justified by the fact that the Newtonian potential is used only close to the turning points of the particles, when they slow down to nonrelativistic velocities.)

Note that we have considered interactions in first order of a perturbative expansion. In higher order, when one takes into account more vertices, the interaction process becomes smoother, it is divided into more steps and sets in earlier, i.e. at larger distances, than in first order. In consequence, in higher order diagrams the influence of gravity will become weaker, so the above first-order estimates are rather an upper bound for gravitational modifications.

To summarize, classical gravity influences the in- and outgoing particles when they are close to their vertices, if the energy is sufficiently high. This is described in two kinds of variables, both of which have an immediate physical meaning: The effective ones, $E_{\rm eff}$ and $p_{\rm eff}$, appearing at the vertices and entering cross section calculations, and the asymptotic ones, denoted by $E$ and $p$, playing the role of “bare" variables in connection with classical gravity.

Non-central collision
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In the central collisions considered above the minimal distance of colliding particles and the energy of a virtual particle have been modified, quantities 