content_image/364614.jpg content_image/364616.jpg
estimated: 

<img src='content_image/364614.jpg'>

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 , 

where the first and the second uncertainties are statistical and systematic, respectively. 

## DISCUSSION 

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. 

<img src='content_image/364616.jpg'>

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 

