10 - H1 - Desy

120 Cross section building
8.6.2 Toy MC results
The background contamination of real data was simulated by mixing all the toy MC samples
with background MC events (MC set XVI). The statistics of the toy MC was chosen
such as to simulate the expected data statistics. The E γ T and ηγ distributions have been
unfolded using unfolding matrix filled with the original MC. Since the distributions of
the unfolded MC and MC used to fill the matrix differs, the model inaccuracy is artificially
introduced in a controlled way. The same distributions were determined using the
fitting procedure and bin-to-bin correction where original MC was used to fill signal and
background discriminator distributions as well as to determine the acceptance corrections.
In order to compare results to the real MC distribution the χ 2 variable is calculated
according to the formula:
χ 2 = ∑ i
(R i − T i ) 2
δR i
, (8.49)
where T i is the toy MC cross section in the bin i, R i is the cross section obtained by
unfolding or fitting procedure in bin i, δR i is the calculated error of the results in bin i
and index i runs over all the E γ T or ηγ bins. All the calculated χ 2 results are presented in
table 8.7.
Toy MC Fitting χ 2 /ndf Unfolding χ 2 /ndf
sample E γ T
η γ E γ T
η γ
fE 005
T
0.143 0.190 0.075 0.110
fE 010
T
0.155 0.198 0.073 0.106
fE 020
T
0.175 0.214 0.070 0.096
fE 050
T
0.245 0.270 0.083 0.068
fE 100
T
0.380 0.388 0.143 0.034
fE 150
T
0.528 0.530 0.240 0.014
fE 250
T
0.343 0.412 0.080 0.198
fη 005 0.138 0.186 0.078 0.118
fη 010 0.140 0.190 0.078 0.118
fη 020 0.150 0.198 0.078 0.120
fη 050 0.175 0.222 0.078 0.128
fη 100 0.215 0.264 0.078 0.142
fη 150 0.258 0.312 0.078 0.160
fη 250 0.343 0.412 0.080 0.198
f toy
E T ,η
3.70 3.32 1.43 0.120
Table 8.7: The difference between true E γ T and ηγ distributions of toy MC and distributions
obtained by fitting or unfolding procedures quantified by χ 2 /ndf values.