10 - H1 - Desy

8.2 Unfolding application 99
8.2 Unfolding application
Having the short theoretical introduction to the unfolding problem, this section explains
the way the unfolding is treated in this particular analysis.
The cross sections binned in the interesting variables (see section 1.5) are obtained by
bin averaging (see section 8.4.1) of higher dimensional unfolding output, so more than
one cross section can be actually derived from a single unfolding. Table 8.1 associates all
the final cross sections with their codes 1 Every unfolding code, defined in the same table,
corresponds to one independent unfolding solution. All the variables and phase spaces
are defined in section 1.5.
Phase space Variable Cross Section Code Unfolding Code
inclusive E γ T
i A
inclusive η γ ii A
exclusive E γ T
iii B
exclusive η γ iv B
exclusive E jet
T
v C
exclusive η jet vi D
exclusive x LO
γ vii E
exclusive x LO
p viii F
direct p ⊥ ix G
direct ∆φ x H
resolved p ⊥ xi I
resolved ∆φ xii J
Table 8.1: The definition of cross sections codes and unfolding codes.
8.2.1 Migration matrix
In this analysis, unfolding plays an essential role. It addresses features of the analysis such
as correct treatment of bin to bin migration effects, detector acceptance and efficiency
corrections as well as signal and background discrimination. The migration matrix, being
the most important unfolding component, has been carefully developed.
The main advantage of the unfolding procedure is its relatively high reliability in the
presence of existing model inaccuracies, particularly in case of high bin to bin migrations.
The model independency can be achieved only for the variables used as unfolding
output, so it is important to correctly select relevant variables and even, if possible, use
multi dimensional binning. Table 8.2 lists all the unfolding codes with the chosen input
1 For a simplification, through out of this chapter cross sections codes are used.