Violation in Mixing

26 �È Violation in the �� System
where ¦ depends on the eigenstate ���È .
� �� ¦ � �È Ú�ÓÐ�Ø�ÓÒ� (1.42)
Both �È violation in decays (1.37) and �È violation in mixing (1.39) lead to the condition 1.42 through
��� �� . But even in the case in which, to a good approximation, ��� � and ����� � , yet there can be
�È violation if:
��� � � ÁÑ��� �
This type of �È violation is called �È violation in the interference between decays with and without mixing
or more briefly “interference between mixing and decay”. This type of �È violation has also been observed
in the neutral kaon system.
Figure 1-3. �È -violating asymmetries result from interference effects involving phases that change sigh
under the �È operator. The weak phase of the �ÃÅ matrix has this property. One way to observe �È
violation is to use the interference between the direct decay � � ��È and the process � � � � ��È :
the Standard Model predicts substantial asymmetries between this process and the one in which the initial
meson is a � .
For the neutral � system, �È violation in the interference between decays with and without mixing can be
observed by comparing:
- direct decays � � �, where � is a final state accessible in both � and � decays;
- � � � mixing followed by the � � � decay.
The state � can be a �È eigenstate, but that’s not a necessary condition. From the analysis proposed in
Sec. 1.2.6, one gets:
MARCELLA BONA
���È � � Ô�Ý× Ø � ��È � Ô�Ý× Ø � ��È
� Ô�Ý× Ø � ��È � Ô�Ý× Ø � ��È
� (1.43)