Violation in Mixing

158 Measurement of Branching Fractions for � � Ã Ë Ã Ë Decays
Table 6-5. Upper limits from a cut based analysis estimated with different � Ó× � Ë� cuts and with the Fisher
cut giving the best upper limit.
� Ó× �Ë� Fisher � of expected bkg events upper limit eff. upper limit on
cut cut in the signal box on signal yield � �
0.9 -0.3 1.7 3.9 17.5 8.9
0.8 -0.3 1.7 3.9 17.5 8.9
0.7 -0.2 3.0 4.4 20.5 8.6
0.6 -0.3 1.4 3.4 16.2 8.4
Table 6-6. Upper limits from a cut based analysis estimated with different � Ó× � Ë� cuts, with the Fisher cut
giving the best upper limit and the reduced signal box.
� Ó× �Ë� Fisher � of expected bkg events upper limit eff. upper limit on
cut cut in the signal box on signal yield � �
0.9 -0.3 1.0 3.4 17.0 8.0
0.8 -0.3 1.0 3.4 17.0 8.0
0.7 -0.5 0.0 2.4 9.4 10.2
0.6 -0.5 0.0 2.4 9.3 10.3
We estimate the number of background events in the signal box counting the number of events in the Ñ�Ë
side-band region and scaling it by the ratio area(signal box)/area(Ñ�Ë side-band), where the area is the
integral of the ARGUS function. We assume that no signal events are observed in the signal box (i.e. no
exceeding events are counted in that region). We estimate the ARGUS shape from events having � Ó× �Ë� �
�� to have a common parameterization for all the sets of cuts: from the fit in this sample, we get � �
� ¦ �� . With this � value, the ratio area(signal box)/area(Ñ�Ë side-band) is � .
Some results from this exercise are shown in Tab. 6-5: we quote the results with different cuts on � Ó× �Ë�
and with the Fisher cut giving the best upper limit. The yield upper limit is evaluated from the Feldman-
Cousins tables [64] assuming that the number of events found is always equal to the estimated number of
background events.
The results obtained reducing the signal box to �¡�� � � Å�Î are summarized in Tab. 6-6.
The best upper limit on the à à branching ratio is about � ¡ � .
MARCELLA BONA