Violation in Mixing

126 Measurement of Branching Fractions for � ¦ � Ã � ¦ decays
statistical significance (in 20 fb -1 )
5
4.5
4
3.5
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2.5
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1.5
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0.5
optimization with continuum MC
0
0.43 0.435 0.44 0.445 0.45 0.455 0.46 0.465 0.47 0.475 0.48
efficiency on signal
statistical significance (in 20 fb -1 )
5
4.5
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3.5
3
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optimization with offresonance data
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0.43 0.435 0.44 0.445 0.45 0.455 0.46 0.465 0.47 0.475 0.48
efficiency on signal
Figure 5-6. Significance as a function of a cut on Ø ÃË ��Ø ÃË
resonance (center) and on-resonance (right) side-band.
statistical significance (in 20 fb -1 )
optimization on onresonance upper and lower side bands
5
4.5
4
3.5
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0.43 0.435 0.44 0.445 0.45 0.455 0.46 0.465 0.47 0.475 0.48
efficiency on signal
for continuum Monte Carlo (left), off-
isolate samples of events that are consistent with the Ã Ë � and Ã Ë Ã hypotheses, and signal yields are then
obtained from an unbinned maximum likelihood fit (Sec. 5.5).
5.4 Background Suppression and PDF Parameterization
5.4.1 ¡� PDF and Definition of Signal and Side-band Regions
Signal events are Gaussianly distributed in ¡� with a mean near zero as one can see from the distribution
of Monte Carlo signal events (Fig 5-7), while the continuum background events fall quadratically over the
signal region (Fig 5-8).
For this analysis, since the pion mass is assigned to all tracks, the Ã Ë Ã decays have ¡�� shifted from
zero by an amount depending on the momentum of the tracks. From Monte Carlo simulation we find an
average shift of � Å�Î for the Ã Ë Ã decays (Fig 5-7). In the global likelihood fit we take into account
the shift depending on the momentum of the tracks using a ¡� PDF for � � Ã Ë Ã decays that consists of
a Gaussian with a mean given by the analytical form in 4.13.
The ¡�� distribution was fitted with a Gaussian width of ��Å�Î for Ã Ë Ã and �� Å�Î for Ã Ë �
Monte Carlo. A comparison of � � � � decays in data and Monte Carlo indicates that the Monte
Carlo resolution should be scaled by a factor � � ¦ � � to agree with data (see study in Sec. 4.2.2.1). As a
consequence, in case of Ã Ë � decays, we have estimated the resolution on ¡� in real data to be �¦�Å�Î.
Monte Carlo shows that the mean in ¡� for Ã Ë � signal events is around ��Å�Î 1 . The estimated mean of
¡� in data is therefore taken from the � � � � control sample ( � ¦ �Å�Î, see Sec. 4.2.2.1).
1 This effect in MC is not understood yet, but goes in the same direction as the shift seen in MC in the reconstructed ÃË mass.
The reconstructed value in MC is higher than the PDG value, while in data the Ã Ë mass is in perfect agreement with the PDG (see
Sec. 2).
MARCELLA BONA