10 - H1 - Desy

8.7 Corrections to the QCD calculations 127
analysis bin i a ±δ PDF is calculated according to:
+ δ PDF
i
−δ PDF
i
= max j ( Nj i − Nref i
N ref
i
= max j ( Nref i − N j i
N ref
i
) × 100%, (8.54)
) × 100%, (8.55)
where N ref
i is the number of events in the bin i produced with the reference PDF set and
index j runs over all the PDF sets, including the reference one.
For the uncertainty applied to the FGH calculation (see section 2.2.1), the reference
cross section was chosen to be the one produced with CTEQ6L proton PDF and AFG04
photon PDF, as exactly this set was used during calculations. Since the chosen PDF set
consistently produces the lowest cross sections in the studied phase space, the resulting
error is highly asymmetric.
The ZL calculation (see section 2.2.2) uses the k ⊥ unintegrated PDF, which could not be
easily applied to the MC. For that purpose, the compromise solution was found, to use
the same PDF uncertainty as evaluated for FGH, but apply it in a symmetric way.
Figure 8.17 presents the PDF uncertainty obtained for the final cross sections, as applied
to the both sets of calculations. The choice of the PDF arises to the leading uncertainty
source in most of the studied phase space being on average slightly below 10% and reaching
even 15% in some bins of resolved enhanced phase space.
Due to possible cancellations, special attention was taken to ensure correct multiplication
of the different corrections. The ftheor MPI correction, being the first correction applied to the
calculation was determined studying the MC on parton level and with a cone isolation
criteria. The ftheor isol correction was determined with MCs including MPI, but still on parton
level. And finally, for the determination of the third correction, ftheor had , both MCs were
generated with MPI and the cross section phase space was already based on a z variable.
In this way, the final correction factor f theor may be calculated with a reduced formula 7 :
f theor
= f MPI
theor × f isol
theor × f had
= N had,z,MPI
i
theor (8.56)
/N par,cone,∼MPI
i , (8.57)
where N par,cone,∼MPI
i is the number of events in bin i on parton level, with cone based
isolation and without MPI (the phase space directly calculated by the QCD calculations),
while N had,z,MPI
i is the number of events in bin i on hadron level, with z-based isolation
and with MPI (the phase space being the result of the measurement).
All the theory corrections ftheor MPI,
fisol theor , fhad theor , together with their uncertainties and the
PDF uncertainty δ PDF are listed in the relevant tables in appendix C.
7 In practice though, the correction is calculated with an extended triple correction formula, due to
the ftheor had correction determination method, which includes the usage of two different MC generators.