momenta in the center-of-mass (CM) frame is required to be less than 10 GeV/ c , and the sum of energies deposited in the calorimeter is required to be less than 10 GeV. The largest of the four tracks’ transverse momenta is required to be greater than 0.5 GeV/ c to reject two-photon events, which typically have low transverse momentum tracks. To reject beam- related background, we require the position of the reconstructed event vertex to be less than 3 cm from the interaction point along the beam direction, and separated by less than 0.5 cm in the transverse plane. The missing mass, M 2 miss = ( p$_{init}$ − ∑ $_{tr}$p$_{tr}$ − ∑ $_{γ}$p$_{γ}$ ) $^{2}$, and the polar angle of the missing momentum in the CM frame are efficient variables for rejecting two-photon and Bhabha backgrounds. In the definition of the missing mass, p$_{tr}$ and p$_{γ}$ are the four-momenta of measured tracks and photons, respectively, and p$_{init}$ is the initial CM frame four-momentum of the e $^{+}$e − beams. We require that the missing mass be larger than 1 GeV/ c 2 and less than 7 GeV/ c $^{2}$, and that the polar angle with respect to the beam direction in the CM frame be larger than 30 ◦ and less than 150 $^{◦}$. Detailed information on the τ $^{+}$τ − pair selection and background suppression using missing mass can be found in [15]. Particle identification is used to select τ events that contain one lepton (electron or muon) and three hadrons (pions or kaons). The magnitude of thrust is evaluated and is required to be larger than 0.9 to suppress two-photon and e $^{+}$e − → q ¯ q backgrounds, where the thrust is defined by the maximum of ( ∑ i | ˆ n · ⃗ p$_{i}$ | ) / ( ∑ i | ⃗ p$_{i}$ | ). Here ⃗ p$_{i}$ is the momentum of the i -th track and ˆ n is the unit vector in the direction of the thrust axis – the direction maximizing the thrust. We require that the angle between the total momentum of the hadrons and the lepton momentum in the CM system be larger than 90 $^{◦}$, since the tag-side lepton and signal- side hadrons usually lie in opposite hemispheres: the so-called 1–3 prong configuration, due to the large transverse momenta of τ leptons. The invariant mass of charged tracks and gamma clusters on each side is required to be less than the τ mass. Finally, we require that there be no K 0 $_{S}$, π $^{0}$, or energetic γ on the signal side, where the selection criteria for these particles are described below. Figure 2 shows distributions of the variables used to select the 1–3 prong sample, where in each case, the selection value is indicated by a vertical line in the figure. The surviving events are candidates for τ − → h − 1 h + 2 h − 3 ν$_{τ}$ , where h$_{1}$$_{,}$$_{2}$$_{,}$$_{3}$ is either a pion or a kaon candidate. At this stage, the efficiencies for reconstructing 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 as τ − → h $^{−}$h $^{+}$h $^{−}$ν$_{τ}$ are 26 . 7%, 27 . 5%, 27 . 2%, and 24 . 8%, respectively, while the reconstruction efficiencies of the dominant background modes, τ − → π $^{−}$π $^{+}$π $^{−}$π $^{0}$ν$_{τ}$ , τ − → K 0 $_{S}$π $^{−}$ν$_{τ}$ , and e $^{+}$e − → q ¯ q , are 6