Violation in Mixing

7.4 Data samples and event selection 171
Figure 7-2. The fitted �� yield divided by its error for three samples of 1000 toy experiments corresponding
to different cuts on Ó× �Ë.
The separation between signal and background in the Fisher variable is reduced when cutting harder on
� Ó× �Ë�, which partially compensates the increased signal-to-background ratio. To optimize this cut,
toy experiments were generated corresponding to each of the three samples. Each experiment is fit with
the likelihood function used in the branching ratio analysis with the usual PDFs for Ñ�Ë, ¡�, and � and
the appropriate re-parameterized Fisher PDF based on the � Ó× �Ë� cut. Events are generated with Poisson
statistics corresponding to the published Run 1 result (see Sec. 7.2), scaled up to fb and modified by the
relative efficiency of the different Ó× �Ë cuts. The signal efficiency is obtained assuming a flat distribution,
while the background efficiency is obtained from the on-resonance Ñ�Ë side-band data.
Figure 7-2 shows the distribution of fitted �� yield divided by its error, which is an estimate of Ë� Ô Ë �,
for each of the toy samples. The �� and �� samples give the same significance, while the �� sample is less
optimal. The cut at �� removes � of the background and leads to more Gaussian Fisher distributions.
The reduction in background means that the time-dependent fits and toy Monte Carlo studies run twice as
fast, which is not an insignificant advantage. We have therefore decided to use � Ó× �Ë� � �� as our default
cut.
ANALYSIS OF THE TIME-DEPENDENT �È -VIOLATING ASYMMETRY IN � � � � DECAYS