We study the amplitudes with a large number of external legs in gφ4 theory within the Lipatov approach. This approach has been originally suggested to determine how the amplitudes with a fixed number of external lines depend on the order of perturbation theory, at large orders. We discuss the generalization of this method to amplitudes with a large number of external legs, N, and few or no loops at all (tree-level multiparticle amplitudes). We show that the N-dependence in this limit is under theoretical control and we reproduce the factorial growth discussed in the literature. We elucidate the relation between the alleged onset of the strong-coupling regime in multiparticle production and the well-known problem of the divergence of perturbation theory at large orders. We argue that if the number of particles produced exceeds a critical value the cross sections are bounded by exp(-const./g).
|Original language||English (US)|
|Number of pages||17|
|Journal||Nuclear Physics, Section B|
|State||Published - Aug 3 1992|
Bibliographical noteFunding Information:
The authors are grateful to L. McLerran, A. Vainshtein and M. Voloshin for valuable discussions. The work of M.M. was supported by a grant from Istituto Nazionale di Fisica Nucleare (INFN).
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