Measurement of the Z boson cross-section in - Harvard University ...

Chapter 7: Background Estimation 214
distributions of the pull quantity p for the signal and background ensembles together
with Gaussian fits. Ideally, both of these distributions would be centered around zero.
We see that this is not the case, which points to a systematic overestimation of the
background fraction by the template fit.
Number of ensembles
120
100
80
60
40
20
Signal fraction from fit
2
χ / ndf
13.41 / 17
Constant 128.2 ± 5.0
Mean 0.991 ± 0.000
Sigma 0.0009205 ± 0.0000214
0
0.988 0.989 0.99 0.991 0.992 0.993 0.994
Number of ensembles
120
100
80
60
40
20
bb
fraction from fit
2
χ / ndf
12.77 / 17
Constant 127.6 ± 5.0
Mean 0.008971 ± 0.000030
Sigma 0.0009248 ± 0.0000218
0
0.006 0.007 0.008 0.009 0.01 0.011 0.012
Figure 7.4: Distribution of Z fraction (left) and b ¯ b fraction (right) from the template
fit in 1000 pseudo-experiments, in which the content of each pseudo-data bin is randomly
varied within their Poisson fluctuation. Both distributions have been fitted to
Gaussians.
To derive a correction factor for the systematic overestimation, we repeat the
ensemble test several times, each time varying the input QCD fraction in the pseudo-
data. For each input QCD fraction, we obtain a ‘measured’ fraction from the Gaussian
fit to the distribution of template fit results a la Figure 7.4. Table 7.1 lists the input
and measured QCD fractions in each test. Figure 7.6 shows a plot of the measured
QCD fraction vs. the input fraction, with a straight-line fit. The fit has a slope of