Violation in Mixing

6.3 The maximum likelihood analysis 151
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ALLCHAN 5588.
Constant
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898.8 15.12
Mean 5.280 0.5393E-04
Sigma 0.2460E-02 0.3380E-04
0
5.2 5.22 5.24 5.26 5.28 5.3
m ES (GeV/c 2 )
Figure 6-1. Ñ�Ë distribution in the signal Ã Ë Ã Ë Monte Carlo sample.
The likelihood, Ä, for the selected sample is given by the product of the probability density functions
(PDFs) for each individual candidate and a Poisson factor. We use Ñ�Ë, ¡� and � to separate signal
and background.
To be used in the fit, a candidate must pass the preliminary selection, the cut on the ÃËinvariant mass and
the cut on ØÃË��Ø (see Sec. 5.2).
ÃË
6.3.1 Definition of PDFs
The beam energy substituted mass of the � candidate, Ñ�Ë, is parameterized as a Gaussian, with mean
and width fixed to �� � ��� and ���� , respectively, for the signal (Fig. 6-1) and as an ARGUS
function for the background. The value of the mean and the width of the signal Ñ�Ë distribution come from
the � � � � control sample.
The value of the � parameter of the ARGUS function is determined to be �� ¦ �� from a fit to onresonance
¡� side-band data (Fig. 6-2). A similar fit performed on off-resonance grand side-band region
gives � � ��¦ � , and we find � � ���¦ �� in continuum Monte Carlo events (Fig. 6-3). All the
values obtained from these samples are well compatible with each other and with the on-resonance fit. We
use the value � � �� ¦�� in the rest of the likelihood analysis.
MEASUREMENT OF BRANCHING FRACTIONS FOR � � Ã Ë Ã Ë DECAYS