Violation in Mixing

102 Strategy and Tools for Charmless Two-body � Decays Analysis
where �Ë is the angle between the sphericity axis of the � candidate and the one of the rest of the event (using
all charged tracks and neutral particle candidates which are not used in the � candidate). Right plot in Fig.
4-1 shows the � Ó× �Ë� distribution for Monte Carlo background and signal events: a cut at �� removes the
background peaking at in this variable. All the cuts previously described are called the two-body standard
selection.
4.2.2 � candidate selection: kinematic Variables
Candidate � mesons are reconstructed by forming all pairs of oppositely charged tracks, or a charged track
and a Ã Ë or � candidate, or two Ã Ë or � candidates. The charged tracks used to form a � candidate are
selected on the basis of the GoodTracksAccLoose criteria:
¯ Æ ��À hits �
¯ � � �� Ñ, Þ � Ñ
¯ ÔÌ � Å�Î�
¯ �� ��� ��� Ö��
where Æ ��À hits is the number of ��À hits, � is the distance in the Ü� Ý plane of the POCA (Point
Of Closest Approach) of the track from the measured beam-spot, Þ is the Þ position of the POCA, ÔÌ is the
transverse momentum of the track and � is its polar angle.
Instead, the Ã Ë daughters are selected as described in Sec. 3.3. The vertex algorithm is used to estimate
the decay vertex of the candidate �. The momentum vectors of the daughter particles are recalculated using
this point as their production vertex. Simple four-vector addition, assuming the pion mass for the charged
tracks, is then used to form the � candidate four-vector. A loose mass cut of ¦� Å�Î� around the PDG
� mass value [14] is applied as part of the preselection cuts.
We define the beam energy-substituted mass [50]:
Ñ�Ë �
Ö
× Ô ¡ Ô� �� Ô � � (4.5)
where Ô × and � are the total energies of the � � system in the CM and lab frames, respectively; Ô
and Ô� are the momentum vectors in the lab frame of the � � system and the � candidate, respectively;
and Ô� is the magnitude of the � candidate momentum in the lab frame. Evaluated in the CM frame, this
variable looks like:
Õ Ô×�
Ñ�Ë �
Ô £
�
which clarifies its physical meaning. The advantage of using the definition in the lab frame with respect to
the one computed in the CM frame is that the first does not require assigning mass hypotheses to the charge
tracks.
The mean value of Ñ�Ë and its Gaussian width � Ñ�Ë are determined from a sample of fully reconstructed
� � � � decays (see next section). The values used are Ñ�Ë � �� � ¦ � � ��Î� and
MARCELLA BONA