FIG. 10: The reconstructed invariant mass distributions: (a) M ( πππ ) distribution for τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ , (b) M ( Kππ ) distribution for τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ , (c) M ( KKπ ) distribution for τ − → K $^{−}$K $^{+}$π $^{−}$ν$_{τ}$ , and (d) M ( KKK ) distribution for τ − → K $^{−}$K $^{+}$K $^{−}$ν$_{τ}$ . For all histograms, the black points with error bars represent the data, the gray histograms are the sum of all backgrounds other than the three-prong cross-feed, and the hatched histograms are the sum of three-prong cross-feed backgrounds. Note that the cross-feed backgrounds are estimated from the unfolding of the data. The uncertainties shown for the data are statistical only. After taking into account the backgrounds, the efficiencies and various sources of sys- tematic uncertainties discussed above, we obtain the following branching fractions for three- prong decays: 21 ] 2 c ) [GeV/ M( 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 ) 2 c Events / (10 MeV/ 0 50 100 150 200 3 10 (a) ] 2 c ) [GeV/ M(K 0.8 1 1.2 1.4 1.6 1.8 ) 2 c Events / (10 MeV/ 0 5000 10000 15000 20000 (b) ] 2 c ) [GeV/ M(KK 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 ) 2 c Events / (10 MeV/ 0 1000 2000 3000 4000 (c) ] 2 c M(KKK) [GeV/ 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 ) 2 c Events / (10 MeV/ 0 50 100 150 (d)