Violation in Mixing

112 Strategy and Tools for Charmless Two-body � Decays Analysis
The Poisson factor in Eq. 4.6 is the probability of observing Å total events (the number of events used in
the fit) when Å are expected. The quantity ÐÓ� Ä is minimized, which is equivalent to maximizing Ä
itself, with respect to the fit variables.
As a cross-check, a counting analysis is performed: this is very similar to the likelihood one, but differs
in its treatment of PID (see Sec. 4.4.2). Standard BABAR particle selector algorithms are used to separate
the selected sample into subsamples which have identified �’s and Ã’s in the final states. A cut is placed
on �. The fit includes events passing all cuts except the requirement that the tracks have an associated �
measurement.
A maximum likelihood fit which uses all quantities except � and � is then used to determine the signal
yields in each of the subsamples. These yields are corrected by an efficiency/cross-feed matrix which takes
into account both the selector efficiencies and residual cross feed of the other signal decays into each of the
subsamples. The corrected number of candidates are then normalized to the total efficiency of the selection
cuts and to the total number of �� pairs: the branching fraction is therefore determined. The results from
this analysis are compared with the official results, described above.
In the following section, descriptions of the PDFs, as well as the samples used to estimate them, are
presented.
4.6.1 Sample definitions
The functional forms of the PDFs of the variables introduced in the previous section are derived from data
samples that are independent of the sample used in the fit. These include: off-resonance data, on-resonance
data from ¡� side-bands, control samples of fully reconstructed � � �� decays, control samples of
� � £ � decays and Monte Carlo simulated events. The definitions of the samples used in this analysis
are described below, followed by descriptions of how the PDFs used in the fit are derived from these samples.
Monte Carlo simulated events
A large sample of Monte Carlo simulated events is used to study both background and signal distributions
and selection efficiencies.
¡� side-band data:
� candidates are selected in a ¡� range which is mode dependent. Let’s consider the example of the � �
decay mode in which case the range considered is �¡�� � �� ��Î. The ¡� variable is used to subdivide
the data into two samples:
� � � �¡�� � �� ��Î Ë��� ��Ò� (4.10)
� � � ¡� � � � ��Î Ë��Ò�Ð (4.11)
The same can be done in each mode. The signal range defines the region in which of the signal lies.
The side-band region is used to study characteristics of the background.
MARCELLA BONA