High-Energy Scattering in Phi3 Theory and Breakdown of Eikonal Approximation .2.
Journal
Physical Review D
Journal Volume
6
Journal Issue
6
Pages
1693-&
Date Issued
1972
Author(s)
Abstract
In this paper we study, in φ3 theory, the high-energy amplitudes for the exchange of two or more ladders. We obtain these amplitudes in closed forms to all orders of the coupling constant. The conclusions are as follows: (i) All of the scattering amplitudes satisfy the impact-factor representation. (ii) Except for the leading term (in the coupling constant) the scattering amplitude of two-ladder exchange is not in the form dictated by the eikonal approximation. (iii) The scattering amplitudes for the exchange of N ladders, N3, are never in the form dictated by the eikonal approximation - even for the leading term. (When the coupling constant approaches zero, all of them are of the order of s-3 instead of s-2N+1, as dictated by the eikonal approximation.) Thus the eikonal approximation is not valid in φ3 theory. The amplitude for the exchange of n scalar mesons, n>4, is also given. Contrary to the popular notion, it is not of the order of s-n+1 when n>4. Summing over such amplitudes does not lead to the exponentiation form commonly conceded in the past. © 1972 The American Physical Society.
SDGs
Type
journal article