High-energy quark-quark scattering and the eikonal approximation

The high–energy quark–quark scattering amplitude is calculated first in the case of scalar QCD, using Fradkin’s approach to derive the scalar quark propagator in an external gluon field and computing it in the eikonal approximation. The results are then extended to the case of “real” (i.e., fermion) QCD. The high–energy quark–quark scattering amplitude turns out to be described by the expectation value of two lightlike Wilson lines, running along the classical trajectories of the two colliding particles. Interesting analytic properties of the high–energy quark–quark scattering amplitude can be derived, going from Minkowskian to Euclidean theory: they could open the possibility of evaluating the high–energy scattering amplitude directly on the lattice.