These codes are based on NLO calculations of large-pT cross
sections and therefore have
limitations peculiar to this type of approach. We discuss here two of them,
the scale dependence of the
cross section and the infra-red sensitive observables, in order to
assess the validity of the
predictions obtained by these codes.
- Scale dependence
A QCD cross section calculated at fixed order in alphas (here
NLO) depends on the
factorisation and on the renormalisation scales. In general this
dependence is strong when the
kinematic variable which fixes the "large scale" of the reaction
(here pT, the transverse momentum of the final state photon or hadron)
is not large
enough and alphas(pT) not small enough. Of course this is a
vague statement which just
says that users must be careful when calculating cross sections at
small values of pT. For the production of hadrons, we
give in hep-ph/0206202 a discussion of the pT -range in which the
results of the code should be reliable.
For instance, we found that pT = 3 GeV is too small to
prevent a strong scale
dependence at HERA energies of the gamma p --> hadron jet X cross section.
-
Infra-red sensitive observables
Infra-red sensitive observables are observables which are strongly constrained by
the phase space of the final state
partons if stringent kinematic cuts are imposed. For example, consider the
reaction gamma p -->
gamma jet X and the distribution dsigma/dET dphi where phi
is the azimuthal angle
between the final photon and the jet and ET the transverse energy
of the photon. The Born
term and the NLO virtual corrections are proportional to delta(phi - pi).
The real NLO corrections with 3 partons in the final state give rise to
contributions which are different
from zero in the range 0 <= phi <= 2 pi. If we are not
interested in the
phi-distribution, an integration over phi between 0 and 2pi
leads to the inclusive
distribution dsigma/dET. If on the contrary we are interested in
the behaviour of dsigma(Delta)/dET =
int_{pi - Delta}^{pi} dphi (dsigma/dET dphi),
we find Log2(Delta)-terms in the cross section which can be
large if Delta
is small and invalidate the
perturbative calculation. This comes from the fact that the real
phase space is strongly
constrained in comparison to the virtual one. Therefore one must not
use a too small value of
Delta when studying the phi-distribution.
Another example is the constraint put by fixing a minimum value of
the transverse energy
ET(jet) of the jet recoiling against the photon in the
gamma p --> gamma jet X reaction.
If ET,min(jet) is too close to
the ET,min(photon), the
real phase-space is
severely constrained and a perturbative NLO calculation can be
inaccurate.
A detailed discussion of this point is given in
Eur.Phys.J. C 22 (2001) 303 [hep-ph/0107262].