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We present a study of tau^- -> K^- pi^+ pi^- nu_tau decay using ~669 /fbdata, 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 resultfor the branching ratio is : B = (3.25 +- 0.02(stat.) +0.16 -0.15(sys.))x10^-3>. We also present results of the precise measurement of the branching ratio ofother 3-prong decay modes, tau^- -> pi^- pi^+ pi^- nu_tau, tau^- -> K^- K^+pi^- nu_tau, and tau^- -> K^- K^+ K^- nu_tau .

Study of the tau^- -> K^- pi^+ pi^- nu_tau decay