  We derive a nonperturbative expression for the non-vacuum,
qqbar-Reggeon-exchange contribution to the meson-meson elastic scattering
amplitude at high energy and low momentum transfer, in the framework of QCD.
Describing the mesons in terms of colourless qqbar dipoles, the problem is
reduced to the two-fermion-exchange contribution to the dipole-dipole
scattering amplitudes, which is expressed as a path integral, over the
trajectories of the exchanged fermions, of the expectation value of a certain
Wilson loop. We also show how the resulting expression can be reconstructed
from a corresponding quantity in the Euclidean theory, by means of analytic
continuation. Finally, we make contact with previous work on Reggeon exchange
in the gauge/gravity duality approach.
