Violation in Mixing

6.3 The maximum likelihood analysis 153
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Constant 1267. 24.31
Mean 0.6610E-02 0.2302E-03
Sigma 0.1683E-01 0.2216E-03
0
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
Figure 6-4. ¡� distribution in the signal Ã Ë Ã Ë Monte Carlo sample.
The difference between the � candidate’s energy and Ô ×� , ¡�, is parameterized as a Gaussian for the
signal (Fig. 6-4) and as a second order polynomial for the background (Fig. 6-5).
In the signal, the width of the Gaussian is ���Å�Îfor Ã Ë Ã Ë Monte Carlo. A comparison of � � � �
decays in data and Monte Carlo indicates that the Monte Carlo resolution should be scaled by a factor
� �¦ � � to agree with data. As a consequence, in case of Ã Ë Ã Ë decays, we have estimated the resolution
on ¡� in real data to be � ¦ �Å�Î. To test the dependence of the fit from the ¡� resolution, we fitted
1000 toy MC experiments with a single Gaussian signal ¡� distribution having the same toy MC resolution
or � � times better or � � times worse: the results of these fits are perfectly consistent with each others.
The distribution of the Fisher discriminant for the event, �, is fitted with a double Gaussian for both
background and signal. For the parameterization of the Fisher variable in signal events we have used signal
Ã Ë Ã Ë MC, while for the Fisher variable in the background events, we have used the on-resonance Ñ�Ë
side-band (Figure 6-6) defined as �� �Ñ�Ë � �� � ��Î� .
The Fisher distribution in on-resonance Ñ�Ë side-band has been validated against continuum MC and offresonance
data (Figure 6-7).
Table 6-2 summarizes the functional form of PDFs and the samples used to obtain them.
MEASUREMENT OF BRANCHING FRACTIONS FOR � � Ã Ë Ã Ë DECAYS