We discuss the issue of the momentum dependence of instanton-induced amplitudes. We consider multi-loop graphs in gφ4, which on the one hand can be computed through the Lipatov approach using instantons and on the other hand are given by the usual Feynman graphs. Using this correspondence we can understand the peculiar momentum dependence. We find that the momentum dependence characteristic to the one-instanton amplitudes corresponds to low-multiplicity cuts, while the genuine ultraviolet behavior is dominated by high-multiplicity cuts which are not reproduced in the one-instanton approximation and presumably could be related to multi-instantons. The contribution of the multi-instanton configurations is estimated, and a boundary value of the momentum transfer where the regimes are changed is found.
Bibliographical noteFunding Information:
The authors are grateful to H. Leutwyler, L. McLerran, A. Vainshtein and M. Voloshin for useful discussions. This work was started when both authors were at the Institute for Theoretical Physics, University of Bern. We are grateful to Schweizerischer Nationalfonds for financial support. The work of M.M. was supported by a grant from Istituto Nazionale di Fisica Nucleare (INFN). The results obtained at the initial stages have been reported by M.S. at the CERN Theory Seminar in the beginning of 1990.