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 B(τ-→π-π-π+ντ(ex.KS0))=(8.83±0.01±0.13)%, B(τ-→K-π-π+ντ(ex.KS0))=(0.273±0.002±0.009)%, B(τ-→K-π-K+ντ)=(0.1346±0.0010±0.0036)%, and B(τ-→K-K-K+ντ)=(1.58±0.13±0.12)×10-5, where the uncertainties are statistical and systematic, respectively. These include significant improvements over previous measurements and a first measurement of B(τ-→K-K-K+ντ) in which no resonance structure is assumed. We also report a first measurement of B(τ-→ϕπ-ντ)=(3.42±0.55±0.25)×10-5, a new measurement of B(τ-→ϕK-ντ)=(3.39±0.20±0.28)×10-5 and a first upper limit on B(τ-→K-K-K+ντ(ex.ϕ)).
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