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Hadron scattering processes involving low values for the fraction of the momentum of the hadrons transfered to the partonic process require factorization prescriptions other than collinear factorization. These admit pdfs with resummed logarithms of this momentum fraction. One of their characteristics is that they provide an explicit transverse momentum to the parton, rendering it off-shell. Consequently, the exact definition and calculation of the matrix element needs special attention. The program AMP4HEF numerically evaluates multi-parton amplitudes and matrix elements with up to two of them off-shell. [ABSTRACT FROM AUTHOR]

We review existing theoretical approaches for the deep-inelastic lepton --hadron interactions and the high energy hadron--hadron scattering in the Regge kinematics. It is demonstrated, that the gluon in QCD is reggeized and the Pomeron is a composite state of the reggeized gluons. A gauge invariant effective action for the reggeized gluon interactions is constructed. Remarkable properties of the BFKL equation for the Pomeron wave function in QCD and supersymmetric gauge theories in leading and next-to-leading approximations are outlined. It is shown, that due to the AdS/CFT correspondence the BFKL Pomeron is equivalent to the reggeized graviton in the extended N = 4 supersymmetric model. Its intercept at large coupling constant is calculated in this model. [ABSTRACT FROM AUTHOR]