These codes are based on NLO calculations of large-p_{T} 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 alpha_{s}(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 p_{T}, the transverse momentum of the final state photon or hadron) is not large enough and alpha_{s}(p_{T}) 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 p_{T}. For the production of hadrons, we give in hep-ph/0206202 a discussion of the p_{T}-range in which the results of the code should be reliable. For instance, we found that p_{T}= 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/dE_{T}dphi where phi is the azimuthal angle between the final photon and the jet and E_{T}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/dE_{T}. If on the contrary we are interested in the behaviour of dsigma(Delta)/dE_{T}= int_{pi - Delta}^{pi} dphi (dsigma/dE_{T}dphi), we find Log^{2}(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 E_{T}(jet) of the jet recoiling against the photon in the gamma p --> gamma jet X reaction.

If E_{T,min}(jet) is too close to the E_{T,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].

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