10 - H1 - Desy

116 Cross section building
8.4.3 Cross sections
The output of the bin averaging procedure explained in section 8.4.1 is the final number
of prompt photons N i measured in bin i. The error treatment associates with it a fully
correlated error a i and a fully uncorrelated error δ i . The single differential cross section
in bin i of variable x and double differential cross section in bin i of variable x and bin j
of variable y is calculated with the formula
( dσ
dx ) i =
( dσ
dxdy ) i,j =
N i
L · w x,i
±
N i,j
L · w x,i · w y,j
±
a i
L · w x,i
(corr.) ±
a i,j
L · w x,i · w y,j
(corr.) ±
δ i
L · w x,i
(uncr.) (8.40)
δ i,j
L · w x,i · w y,j
(uncr.) (8.41)
(8.42)
where L is the integrated luminosity (see section 3.1) of the considered event selection
(340 pb −1 ), and w x,i (w y,j ) is the width of i th (j th ) bin of variable x (y).
The total cross section σ tot is determined for each unfolding by averaging over all the
Signal Bins of ⃗x true within the phase space. Since it is a single number, and the error
division into a correlated and uncorrelated error does not make sense, the total cross
sections are quoted together with statistical error (averaged over the sum of E unf and
E mc and systematic error (averaged over the sum of E i sys ).
8.5 Total cross section consistency check
The unfolding procedure has been repeated ten times, in order to calculate cross sections
binned in different variables. Particularly, one of those unfoldings (A) leads to the inclusive
prompt photon production cross sections, five (B, C, D, E, F) were performed
in the exclusive photon plus jet phase space, two (G, H) in the direct enhanced phase
space and two (I, J) in the resolved enhanced phase space. Different unfoldings in the
same phase space produce the same cross sections projected on a different direction, so
the comparison of the total cross sections can be treated as a consistency check.
Figure 8.9 presents the comparison of the total cross sections in the exclusive phase space
obtained with five different unfoldings. The inner error bars represent the statistical error
while outer error bars statistical and systematic added in quadrature. The shaded area
and horizontal lines indicate error ranges for the most precise and least complex unfolding
B. The consistency of all obtained total cross sections increase the confidence level in the
relatively complex method explained in this chapter.
8.6 Toy Monte Carlo study
The most common way of checking the quality of the unfolding procedure is a toy Monte
Carlo study like the one presented in this section. The whole set of toy MC samples