  The high-energy scattering amplitude of two colour-singlet quark-antiquark
pairs is governed by the correlation function of two Wilson loops, which follow
the classical straight lines for quark (antiquark) trajectories. This quantity
is expected to be free of IR divergences, differently from what happens for the
parton-parton scattering amplitude, described, in the high-energy limit, by the
expectation value of two Wilson lines. We shall explicitly test this IR
finitness by a direct non-perturbative computation of the loop-loop scattering
amplitudes in the (pedagogic, but surely physically interesting) case of
quenched QED. The results obtained for the Abelian case will be generalized to
the case of a non-Abelian gauge theory with N_c colours, but stopping to the
fourth order in perturbation theory. In connection with the above-mentioned IR
finitness, we shall also discuss some analytic properties of the loop-loop
scattering amplitudes in both Abelian and non-Abelian gauge theories, when
going from Minkowskian to Euclidean theory, which can be relevant to the still
unsolved problem of the s-dependence of hadron-hadron total cross-sections.
