Violation in Mixing

6.4 Counting analysis 157
120
100
80
60
40
20
Entries
Mean
RMS
NksksBkg
1000
-0.9253E-01
1.050
81.07 / 17
Constant 97.63 4.016
Mean -0.7045E-01 0.3493E-01
Sigma 1.015 0.2642E-01
0
-4 -3 -2 -1 0 1 2 3 4
300
250
200
150
100
50
0
Entries
Mean
RMS
1000
4.417
1.764
0 2 4 6 8 10 12
upper limit on the KsKs yield in 1000 ToyMC events
Figure 6-8. The pull distribution for the number of background events (left) and the upper limit distribution
(right) in 1000 Ã Ë Ã Ë toy MC experiments with the � Ó× �Ë� cut value at ��.
Table 6-4. Results of several Toy Monte Carlo experiments with different cuts.
� Ó× �Ë� mean value of mean value of upper limit eff. upper limit on
cut � bkg events distribution (on the yield) � �
� �� 282 4.4 34.9 5.0
� �� 147 3.9 30.8 5.0
� �� 80 3.4 26.9 5.0
6.4 Counting analysis
Along with the maximum likelihood fit, a counting analysis has been optimized in order to estimate the best
upper limit on � � � Ã Ã we can extract with this technique from the Run1 data sample.
The counting analysis consists of cutting and counting the events in a 2-dimensional signal box within the
¡�–Ñ�Ë plane defined with � � ¡� � � ��Î and �� ��� �Ñ�Ë � �� �� ��Î� (i.e. twice the
Ñ�Ë resolution). The region where �� ��� �Ñ�Ë � �� �� ��Î� is called Ñ�Ë signal band and the one
where �� �Ñ�Ë � �� � ��Î� is the already defined Ñ�Ë side-band.
The optimization is done to choose the best cuts on the remaining discriminating variables used in two-body
analysis: � Ó× �Ë� cut and Fisher cut. We define the best cuts for this analysis the ones which give the lowest
upper limit on � � Ã Ã branching ratio.
MEASUREMENT OF BRANCHING FRACTIONS FOR � � Ã Ë Ã Ë DECAYS