Violation in Mixing

4.6 Analysis methods 119
θ c radians
0.85
0.825
0.8
0.775
B A B AR
π
K
2 3 4 5
p GeV/c
Number of σ separation
10
8
6
4
2
0
b)
BABAR
2 2.5 3 3.5 4
K-π separation versus p GeV/c
Figure 4-14. The � ��Ö�Ò�ÓÚ angle (a) and Ö� separation (b) as functions of momentum for tracks in the
� control sample. Both tracks must be in the same momentum bin to achieve a given � separation. Tracks
below the dashed line in (a) are rejected as proton candidates.
kaon(pion) tracks and has a width three times that of the primary peak. Left plots in Fig. 4-13 display
the quantity � � for kaon tracks in four representative momentum bins. Overlayed on the distributions
are the results of the double Gaussian fits to both the primary peaks and the satellite peaks. No significant
momentum or Ó× � dependence is observed. The effect is present in Monte Carlo simulated decays at a
somewhat smaller level (� ).
The satellite peak is included in the � PDFs as a second Gaussian with width and relative area fixed to the
values described above, and centered at the opposite particle hypothesis. As will be demonstrated later, the
presence of these satellite peaks has a very small effect on the fit results.
The � measurements for pions and kaons in Monte Carlo simulated � � � � decays have been
compared with those derived from the Monte Carlo � £ control sample and good agreement is found.
This validates the use of the � £ decays in the data as a means of parameterizing the � resolutions and
offsets for the signal samples.
4.6.6 Correlations between PDFs
The PDFs described in the previous sections are assumed to be uncorrelated in the maximum likelihood fit.
To check this assumption, in each decay mode, the linear correlation coefficient �� between the PDFs for
STRATEGY AND TOOLS FOR CHARMLESS TWO-BODY � DECAYS ANALYSIS