Violation in Mixing

1.4 �È Violation in the Standard Model 27
As shown in Eq. 1.33, the value of the time-dependent asymmetry is given by:
���È � ����È� Ó× ¡Ñ�Ø ÁÑ���È
����È� ×�Ò ¡Ñ�Ø
� (1.44)
This asymmetry will be non-vanishing if any of the three types of �È violation are present. In the particular
case of ��È being the �È eigenstate Â��Ã Ë (the so called golden mode), one can measure �È violation
effect given by ×�Ò ¬. In such decays for which ��� � , the expression 1.33 simplifies considerably:
���È � ÁÑ���È ×�Ò ¡Ñ� Ø (1.45)
with no hadronic uncertainties from the strong interactions. In case no �È violation in decay is present,
�È violation in the interference between mixing and decay can be cleanly related to CKM parameters: in
particular, if decays are dominated by a single �È -violating phase, ���È is cleanly translated into a value
for ÁÑ�(see Eq. 1.45) which, in this case, is easily interpreted in terms of purely electroweak Lagrangian
parameters.
On the other hand, when �È violation in decay is present, the asymmetry in 1.43 depends also on the ratio
of the different amplitudes and their relative strong phases, and thus the result is not cleanly interpreted
because of the hadronic uncertainties. In some cases, however, it is possible to remove any large hadronic
uncertainties by measuring several isospin-related rates and extract a clean measurement of �ÃÅ phases
(this is the case of two pion decays, see Sec. 1.5.2).
There are also many final states for � decay that have �È self-conjugate particle content but are not �È
eigenstates because they contain admixtures of different angular momenta and hence different parities. In
certain cases angular analyses of the final state can be used to determine the amplitudes for each different
�È contribution separately (this is the case of � � Â��à £ decays [24]).
1.4 �È Violation in the Standard Model
1.4.1 The �ÃÅ Picture of �È Violation
The Standard Model [19] is the theory describing the electromagnetic, weak and strong interactions. It is
based on a ËÍ � ¢ ËÍ Ä ¢ Í � gauge symmetry with three fermion generations. �È violation is
accommodated in this model through a phase in the mixing matrix for quarks [3]. Each quark generation
consists of three multiplets:
É Á Ä �
� Á �
ÍÄ � � ��� Ù Á Ê � � � � � Á Ê � � � �
� Á Ä
�È VIOLATION IN THE �� SYSTEM