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

Chapter 7: Background Estimation 213
window, the QCD background estimate should be taken as an overestimation of the
background within the window.
We test the robustness of the template fit method using Monte Carlo. We use
b ¯ b events with non-isolated muons as our QCD template, and b ¯ b events with isolated
muons as our QCD pseudo-data. Half of our Z → µµ Monte Carlo sample is used
as the signal template, while the other half is treated as signal pseudo-data. The
invariant mass distributions for the QCD and signal pseudo-data events are added in
known fractions to simulate the pseudo-data distribution.
We perform an ensemble test by simulating a number of pseudo-experiments. We
take the invariant mass distributions for the Z → µµ and QCD pseudo-data, and
change the content of each bin within their Poisson fluctuation. Then we add the dis-
tributions and perform the template fit as described above. We repeat the procedure
1000 times, each time varying the bin contents of the signal and background pseudo-
data distributions but using the same templates. We make two sets of distributions
from the results of the pseudo-experiments:
• the signal and background fractions from the template fit in each experiment
• the quantity p =
each experiment
True fraction - fit fraction
Error in fit fraction
for both signal and background in
Figure 7.4 shows the distributions of the signal and QCD background fractions.
We expect them to be Gaussian-distributed; Gaussian fits yield 99.10 ± 0.09% for the
signal fraction and 0.90 ± 0.09% for the background fraction. Figure 7.5 shows the
sum of the input distributions. We need more statistics to be able to make the fit within the Z mass
window.