Violation in Mixing

4.6 Analysis methods 113
Ñ�Ë side-band data:
� candidates are selected in the range �� �Ñ�Ë � �� ��Î� . The Ñ�Ë side-band sample is defined to
be all candidates which are in the signal ¡� region, given above, and have �� �Ñ�Ë � �� � ��Î� .
charmless �� Monte Carlo:
The charmless �� Monte Carlo sample is used to estimate the amount of feed-down from other charmless
� decays. It is found to be negligible 5 in the ¡� signal region.
Off-resonance data:
Data taken � Å�Î below the § �Ë resonance is used to study continuum � � � ÕÕ background, free
from any �� contamination.
� � � � control sample:
The resolution of Ñ�Ë and ¡� for charmless two-body decays can be studied using a sample of fully
reconstructed � � � � decays, where � � à � (see Sec. 4.2.2.1). The Ñ�Ë resolution is
dominated by the spread in the beam energies for � decays involving only charged tracks in the final state.
The relatively large statistics of the � � � � signal can be used to accurately measure both the mean
and resolution of Ñ�Ë for the � � � � or � � Ã Ë � signals. The ¡� resolution, on the other hand,
is dominated by the track momentum resolution and differs between the control sample and the signal, due
to the softer momentum spectra of the tracks in the control sample. However, a comparison of the ¡�
resolutions obtained in data and Monte Carlo simulated � � � � decays can be used to estimate the
amount of additional momentum smearing that should be applied to Monte Carlo simulated decays in order
to accurately represent what is expected in the data.
� � £ � control sample:
A very pure sample of kaon and pion tracks is derived from reconstructed � £ � � � � Ã � �
decays, as already described in Sec. 4.4.1. The � Ã track is always the one with the same(opposite) charge
as the � £ . The control sample used is limited to those decays for which one of the � daughter tracks is in
the momentum range relevant for two-body decays: ���–�� � ��Î� . This sample is used to evaluate and
parameterize the � measurement from the �ÁÊ� for high momentum tracks.
Table 4-5 summarizes the functional forms used for the PDFs and the samples from which they are derived.
Details of the PDFs are given in the following subsections. In all cases, reliance on Monte Carlo simulated
data was avoided as much as possible.
4.6.2 Beam energy-substituted mass Ñ �Ë
The background shape in Ñ�Ë is parameterized using the ARGUS function [53]:
�Æ
� Æ ¡ Ñ�Ë ¡
�ÆÑ�Ë
Ô � �
Ü ¡ �ÜÔ � ¡ Ü � (4.12)
where Ü � Ñ�Ë�ÑÑ�Ü and the parameter � is determined from a fit. The end-point of the ARGUS curve,
ÑÑ�Ü, is determined in a mode-independent way by finding the value which minimizes the � of the �
5 This is not true in the � � ¦ and � � decay modes, which are not taken into account in the following.
STRATEGY AND TOOLS FOR CHARMLESS TWO-BODY � DECAYS ANALYSIS