10 - H1 - Desy

100 Cross section building
(Reconstructed bins) and output (Signal bins) coded binning. The actual bin edges
are given in appendix A (tables A-2 − A-5).
Unfolding
Code
Reconstructed bins
Signal bins
A, B 10(E γ T,IN10 ) × 10(ηγ IN10 ) × 5(D IN) 4(E γ T,OUT4 ) × 5(ηγ OUT5 )
C
D
8(E jet
T,IN ) × 5(Eγ T,IN5 ) × 8(ηγ IN8 ) × 5(D IN)
8(η jet
IN ) × 5(Eγ T,IN5 ) × 8(ηγ IN8 ) × 5(D IN)
4(E jet
T,OUT ) × 2(Eγ T,OUT2 ) × 5(ηγ OUT5 )
4(η jet
OUT ) × 2(Eγ T,OUT2 ) × 5(ηγ OUT5 )
E 10(x γ,IN ) × 5(E γ T,IN5 ) × 8(ηγ IN8 ) × 5(D IN) 5(x γ,OUT ) × 2(E γ T,OUT2 ) × 5(ηγ OUT5 )
F 8(x p,IN ) × 5(E γ T,IN5 ) × 8(ηγ IN8 ) × 5(D IN) 4(x p,OUT ) × 2(E γ T,OUT2 ) × 5(ηγ OUT5 )
G, I 9(p ⊥,IN ) × 5(E γ T,IN5 ) × 8(ηγ IN8 ) × 5(D IN) 4(p ⊥,OUT ) × 2(E γ T,OUT2 ) × 5(ηγ OUT5 )
H, J 7(∆φ IN ) × 5(E γ T,IN5 ) × 8(ηγ IN8 ) × 5(D IN) 4(∆φ OUT ) × 2(E γ T,OUT2 ) × 5(ηγ OUT5 )
Table 8.2: The definition of input and output binning used for migration matrix definition.
Here only numbers of bins and binning codes are given, the actual bin edges are
listed in appendix A.
Each of the input bins is additionally subbinned in the discriminator (D IN ) defined in
section 6.3. That allows the determination of the signal content in every of the input
bins during unfolding. As it was already noted, the discriminator, built on shower shape
variables, depends on E γ T and ηγ of the studied photon candidate. For that reason, each
input binning, even when not directly needed, is binned in both observables with ten η γ
bins (eight for more complex unfoldings) sensitive to the LAr calorimeter wheel edges and
ten (five) E γ T
bins. A similar, though less fine binning is chosen for the output binning.
In this way, not only the discriminator is properly taken into account, but also unfolding
becomes relatively insensitive to the possible model bias introduced along the η γ and E γ T
directions. Every output bin set, if possible, includes the underflow and overflow bin to
correctly treat the migration from outside of the hadron level phase space.
The migration matrix is build with the help of signal MC (MC sets I-II in table 2.3).
The Reconstructed bin is chosen for events passing the selection criteria (summarized
in table 5.1), while Signal bin is defined for events from within the measurement phase
space (tables 1.4 and 1.5) on the hadron level. The main part of the migration matrix
body is filled with events both generated in the phase space and passing selection criteria.
The treatment of other events is discussed later in this chapter.
The high goals set for the unfolding procedure already in the beginning of this section are
reflected in the relative complexity of the migration matrix. The simplified sketch of the
matrix can be seen in figure 8.2. The Input side of the matrix is drawn horizontally, where
in addition to the Reconstructed bins (here in this simplified picture with 5D ×3E γ T ×
2η γ bins) so called Side bins are included. Similarly, along the vertical Output direction