Eikonalization of the scattering amplitude in some field theory models at high energies

Conclusions

The various examples of interactions considered above, which are more complicated than processes described by generalized ladder diagrams, show that in this case too the eikonal representation holds, but with a very different phase. Comparing the eikonal formula obtained in §1 with the asymptotic behavior of the individual diagrams of perturbation theory for Fig. 3, we conclude that, as in the case of the theory ϕ³, there is probably a compensation of the contributions of the asymptotic behaviors of the individual diagrams. For example, the diagrams of Fig. 3 have a higher power of ln s [the diagram of order (g²h)⁴ is proportional to (ln s)³], whereas the corresponding terms of the expansion of (1.10) in a series have no logarithmic terms in s at all.