TABLE III: Summary of the relative errors of the unfolded mass spectra, 1 /N ( dN/dM ) (in %) from different sources of uncertainties: the unfolding procedure (UNF1, UNF2), the kaon identification (KID), the background estimation (BGE), the γ veto (GAM), and the momentum scale (MOM). The “average” uncertainties (the 2nd, 4-th, 6-th, and 8-th columns) are evaluated by taking average of errors in all bins. The “peak” uncertainties (the 3rd, 5-th, 7-th, and 9-th columns) represent the errors at the peak position of the spectra. See the text for a more detailed description. B τ → eνν + B τ → $_{µνν}$. The true yields N true i obtained from Eq. 2 are given in the third column of Table II. This normalization method requires a precise measurement of the number of { e, µ } events and a careful determination of the corresponding efficiency. Figure 9 shows a comparison of the invariant mass of the electron and muon system and the cosine of the angle between electron and muon, for real { e, µ } events and the sum of MC expectations. The MC reproduces the data reasonably well. The background fraction is estimated to be 5 . 9% using MC. After subtracting background, we obtain the number of { e, µ } events. Figure 10 shows the observed distributions of M ( πππ ), M ( Kππ ), M ( KKπ ), and M ( KKK ). The backgrounds are represented by the hatched and the gray histograms for the 17 Sources τ → τ → τ → τ → of πππν Kππν KKπν KKKν uncertainties average peak average peak average peak average peak (UNF1) 0.5 0.5 0.1 0.1 0.4 0.4 0.6 0.6 (UNF2) 0.1 0.1 1.6 1.5 0.9 0.9 7.3 4.0 (KID) 0.4 0.4 1.0 0.8 1.5 1.1 1.9 0.9 (BGE) 0.2 0.2 0.6 0.5 0.4 0.3 1.9 1.1 (GAM) 0.6 0.4 0.9 0.4 1.2 0.9 4.6 3.2 (MOM) 0.1 0.0 0.4 0.2 0.3 0.3 2.7 3.1 Total systematics 0.7 0.7 2.2 1.9 2.2 1.7 9.5 6.2 Statistics 0.2 0.2 1.1 0.8 1.0 0.8 7.1 4.6 Total 0.9 0.8 2.4 2.0 2.4 1.9 11.8 7.7