These pseudo cross sections, as well as the transition matrix elements on the part II c, are then used to sample unweighted kinematic configurations, in the framework of a partonic event generator, described in the following.
Each of the subprocesses corresponding to a direct, respectively fragmentation photon in the final state (and to a direct/resolved photon in the initial state in the photoproduction programs) is treated separately. In the case of DIPHOX for example one has three separate subprocesses: `two direct', `one fragmentation' and `two fragmentations'.
Firstly, the contribution of a given subprocess to the integrated cross section is calculated with the Monte-Carlo integration package BASES [S.Kawabata, Comp.Phys.Comm. 88 (1995) 309.] The Phox programs are self-contained (apart from the cernlib), i.e. they provide the BASES packages. Some kinematic cuts on the rapidity range of the two hard particles, their transverse momenta, etc. may be already taken into account at this stage. In particular, in the case of production of isolated particles, the phase space constraint implied by the isolation criterion is implemented at this level (although this procedure requires to redo the whole calculation each time the isolation criterion is changed, this way turns out to be simpler to implement and numerically more efficient than imposing the isolation criterion at a subsequent stage). For the processes with a final state other than jet-jet, two possibilities are available, which the user has to specify in the input file acording to her or his interests:
Notice that each of these two possibilities can work independently of the other:
integrated cross sections can be calculated without the computation of the grid;
conversely the computation of the grid does not require the calculation of the
integrated cross section.
For the processes with a jet-jet final state, the first possibility only is
available so far.
Let us consider the option `partonic event generation' further. For each given subprocess, the 2 --> 2 and the quasi 2 --> 2 contributions on the parts I, II a and II b of the phase space are treated separately. So is the inelastic contribution on the part II c. For each of them, unweighted partonic events are generated with SPRING. More precisely they are generated by importance sampling but with a weight ± 1 depending on the sign of the integrand at this point of the phase space. This trick circumvents the fact that SPRING works only with positive integrands, while the pseudo cross sections are not positive. The generated events are thus "unweighted up to a sign".
Here again, two possibilities are available, which the user has to specify in the input file: