10 - H1 - Desy

110 Cross section building
contribution of higher Q 2 values was subtracted by correcting each bin i of data input
vector:
y ′ i
obs = yi obs × yi obs,MC,Q2
y i obs,MC
(8.22)
The correction affects mainly cross section in the backward region with its maximum value
of 5%. The ratio y obs,MC,Q2 /y obs,MC is presented in figure 8.8 as a function of pseudorapidity
of the photon candidate.The final results are correctly quoted in the photoproduction
range of Q 2 < 1 GeV 2 .
)
γ
(η
obs,MC,Q2
y
)
γ
(η
obs,MC
y
1
0.98
0.96
0.94
-1 0 1 2
γ
η
Figure 8.8: The Q 2 selection correction factor as a function of pseudorapidity of the
photon candidate.
8.3 Error matrix evaluation
The final error matrix E x consists of three components and is built in the following way:
E x = E u + E mc + ∑ i
E i sys (8.23)
where E u is the covariance matrix of the unfolding output bins calculated with the equation
8.12, E mc is the error originating from the limited statistics of MC used to determine
the migration matrix and E i sys is the error due to particular systematic effects i. Both
E mc and E sys are calculated using error propagation rules [99] shortly explained in this
section.
Considering n η functions η i , building vector ⃗η and depending on n θ variables θ: η i (θ 1 , · · ·θ nθ )
the covariance matrix U ij = cov|η i , η j | can be approximated by the first order in the Taylor