TABLE V: The correlation coefficients in the branching fraction measurements. TABLE VI: Comparison of the branching fraction results 23 In Fig. 11, our results are compared with the previous measurements. For all modes studied, the precision of the branching fractions for both BaBar and Belle is significantly The results of this analysis for the branching fractions of various three-prong modes are listed in Table VI together with recent results from BaBar [7]. Note that for the τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ and τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ modes, the branching fractions listed do not include any K 0 contribution. where the first and the second uncertainties are statistical and systematic, respectively. estimated: B ( τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ ) / B ( τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ ) = (3 . 92 ± 0 . 02 +0 . 15 − 0 . $_{16}$) × 10 − 2 , B ( τ − → K $^{−}$K $^{+}$π $^{−}$ν$_{τ}$ ) / B ( τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ ) = (1 . 84 ± 0 . 01 ± 0 . 05) × 10 − 2 , and B ( τ − → K $^{−}$K $^{+}$K $^{−}$ν$_{τ}$ ) / B ( τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ ) = (3 . 90 ± 0 . 20 +0 . 22 − 0 . $_{23}$) × 10 − 4 , τ − → τ − → τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ K $^{−}$K $^{+}$π $^{−}$ν$_{τ}$ K $^{−}$K $^{+}$K $^{−}$ν$_{τ}$ τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ +0 . 175 +0 . 049 − 0 . 053 τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ +0 . 080 +0 . 035 τ − → K $^{−}$K $^{+}$π $^{−}$ν$_{τ}$ − 0 . 008 DISCUSSION Decay mode BaBar Belle τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ , % 8 . 83 ± 0 . 01 ± 0 . 13 8 . 42 ± 0 . 00 +0 . 26 − 0 . 25 τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ , % 0 . 273 ± 0 . 002 ± 0 . 009 0 . 330 ± 0 . 001 +0 . 016 − 0 . 017 τ − → K $^{−}$K $^{+}$π $^{−}$ν$_{τ}$ , % 0 . 1346 ± 0 . 0010 ± 0 . 0036 0 . 155 ± 0 . 001 +0 . 006 − 0 . 005 τ − → K $^{−}$K $^{+}$K $^{−}$ν$_{τ}$ , 10 − 5 1 . 58 ± 0 . 13 ± 0 . 12 3 . 29 ± 0 . 17 +0 . 19 − 0 . 20