Violation in Mixing
Violation in Mixing
Violation in Mixing
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7.8 Validation studies 185<br />
Figure 7-9. Left plots: pull plots for signal yields and the � charge asymmetry <strong>in</strong> ��� toy experiments<br />
generated with fb equivalent lum<strong>in</strong>osity. Right plots: pull plots for background yields and the �<br />
charge asymmetry <strong>in</strong> ��� toy experiments generated with fb equivalent lum<strong>in</strong>osity.<br />
7.8 Validation studies<br />
Numerous studies us<strong>in</strong>g toy Monte Carlo, simulation, and real data have been performed to optimize and<br />
validate the analysis strategy. Figures 7-9 through 7-11 show pull plots for all free fit parameters <strong>in</strong> ��� toy<br />
experiments correspond<strong>in</strong>g to the nom<strong>in</strong>al �È fit. Signal and background yields are generated accord<strong>in</strong>g<br />
to a Poisson distribution with means equal to the PRL result scaled to fb . The yield for signal ÃÃ<br />
is generated with zero branch<strong>in</strong>g fraction and fit with the constra<strong>in</strong>t ÆÃà � . Random values of ���<br />
are generated between ¦ and random values of Ë�� are generated with<strong>in</strong> the bounds given by the selected<br />
value of ���. The numbers of � and � tags are consistent with the generated value of ���. The most<br />
probable �È asymmetry fit errors are �Ë�� � �� and ���� � ��� (Fig. 7-12).<br />
7.8.1 Toy Monte Carlo<br />
Due to the two-body nature of the decay, the daughter tracks <strong>in</strong> � � � � are essentially anticorrelated<br />
<strong>in</strong> momentum and polar angle. First two plots <strong>in</strong> Fig. 7-13 show scatter plots of these two variables<br />
for tracks <strong>in</strong> signal �� Monte Carlo. In addition, the assignment of the pion mass to all tracks leads to a<br />
systematic shift <strong>in</strong> the mean ¡�, which is momentum dependent due to the boost (see right plot <strong>in</strong> Fig. 7-13).<br />
This underly<strong>in</strong>g momentum dependence of � and ¡� is the source of the large correlations between these<br />
variables reported <strong>in</strong> Table 7-14.<br />
ANALYSIS OF THE TIME-DEPENDENT �È -VIOLATING ASYMMETRY IN � � � � DECAYS