Violation in Mixing

4.5 Tracking Corrections 111
Ë�Ð� ØÓÖ ¯ ��� ¯ ��� ¯ ��� ¯ ���
SMS(Loose) 89.0¦0.4 6.3¦0.3 11.0¦0.3 93.7¦0.4
Table 4-4. Selector efficiencies for a single track within the �ÁÊ� acceptance.
With exception of �-momentum correlation, the efficiency shows no significant � angle dependence for high
momenta. The fall in efficiency for low momenta vertical tracks almost disappears above ����� (see
the right plots in Fig. 4-8).
4.5 Tracking Corrections
The difference in track reconstruction efficiency between data and Monte Carlo simulated events is taken
into account by following the standard procedure outlined by the BABAR Tracking Efficiency Task Force [52].
Look-up tables are used to scale the reconstruction efficiency for each track in the Monte Carlo sample. The
scale factors are functions of the ÔØ, polar and azimuthal angles of the track, as well as the track multiplicity
of the event. The overall correction factor to the efficiency is estimated on a mode by mode basis.
4.6 Analysis methods
The analyses are based on an unbinned maximum likelihood fit to determine from the data yields and
asymmetries. The signal yields are divided by the efficiency estimates and by the number of neutral �
mesons produced in the data-set in order to obtain branching ratio measurements.
The distributions for Ñ�Ë, ¡� and � provide good discrimination between signal and background, while
the use of the � ��Ö�Ò�ÓÚ angles, � allows the fitter to measure the particle ID content of the � candidates.
The quantity ¡� provides additional separation power between signal modes which differ for PID contents
of their final states.
The likelihood, Ä, for a given candidate � is obtained by summing the product of event yield Ò� and
probability � over all possible signal and background hypotheses �. The � are determined by maximizing
the extended likelihood function Ä
Ä � � È Å
�� �
�
� �
��
��
Ò�È� � Ü �� � « �
where È� � Ü �� � « � is the probability for candidate � to belong to category � (of Å total categories),
based on its characterizing variables � Ü � and parameters � « � that describe the expected distributions of
these variables. The probabilities È� � Ü �� � « � are evaluated as the product of probability density functions
(PDFs) for each of the independent variables � Ü �, given the set of parameters � « �:
È� � È Ñ�Ë
� È ¡�
� � � �
�
�
(4.8)
� (4.9)
STRATEGY AND TOOLS FOR CHARMLESS TWO-BODY � DECAYS ANALYSIS