Violation in Mixing

44 �È Violation in the �� System
6–98
8418A2
1
2
A(B° π°π°)
A(B° π + π – ~
)
A(B + π + κππ
1
2
π°)
Δκππ
A(B° π + π – )
~
A(B π – π°)
T+C
~ ~
C
PEW + PEW ~
A(B° π°π°)
C
PEW + PEW Figure 1-10. Isospin analysis of � � �� decays with the inclusion of electroweak penguins.
�Ì �� ���� �È��Ç � ���� �È�Ï� �Ç � �È � �Ï� �Ç � (1.74)
where � � % and it is simply a size-counting factor. These newly defined amplitudes still form the
triangles of Eq. 1.70, but there are now two amplitudes, with different weak phases, which contribute to
� � � � and to its �È conjugate. This means that the two triangles no longer have a common base:
Fig. 1-10 shows the new triangles. Thus the presence of EWP’s introduces another theoretical uncertainty
¡�� in the extraction of the angle ��� and then in the determination of « [27]:
¡« � ¡�� �
¬
¬ È�Ï È � �Ï
Ì �
¬
¬ � (1.75)
However, this uncertainty is small (of the order Ç � � �%) and so taking into account the electroweak
penguins does not significantly pollute the isospin analysis. Moreover this conclusion is largely independent
of assumptions about the size of color suppression in � � �� decays, since if the � (and È � �Ï )
contributions turn out to be larger than expected, the uncertainty in « is still at most about 5%.)
1.5.3.2 � � �Ã
An isospin analysis can be performed for � � �à decays as well as in the previous channels [28, 29].
By measuring the rates for � � � Ã , � � � Ã and � � � Ã , along with the rates and
�È asymmetry in � � � ÃË, it is possible in principle to remove the penguin pollution and measure «.
This analysis though is strongly based on the assumption of negligible electroweak-penguin contributions.
� � �à decays have contributions from both the � � ÙÙ× tree amplitude and the � � × penguin
amplitude. For example, in case one considers the � � × penguin amplitude being comparable with the
MARCELLA BONA