$^{33}$University of Science and Technology of China, Hefei 

$^{30}$Novosibirsk State University, Novosibirsk 

$^{31}$Osaka City University, Osaka 

$^{32}$Panjab University, Chandigarh 

$^{34}$Seoul National University, Seoul 

$^{36}$Sungkyunkwan University, Suwon 

$^{37}$School of Physics, University of Sydney, NSW 2006 

$^{38}$Tata Institute of Fundamental Research, Mumbai 

$^{35}$Shinshu University, Nagano 

$^{39}$Excellence Cluster Universe, Technische Universit¨ at M¨ unchen, Garching 

$^{42}$Department of Physics, University of Tokyo, Tokyo 

$^{44}$Tokyo University of Agriculture and Technology, Tokyo 

$^{40}$Toho University, Funabashi 

$^{41}$Tohoku Gakuin University, Tagajo 

$^{43}$Tokyo Metropolitan University, Tokyo 

$^{45}$IPNAS, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 

$^{46}$Yonsei University, Seoul 

## Abstract 

We present a study of τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ , τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ , τ − → K $^{−}$K $^{+}$π $^{−}$ν$_{τ}$ , and τ − → K $^{−}$K $^{+}$K $^{−}$ν$_{τ}$ decays using a 666 fb − 1 data sample collected with the Belle detector at the KEKB asymmetric-energy e $^{+}$e − collider at and near a center-of-mass energy of 10.58 GeV. The branching fractions are measured to be: B ( τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ )= (8 . 42 ± 0 . 00 +0 . 26 − 0 . $_{25}$) × 10 − $^{2}$, B ( τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ )= (3 . 30 ± 0 . 01 +0 . 16 − 0 . $_{17}$) × 10 − $^{3}$, B ( τ − → K $^{−}$K $^{+}$π $^{−}$ν$_{τ}$ )= (1 . 55 ± 0 . 01 +0 . 06 − 0 . $_{05}$) × 10 − $^{3}$, and B ( τ − → K $^{−}$K $^{+}$K $^{−}$ν$_{τ}$ )= (3 . 29 ± 0 . 17 +0 . 19 − 0 . $_{20}$) × 10 − $^{5}$, where the first uncertainty is statistical and the second is systematic. These branching fractions do not include contributions from modes in which a π $^{+}$π − pair originates from a K 0 S decay. We also present the unfolded invariant mass distributions for these decays. 

PACS numbers: 13.35.Dx, 12.15.Hh, 14.60.Fg 

