of two identical particles with repulsive interaction in the centre-of-momentum reference frame. In perturbative quantum field theory the free particles approach each other, exchange virtual interaction particles and then move away freely. During the free motion the gravitational interaction of particles does not play a role, but we will take it into account in the interaction process. If we assume first a central collision and restrict ourselves to first-order Feynman diagrams, we can describe the situation as follows. At the interaction vertices, when the particles reach a certain minimal distance, they stop and their kinetic energy materializes as a virtual exchange particle. Provided the asymptotic kinetic energy is high enough, the gravitational field of the virtual particle furnishes a significant amount of additional energy for the interaction process in comparison with the gravitation-less interaction, and the particles come closer to each other, as if they had a higher asymptotic kinetic energy. In the following we are going to formulate these considerations up to first order in the gravitational constant $G$.

We assume two particles with masses $m$ and (absolute values of) asymptotic momenta $p$. In the absence of gravity, at the interaction vertices, with the particles at their minimal distance 