Violation in Mixing

182 Analysis of the time-dependent �È -violating asymmetry in � � � � decays
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1 -0.5 0 0.5 1
Offset (mrad) vs K cosθ
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1 -0.5 0 0.5 1
Offset (mrad) vs π cosθ
BaBar Data (2001)
4.5
4
3.5
3
2.5
2
1.5
-1 -0.5 0 0.5 1
Sigma (mrad) vs K cosθ
4.5
4
3.5
3
2.5
2
1.5
-1 -0.5 0 0.5 1
Sigma (mrad) vs π cosθ
250
200
150
100
50
θ-θ exp K (1.75,1.875)
BaBar (2001)
0
-0.05 -0.025 0 0.025 0.05
300
250
200
150
100
50
0
-0.05 -0.025 0 0.025 0.05
250
200
150
100
0
-0.05 -0.025 0 0.025 0.05
θ-θ exp K (1.875,2.0)
θ-θ exp π (1.75,1.875) θ-θ exp π (1.875,2.0)
50
250
200
150
100
50
0
-0.05 -0.025 0 0.025 0.05
Figure 7-8. Left plots: distributions of � offsets (left) and resolutions (right) in the Run 2 � control
sample as functions of track polar angle. Top plots are for kaons, bottom plots are for pions. Right plots:
distributions of � � �ÜÔ Ó«×�Ø for kaons (top) and pions (bottom) in the Run 2 � control sample.
The left (right) plots correspond to the momentum bin ���– ���� ��Î� ( ����– � ��Î� ).
for the coefficients �� and ��� of the sine and cosine terms, respectively. Although the à à final state
is a �È eigenstate, we treat this component as a pure lifetime. The functional form for the Ã� component is
given by Eq. 7.9. We fix the parameters � and ¡Ñ�� to their PDG values [14] and take the error into account
as a systematic uncertainty. The background ¡Ø PDF is given by the triple-Gaussian resolution function
Ê���, with the parameters defined in Table 7-7. The ¡Ø parameterization is summarized in Table 7-12, and
the final set of free parameters in the maximum likelihood fit are listed in Table 7-13.
7.7.2.1 Correlations between PDF variables
An implicit assumption in the construction of the likelihood function is that the PDF dependent variables
are uncorrelated. Table 7-14 summarizes the linear correlation coefficients for all pairs of Ñ�Ë, ¡�, �, � ,
� , ¡Ø, and �¡Ø. Correlations greater than are highlighted.
The correlation between Ñ�Ë and ¡� is not thought to have any significant impact on the fit (mostly because
the MC correlation is inflated by the better ¡� resolution compared with data). The correlations between
the � ��Ö�Ò�ÓÚ angles, and between � and ¡�, inÃ� and Ãà events is due to the underlying momentum
MARCELLA BONA