Signs of intermediate range hadronic forces

We consider high energy hadron-hadron scattering. We show the presence in the amplitude of terms of the form is(q2/m4)ln(−q2/m2) for transferred momentum squared mhadr2≫−q2≥ΛQCD2 and s≫m. We relate such terms to a novel interaction at impact distances ρ≫1/mhadr with a potential of the form V(ρ)∼ρ−4. In the particular cases of photon-photon and pion-pion elastic scattering it appears that higher orders of perturbation theory do modify the lowest order result by a function of αsπlnsm2lnm2−q2. The relation with the structure of the diffractive cone at very small transferred momentum and some possible ways to detect these intermediate range effects are briefly discussed.