Violation in Mixing

4.6 Analysis methods 115
Events/2.5MeV/c 2
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BABAR
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m ES (GeV/c 2 )
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Figure 4-9. Left plot: the Ñ�Ë distribution for fully reconstructed � � � � (� � à � ) decays
(points) and for � � � � decays (histogram) in Monte Carlo simulated data. Right plot: the Ñ �Ë
distribution for fully reconstructed � � � � (� � Ã � ) decays. The fit function is described in the
text.
is the � � � � signal as well as a large “shoulder” to the left of the signal, which is due primarily to
fake � decays.
The widths of the narrower Gaussians are �� � ¦ � � Å�Î and �� ¦ ��� Å�Î for Monte Carlo
simulated decays and for Run 1 data, respectively. From this comparison, one estimates a � degradation
of the ¡� resolution for data, with respect to the Monte Carlo simulation. In addition, the data ¡�
distribution is observed to be offset from zero by ��� ¦ ��Å�Î. Offsets of the order to �Å�Î
are observed in other fully reconstructed � decays as well.
Because this is such a considerable correction factor, a large range of possible ¡� resolutions is used in
computing the associated systematic uncertainty: the lower bound is chosen from using twice the uncertainty
on the correction factor, while the upper bound is chosen to be conservative adding the entire correction
factor. We also assume that in data the reconstructed ¡� is shifted downward by �Å�Î, the same amount
that is observed for the � � � � data sample.
As was described in section 4.2.1, the pion mass is assigned to the charged tracks when forming a �
candidate and calculating ¡�. Therefore, modes with a à in the final state will have a ¡� value which is
not centered at zero, but is shifted to negative values by a quantity which depends on the momenta of the
kaon track(s). This is due to the fact that the candidate energies are calculated in the CM system and the
boost to that frame depends on the mass hypotheses of the tracks. On average, the mean ¡� value for one or
two à in the final state is �� � Å�Î. The variation due to the boost effect is of the order �¦ � Å�Î.
STRATEGY AND TOOLS FOR CHARMLESS TWO-BODY � DECAYS ANALYSIS