Study of the τ^- → K^- π⁺ π^- ν_τ decay

We present a study of τ^- → K^- π⁺ π^- ν_τ decay using ∼669 fb^-1 data, collected with the Belle detector at the KEKB asymmetric-energy e⁺ e^- collider. The data is recorded at a center-of-mass energy 10.58 GeV. The result for the branching ratio is:B = (3.25 ± 0.02 (s t a t .)_{- 0.15}^{+ 0.16} (s y s .)) × 10^{- 3} . We also present results of the precise measurement of the branching ratio of other 3-prong decay modes, τ^- → π^- π⁺ π^- ν_τ, τ^- → K^- K⁺ π^- ν_τ, and τ^- → K^- K⁺ K^- ν_τ.