Eikonal propagators and high-energy parton-parton scattering in gauge theories

In this paper we consider soft high-energy parton-parton scattering processes in gauge theories, i.e., elastic scattering processes involving partons at very high squared energies in the center of mass and small squared transferred momentum. By a direct resummation of perturbation theory in the limit we are considering, we derive expressions for the truncated-connected quark (antiquark) propagator in an external gluon field, as well as for the residue at the pole of the full unrenormalized propagator, both for scalar and fermion gauge theories. These are the basic ingredients to derive high-energy parton-parton scattering amplitudes, using the LSZ reduction formulae and a functional integral approach. The above procedure is also extended to include the case in which at least one of the partons is a gluon. The meaning and the validity of the results are discussed.