Violation in Mixing

4.3 Background fighting 105
Figure 4-4. Comparison of CLEO cones between off-resonance data and the Monte Carlo sample used to
train the Fisher discriminant.
are defined:
where Í ��×
��
«� �
�
��
Í � ��
Í × ��
� � � � × �
are the elements of the covariance matrices for the background (b) and signal (s) events, and
� ��×
� are the mean values that the � variables assume for background (b) and signal (s). The coefficients
(the covariant matrix elements and the mean values) have to be determined training the algorithm on
large samples of Monte Carlo simulated events (or off-resonance data or side-bands for the background
components).
In this analysis, the discriminating variables � have been chosen to be nine energy cones, the same variables
used in the CLEO analysis. The energy cones are the scalar sum of the momenta of all charged and neutral
particles in the rest of the events (i.e. excluding the � decay products) flowing into nine concentric cones
centered on the � candidate thrust axis in the CM frame. Each cone subtends an angle of Æ and is folded
to combine the forward and backward intervals (see drawing in Fig. 4-4). More energy will be found in the
cones nearer the candidate thrust axis in jet-like continuum background events than in the more isotropic
�� events. A variety of discriminating variables have been considered in addition to the cones, but detailed
comparisons show no significant gain.
The Fisher algorithm is trained on a �� fb sample of continuum Monte Carlo events: Fig. 4-4 shows good
agreement in all nine cones between off-resonance and Monte Carlo data. A sample of 2000 � � � �
STRATEGY AND TOOLS FOR CHARMLESS TWO-BODY � DECAYS ANALYSIS