Violation in Mixing

4
Strategy and Tools for Charmless Two-body
� Decays Analysis
This chapter describes the requirements, the techniques and the variables common to all the hadronic
charmless two-body analyses. These analyses refer to those � decays that do not include quarks in the
final states and whose final states are made up of two particles among charged and neutral � and charged
and neutral Ã.
Crucial issues in the hadronic charmless two-body modes are background fighting and particle identification
(where applicable). The main background to these decays is due to fake � candidates reconstructed in the
continuum � � � ÕÕ production (see Tab. 2-2). This background contamination together with the small
expected branching fractions and the relatively large ÕÕ cross section, would not allow for high purity values
while keeping reasonable efficiencies.
In order to reach a good discriminating power against background, CLEO approach has been adopted [46]: a
Fisher discriminant [47] has been developed and studied to separate signal from background on a statistical
basis. Since the charged tracks resulting from charmless two-body � decays have relatively high momenta
(approximately �� �� ��Î� ), the � ��Ö�Ò�ÓÚ angle � , determined from the �ÁÊ�(Sec.‘2.2.4), is the
only measurement which provides good à � discrimination.
A maximum likelihood fit is used to measure the yields in the various channels from the data sample. The fit
incorporates the Fisher output and kinematic variables of the � candidate, which are used to separate signal
and background, as well as the � ��Ö�Ò�ÓÚ angle (where applicable), which is used to distinguish between
the channels containing a � or a Ã.
A second method, a counting analysis, is used as a cross check in the measurement of the decay rates (see
Sec. 4.6).
4.1 Data samples
The full so called Run 1 data-set is used in the analyses described in the following chapters. The detailed
data sample used is:
¯ �� ¦ � fb of on-resonance data corresponding to �� ¦ �� ¢ � �� events.
¯ �� ¦ � � fb off-resonance