QCD and Monte Carlo generators

where dΓ ({p}m) is the phase space integral measure,M({p}m) represents the m-paraton tree level matrix element and FJ({p}m) is the jet measurement function that defines the physical observable. This calculation is relatively simple. The integral free from the infrared and ultraviolet singularities. The matrix element is basically a complicated expression but it can be generated in a automated way. Several implementations can be found in the literature, Alpgen, Grace, Helac, Madgraph and Sherpa[2]. We can say that the tree level cross sections can predict the shape of the cross sections but in general they have several defects: i) Since it is the leading order term in the strong coupling expansion the result strongly depends on the unphysical renormalization and factorization scheme. ii) The exclusive physical quantities suffer on large logarithms. In the phase space regions where these logarithms are dominant the predictions are unreliable. iii) In the Born level calculations every jet is represented by a single parton, thus we don’t have any information about the jet inner structure. iv) On the other hand in a real measurement, in the detector we can see hadrons and every jet consists many of them. We are not able to consider hadroniziation effects in the Born level calculations.