Violation in Mixing

4.6 Analysis methods 117
Figure 4-11. The ¡� distributions for fully reconstructed � � � � (� � à � ) decays in (left)
Monte Carlo simulated data, and (right) Run 1 data. The fits are described in the text.
The distribution of � for the signal is very similar for all the signal modes, as well as for � � � �
events, and is found to be well-modelled by the Monte Carlo simulation (see Fig. 4-5). Two Gaussians are
used to describe the distribution. Monte Carlo simulated signal decays are used to describe the Fisher PDF
for signal.
4.6.5 Pion and kaon �
The � PDFs are determined by forming the � � distributions for the kaon and pion tracks of the �
decays in the � £ control sample, in Ó× � slices in the range � � � , where � is the polar angle of
the track and � is the expected � ��Ö�Ò�ÓÚ angle: � � Ó× � Ò¬ (Ò � ��� is the mean index of
refraction of the quartz bars of the �ÁÊ�). Only tracks in the momentum range ���–�� � ��Î� are used.
These distributions are fitted to single Gaussians and the widths (�� ) and offsets from zero of the means are
tabulated. Fig. 4-13 displays the offsets and widths of the aforementioned Gaussian fits.
The distribution of � versus track momentum and measured Ö� separation are given in Fig. 4-14. The
Ö� separation is defined as �� � � �� à ����� �. The separation is greater than ��� throughout
the momentum range.
There is a small amount of cases where a true kaon(pion) is assigned a � measurement consistent with a
pion(kaon). This is due to biases in the � reconstruction algorithm and not due to poorly reconstructed
� measurements which lead to long, non-Gaussian tails. The size of the effect is determined by plotting
� � in bins of momentum and observing a “satellite” peak centered at the expected � difference for pions
and kaons. To good approximation, the satellite peak constitutes ( ) of the total number of selected
STRATEGY AND TOOLS FOR CHARMLESS TWO-BODY � DECAYS ANALYSIS