] 2 c ) [GeV/ M( 0.6 0.8 1 1.2 1.4 1.6 1.8 )] 2 c 1/N (dN/dM) [/10(MeV/ 0 0.005 0.01 0.015 0.02 0.025 (a) ] 2 c ) [GeV/ M(K 0.8 1 1.2 1.4 1.6 1.8 )] 2 c 1/N (dN/dM) [/10(MeV/ 0 0.01 0.02 0.03 0.04 (b) ] 2 c ) [GeV/ M(KK 1.2 1.3 1.4 1.5 1.6 1.7 1.8 )] 2 c 1/N (dN/dM) [/10(MeV/ 0 0.01 0.02 0.03 0.04 0.05 (c) ] 2 c M(KKK) [GeV/ 1.5 1.55 1.6 1.65 1.7 1.75 1.8 )] 2 c 1/N (dN/dM) [/10(MeV/ 0 0.02 0.04 0.06 0.08 (d) sum of the three-prong cross-feed backgrounds and other background components, respec- tively. Note that the three-prong cross-feed backgrounds are determined by the unfolding procedure previously described. Table IV summarizes various contributions to the systematic uncertainties on the branch- ing fractions. The uncertainty in the track-finding efficiency is estimated from a comparison of real and MC data for the D ∗ → πD $^{0}$, D 0 → ππK 0 $_{S}$( K 0 S → π $^{+}$π $^{−}$) decay sample. The uncertainties due to the kaon and pion identification are evaluated by applying the un- certainties in kaon identification efficiencies to the efficiency matrix in Table I. First, we 18 FIG. 7: The unfolded mass spectra of the three-prong decays, 1 /N ( dN/dM ): (a) M ( πππ ) distribu- tion of τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ , (b) M ( Kππ ) distribution of τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ , (c) M ( KKπ ) distribution of τ − → K $^{−}$K $^{+}$π $^{−}$ν$_{τ}$ , and (d) M ( KKK ) distribution of τ − → K $^{−}$K $^{+}$K $^{−}$ν$_{τ}$ . The black points correspond to the unfolded mass spectra with statistical uncertainties only, and the gray bands cor- respond to the systematic uncertainty. The solid histograms are the model predictions implemented in the current TAUOLA MC simulation.