Violation in Mixing

114 Strategy and Tools for Charmless Two-body � Decays Analysis
Fit Variable Shape Samples Used
Signal Ñ�Ë Gaussian � � (signal MC)
Background Ñ�Ë ARGUS Side-band (Off-res, MC ÕÕ)
Signal ¡� Gaussian � � (signal MC)
Background ¡� Quadratic Side-band (Off-res, MC ÕÕ)
Signal Fisher Double Gaussian signal MC (� � )
Background Fisher Double Gaussian Side-band (Off-res, MC ÕÕ)
Kaon � Gaussian � £ (MC � £ , signal MC)
Pion � Gaussian � £ (MC � £ , signal MC)
Table 4-5. Summary of functional forms of PDFs used in the fit and the samples used to obtain them.
The samples in parentheses represent additional samples which were used as consistency checks and provide
alternative parameterizations that can be used for studies of systematics.
fit: the chosen value is ÑÑ�Ü � �� ��� ��Î� . The off-resonance and Monte Carlo simulated ÕÕ data
samples are used to demonstrate that the Ñ�Ë distribution obtained from the on-resonance side-band sample
accurately represents the shape of the background in the on-resonance signal region.
As discussed above, the shape of the Ñ�Ë distribution for signal events can very reliably be taken directly
from the Ñ�Ë distribution of fully reconstructed � � � � decays. This is demonstrated in the left
plot in Fig. 4-9, which displays the Ñ�Ë distribution for Monte Carlo simulated � � � � and � �
� � decays. Since there is good agreement between the two modes, we use the Ñ�Ë distribution from
� � � � decays in data, displayed in the right plot in Fig. 4-9, to parameterize the Ñ�Ë PDFs. The
distribution is fitted with a Gaussian for the signal and an ARGUS function for the background. The fit
result gives �Ñ�Ë� ��� � ��Î� and � Ñ�Ë � ��Å�Î� .
4.6.3 Energy difference ¡�
As was done for Ñ�Ë, the on-resonance side-band data are used to determine the shape of ¡� for background
in the signal region. A second order polynomial is found to give the best fit results: an example
is given in Fig. 4-10. Also shown are the distributions of ¡� for off-resonance data and Monte Carlo
simulated continuum events. There is good agreement between the shapes of all three samples.
The � � � � control sample is used to understand the ¡� resolution. The ¡� distributions for
� � � � decays in data and Monte Carlo simulated data are shown in Fig. 4-11. The Monte Carlo
distribution is best fit by the sum of two Gaussians, but the statistics are not large enough in the data sample
to perform a reliable double Gaussian fit. Thus, in fitting the data ¡� distribution, the relative area of
the wider Gaussian and its width are fixed to the values obtained from the Monte Carlo distribution. The
combinatorial background in the ¡� distribution is subtracted off using Ñ�Ë side-band data. What remains
MARCELLA BONA