Violation in Mixing

48 The BABAR Experiment
�� � ¬� � � �� ¡ ��� �Ñ �� �Ñ
which is a quite small value with respect to a typical vertex detector resolution (� � �Ñ).
Figure 2-1. Applied boost in the BABAR laboratory system.
If a boost is applied along the Þ axis, it results in a larger value of ¬­ so that the average � meson decay
distance ¡Þ is increased to values within the detector resolution. In order to produce a boost, PEP-II has
two rings, one for ���Îelectrons and one for � ��Îpositrons: therefore in the laboratory frame, the
§ �Ë resonance has a non-zero momentum Þ component
¬­ § �Ë �
ÚÙ
Ù
Ø � ØÓØ Ñ § �Ë
Ñ § �Ë
� ����
The � � system moves in the boost direction and considering the time expansion effect, the decay vertex
distance increases up to ¬­ � � ��� ¡ ��� �Ñ � � �Ñ, a value the BABAR detector can measure with
good resolution.
The Þ component of a � decay position is related to the meson decay time: in the center of mass frame
(CM), the relation is
Þ�Å � ¦¬�Å Ø�Å Ó× ��Å
where ��Å is the angle between the � decay direction and the Þ axis direction and where ¬�Å is the meson
velocity.
In the laboratory frame, the Þ component of the decay position becomes
MARCELLA BONA