Violation in Mixing

1.3 The Three Types of �È Violation in � Decays 25
To obtain the asymmetry in 1.40 as function of �Õ�Ô�, one can derive from the Eqs. 1.24 and 1.25 the
expressions:
��� �� Ô�Ý× Ø �� �
��� �� Ô�Ý× Ø �� �
¬
¬
¬ Õ
¬ Ô
Ô � Ø
Õ � Ø
¬
and thus �×Ð � �Õ�Ô��
�Õ�Ô� �
Effects of �È violation in mixing in neutral �� decays, such as the asymmetries in semileptonic decays, are
expected to be small, Ç . In addition, to calculate the deviation of Õ�Ô from a pure phase, one needs
to estimate and Å , but they involve large hadronic uncertainties, in particular in the hadronization
models for . The overall uncertainty can be even a factor of – in �Õ�Ô� [13]. Thus even if such
asymmetries are observed, it will be difficult to relate their rates to fundamental �ÃÅ parameters.
Going back to the general case, Eq. 1.26 can be rewrite as [15]:
Õ
Ô �
�
� �
�Å � ×�Ò �Å �
� � � �Å
The order of magnitude of the term ×�Ò �Å � is Ñ �Ñ� . Remembering Eq. 1.8, the main
contribution to �Õ�Ô� can be evaluated as:
�Õ�Ô�
� �
ÑØ
� � Ñ
�
� �
Ñ
�
ÑØ
�
Ò�
Ç � �
and thus the effect of �È violation in mixing in neutral �� decays are supposed to be rather small.
1.3.3 �È Violation in the Interference Between Decays With and Without Mixing.
Taking into account neutral � decays into final �È eigenstates, ��È [16, 17, 18], these states are accessible
from both � and � decays. The quantity that can be used in studying this type of �È violation, is � of
Eq. 1.31,
� � Õ
Ô
���È
���È
� ��È ���� ���È � (1.41)
where ��È is the �È eigenvalue of the ��È state (�È � ��È � � ���È � ��È �) and ��È represents the weak
CKM phase of the ���È amplitude. When �È is conserved, both �Õ�Ô� � and ����È
����È � � , as seen
in the previous sections: also the relative phase between Õ�Ô and ���È
����È vanishes (as one can see
in Eq. 1.33 where ÁÑ�is the coefficient of the ×�Ò� term). Thus, from the definition of � in Eq. 1.31, one
can obtain the condition:
�
�È VIOLATION IN THE �� SYSTEM