Violation in Mixing

174 Analysis of the time-dependent �È -violating asymmetry in � � � � decays
Parameter Run 1 Run 2 MC
� ÓÖ� � � ¦ � � � ¦ � � � � ¦ � �
� ÓÖ� �� � ¦ � �� ¦ � � ��� ¦ �
�Ø��Ð � �� ¦ � � � �� ¦ � � � � ¦ �
�Ø��Ð � � ¦ � � � ¦ � � � � ¦ � ��
�Ø��Ð �� ¦ � � �� � ¦ � �� ���� ¦ � �
�ÓÙØ � �� ¦ � � � �� ¦ � � � ¦ � �
�ÓÙØ (fixed) � (fixed) � (fixed)
�ÓÙØ ����� ¦ � �� � ¦ � �� �� �� ¦ ����
Table 7-7. Parameters for the triple-Gaussian background ¡Ø resolution function Ê ��� in on-resonance
and continuum Monte Carlo samples. Separate parameterizations are used for Run 1 and Run 2. Means and
resolutions are in Ô×.
component, even for events. We therefore choose to parameterize the distribution as the sum of three
Gaussians: core, tail, and outlier, with the same parameters for ��, Ã�, and Ãà background. Attempting
to incorporate event-by-event errors leads to unstable parameterizations, therefore, we do not make use of
the ¡Ø error.
The Gaussian parameters are obtained from an unbinned maximum likelihood fit to the on-resonance sideband
sample, with the outlier mean fixed to Ô×. Figure 7-3 shows the fit result for Run 1 and Run 2 data.
Table 7-7 lists the fitted parameters. The � ��� for the triple-Gaussian fit is �� in Run 1 and �� in
Run 2. The Kolmogorov test returns a probability of �� for both Run 1 and Run 2. There is a significant
negative bias in ���Рin Run 1 and a positive bias in Run 2. The origin of the shifts is not understood, but it
is accounted for in the systematic error (Sec. 7.10).
Several cross-checks have been performed to validate the ¡Ø parameterization. Figure 7-4 shows the onresonance
side-band data compared to a parameterization obtained in the fit region. In this fit the signal
and background yields are determined from Ñ�Ë, ¡�, �, and � simultaneously with the background ¡Ø
parameters. For the signal, we use the same resolution function as the ×�Ò ¬ analysis [70]. Good agreement
is found between the parameters obtained from the fit region and side-band data.
In order to justify using an average of all species, we fit the side-band data with separate parameters for each
species. We find no difference between the �� and Ã� parameters, and only small differences in the ÃÃ
sample. These differences are probably due to the significant correlation between Gaussian parameters and
the fewer number of ÃÃ events in the sample (cf. Table 7-5). The average fit results (Table 7-7) are used
in the �È fit.
Finally, we check the dependence on tagging by fitting the sub-samples corresponding to each category, as
well as the untagged and all-tagged events. We find reasonable consistency across tagging categories, and
between tagged and untagged events. The average background parameterization is used for all categories,
and systematic errors are evaluated using the other parameterizations.
MARCELLA BONA