A suitable sample of events rejected by the FILFO algorithm [16] has been used in order to evaluate the probability (1 − ǫF ILF O) that a Kθ/Kµ selftag event is discarded by the FILFO algorithm. The result obtained for ǫF ILF O on data differs from the unity by less than 10−3, but there are no evident reasons why FILFO should introduce a bias in the ratio Ntagτ′ /Ntag rejecting more/less tagged events containing a τ′ than those with other decays. Compatible results are observed on Monte Carlo.
For these reasons the FILFO effect has been considered negligible and no correc-tions have been applied on BR(τ′) (i.e. ǫθ,µF ILF O/ǫτF ILF O′ in equation (1.7) has been assumed equal to 1).
7 Results and conclusions
The values of Ntagτ′ , Ntag and the other measured quantities involved in the mea-surement of BR(τ′) are reported in Tab. 9, concerning the Kθ and the Kµ selftag.
The efficiencies have been evaluated on different data samples according to what described in Sect. 5, while the measurement of Ntagτ′ and Ntag has been performed on the A data sample (see Tab. 2).
The stability, within the errors, of the efficiencies reported in Tab. 9 has been examined remeasuring the same quantities in data samples different from the ones assigned. Two separate measurements are performed for the two selftags:
BR(K± → π±π0π0)θ = (1.766 ± 0.016stat± 0.017syst) · 10−2 , BR(K±→ π±π0π0)µ= (1.791 ± 0.015stat± 0.017syst) · 10−2 .
The statistical errors include also the contributions from the efficiencies that scale down with the collected statistics. The statistical correlations between the measure-ments performed on the same data sample (e.g. A for Ntagτ′ and ǫK, and B for ǫv and ǫ4onT) have been taken into account 18.
The final measurement of the branching ratio is obtained as their weighted av-erage value 19 :
BR(K± → π±π0π0) = (1.781 ± 0.013stat± 0.016syst) · 10−2
18In general, given two efficiencies (ǫ1and ǫ2) to be measured on subsamples S1and S2extracted from the same original sample S, the value of ǫ1· ǫ2 is computed by averaging its correlated measurement in S1∩ S2 with the product of the uncorrelated estimates of ǫ1 and ǫ2, obtained in S \ S2 and S \ S1, respectively.
19Statistical and systematic errors have been propagated independently only for quantities used in (1.7) which have been actually estimated separately for the two selftags.
Sample tagθ tagµ
Ntagτ′ A 30798 ± 180 52253 ± 230
Ntag A (1.275 ± 0.004) · 107 (1.992 ± 0.004) · 107
ǫK A 0.466 ± 0.001 ± 0.002
ǫvtx B,C,D 0.539 ± 0.003 ± 0.002
hA4clui A 0.799 ± 0.001 ± 0.003
ǫ4onT B 0.697 ± 0.002 ± 0.004 0.745 ± 0.003 ± 0.004 ǫEtot A,MC 0.9947 ± 0.0006 ± 0.0012
ǫτsel′ 0.1392 ± 0.0010 ± 0.0013 0.1488 ± 0.0011 ± 0.0013
ξbckgτ′ MC 0.0075 ± 0.0011
ξbckgtag MC 0.0037 ± 0.0002 0.0021 ± 0.0002
ΛCV C,D 0.999 ± 0.001
Table 9: Summary of the quantities involved in the measurement of the branching ratio for the Kθ- and for the Kµ- selftag. The data (or MC) sample used for the measurement is also shown. In the rows where only a number is reported, a single measurement is used for both tags. The uncertainties on Ntagτ′ and Ntag are statistical only, while those on ξbckgτ′ , ξbckgtag and ΛCV are systematic (see the text for details).
and is plotted in Fig. 29 together with the experimental measurements of BR(τ′) reported in Tab. 1 and the PDG world fit.
In Tab. 10 all the contributions (both statistical and systematic) to the total uncertainty are summarized.
As a consistency check, the value of the branching ratio has been calculated also on Monte Carlo. In this case all the measurements of the quantities involved in (1.7) have been repeated in the same way as done for real data. From MC the estimate of the branching ratio is found to be
hBR(K± → π±π0π0)i
M C = (1.745 ± 0.042stat± 0.036syst) · 10−2 ,
(7.1) in agreement with the value 1.73 [2] used as input in the initial Monte Carlo simula-tion. The systematic error on MC is larger than the one obtained on data since some of the contributions considered in the analysis scale with the collected statistics, that is much lower for the simulated than on the real data.
Source of uncertainty Relative error (10−3)
Ntagτ′ statistics 3.5
Ntag statistics 0.2
Charged kaon reconstruction/identification efficiency 5.7
Vertex reconstruction efficiency 6.6
Splitting recovery algorithm 2.3
Four clusters acceptance 3.6
On-time requirement for clusters 5.1
Total energy cut 1.4
Background subtraction 1.1
Cosmic-ray trigger veto 1.0
FILFO algorithm ≪ 1
BR(π0 → γγ)2 0.7
Total uncertainty 11.6
Table 10: Summary of all the contributions to the total relative error on the mea-surement of BR(K± → π±π0π0).
Figure 29: Comparison between the measurement of BR(τ′) ob-tained in this analysis and the previous world results: the dashed lines delimit the error of the 2002 PDG fit.
0.014 0.015 0.016 0.017 0.018 0.019 0.02 0.021 0.022 0.023
BIRGE 56 ALEXANDER 57 TAYLOR 59 ROE 61 SHAKLEE 64 PANDOULAS 70 CHIANG 72 PDG FIT 2002 KLOE 2003
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