ) = (8.83 \pm 0.01 \pm 0.13) %$, ${\cal{B}} (τ^- \to K^- π^- π^+ ν_τ) = (0.273\pm 0.002\pm 0.009)%$, ${\cal{B}} (τ^- \to K^- π^- K^+ ν_τ) = (0.1346\pm 0.0010 \pm 0.0036)%$ and ${\cal{B}} (τ^- \to K^- K^- K^+ ν_τ) = (1.58\pm 0.13 \pm 0.12)\times 10^{-5}$, where the uncertainties are statistical and systematic, respectively. Events where the $π^+π^-$ pair is consistent with coming from a $K^0_S$ are excluded. These are significant improvements over previous measurements, with the ${\cal{B}} (τ^- \to K^- K^- K^+ ν_τ)$ result being the first resonant plus non-resonant measurement of this mode. We also report a first measurement of ${\cal{B}} (τ^- \to ϕπ^- ν_τ) = (3.42\pm 0.55 \pm 0.25)\times 10^{-5}$ and a new measurement of ${\cal{B}} (τ^- \to ϕK^- ν_τ) = (3.39\pm 0.20 \pm 0.28)\times 10^{-5}$.