FIG. 9: Distributions of the { e, µ } events: (a) Invariant mass of the electron–muon system. (b) Cosine of the angle between the electron and muon. The closed circles and the solid histogram rep- resent the data and the sum of the MC expectations, respectively. The open histogram represents the { e, µ } signal events, while the τ -pair background and the two-photon background are shown by the hatched and the gray histograms, respectively. 20 by varying the unfolded spectra by one standard deviation of their statistical and systematic errors, assuming 100% bin-by-bin correlations for systematic errors. The trigger efficiency for the three-prong modes is ∼ 86% with an uncertainty of ∼ 0.6%. This efficiency is obtained using a trigger simulation program applied to the signal MC samples. The uncertainty due to the γ veto is evaluated by using different selection criteria for photon energy. The uncertainty due to the K 0 S veto is evaluated by removing the veto requirement. The uncertainties in background estimation include the effect of luminosity, the cross section for e $^{+}$e − → τ $^{+}$τ $^{−}$, and the subtraction of background from non-three-prong τ decays and continuum e $^{+}$e − → q ¯ q . The uncertainty on the τ decay background subtraction is evaluated by propagating the errors from the τ branching fractions other than those with three-prongs. The fraction of the e $^{+}$e − → q ¯ q background is negligible for τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ and τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ modes, and is 2 . 0 ± 0 . 2% and 2 . 9 ± 0 . 3% for τ − → K $^{−}$K $^{+}$π $^{−}$ν$_{τ}$ and τ − → K $^{−}$K $^{+}$K $^{−}$ν$_{τ}$ modes, respectively. The uncertainties in the e $^{+}$e − → q ¯ q background are estimated from comparison of the number of events in data and e $^{+}$e − → q ¯ q MC, in the mass region above the τ mass. The effects of the uncertainties in the luminosity and the cross section for e $^{+}$e − → τ $^{+}$τ − [24] are negligible because we use { e, µ } events for normalization. The uncertainties in the leptonic decay branching fractions for the τ are also taken into account. ] 2 c ) [GeV/ M(e 0 2 4 6 8 10 ) 2 c Number of events / (10 MeV/ 100 200 300 3 10 (a) ) cos(e, -1 -0.8 -0.6 -0.4 -0.2 0 Number of events 0 200 400 600 800 3 10 (b)