contain K 0 S and π 0 mesons, we reconstruct K 0 S and π 0 signals explicitly. K 0 S candidates are formed from oppositely charged pairs of pion tracks with invariant mass M ( ππ ) within ± 13.5 MeV/ c 2 ( ± 5 σ ) of the K 0 S mass. To improve the K 0 S purity, the point of closest approach to the interaction point along the extrapolation of each track is required to be larger than 0.3 cm in the plane transverse to the beam direction. The azimuthal angle between the momentum vector and the decay vertex vector of the reconstructed K 0 S is required to be less than 0.1 rad. The distance between the two daughter pion tracks at their point of closest approach is required to be less than 1.8 cm, and the flight length of the K 0 S in the plane perpendicular to the beam direction is required to be larger than 0.08 cm. Finally, we require the invariant mass of each K 0 S candidate to be inconsistent with that of a Λ, ¯ Λ, and a photon conversion, where the daughter tracks are assumed to be pions and protons (antiprotons) or electrons and positrons as appropriate. Candidate π $^{0}$’s are reconstructed from pairs of photon clusters. The energy of each photon is required to exceed 50 MeV for candidates in the barrel part of the calorimeter, and 100 MeV for candidates in the endcap part of the calorimeter. We also require the invariant mass of the two photons, M ( γγ ), to be within ± 16 MeV/ c 2 of the π 0 mass. Events containing one or more reconstructed K 0 S or π 0 are rejected. In addition, in order to reject events containing π $^{0}$’s, we require that there be no photon with energy larger than 0.3 GeV. To estimate the signal efficiency, 97 million signal MC events for the τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ decay mode and 5 million signal MC events for each of the τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ , τ − → K $^{−}$K $^{+}$π $^{−}$ν$_{τ}$ , and τ − → K $^{−}$K $^{+}$K $^{−}$ν$_{τ}$ modes were generated using the TAUOLA [18] based KKMC [19] generator. The detector response for all MC data sets was simulated with the GEANT3 [20] package. The TAUOLA generator provides models for τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ , τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ , and τ − → K $^{−}$K $^{+}$π $^{−}$ν$_{τ}$ decays, where various intermediate resonances are taken into account. To check whether there is efficiency bias related to the specific decay model used, events with phase-space decay distributions were generated using the KKMC program. The efficiencies as functions of the invariant mass for both τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ decay models are compared in Fig. 5. The relative difference in efficiency between the TAUOLA and phase-space decay models is around 1%. Similarly, very small discrepancies between EFFICIENCY ESTIMATION 10