Violation in Mixing

5.7 Determination of branching fraction 147
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Figure 5-17. Ñ�Ë distribution in the ¡� signal region with superimposed the fitted function (sum of an
ARGUS function, with � � � , and a Gaussian with Ñ�Ë ��� � ��Î� and � Ñ�Ë � ��Å�Î� .)
for candidates in which the � ¦ is compatible with the � hypothesis(left) and with the K hypothesis(right).
Branching fractions are calculated as
�Ê Ã � � �Ê Ã � ÃË ¡ �Ê Ã Ë � � �
ÆË Ã Ë �
¯ ¡ Æ ��
� (5.4)
where ÆË is the central value from the fit, ¯ is the total efficiency, and Æ �� � ��� ¦ � � ¢ � is the
total number of �� pairs in our data-set. �Ê Ã � Ã Ë is taken equal to �� and �Ê Ã Ë � � �
equal to ���� [14]. Implicit in Eq. 5.4 is the assumption of equal branching fractions for § �Ë � � �
and § �Ë � � � .
For the Ã Ë Ã mode we calculate the � confidence level upper limit yield and the result is increased by
the total systematic error that, in this case, is reduced to the contributions from the efficiency and the number
of ��, since no contribution comes from varying the likelihood parameters. The results are summarized in
Table. 5-12. The statistical significance of a given signal yield is determined by setting the yield to zero and
maximizing the likelihood with respect to all other variables.
In summary, the branching fraction for � ¦ � à � ¦ is ��
of � ¦ � à à ¦ we set an upper limit of �� ¡ � .
�
�
��
�� ¡ � , while on the branching fraction
MEASUREMENT OF BRANCHING FRACTIONS FOR � ¦ � Ã � ¦ DECAYS