The high energy behavior of scattering amplitudes in perturbation theory. I

✍ Scribed by P.G Federbush; M.T Grisaru

• Publisher: Elsevier Science
• Year: 1963
• Tongue: English
• Weight: 401 KB
• Volume: 22
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(63)90056-3

✦ Synopsis

A procedure is described for extracting the dominant behavior at high energies of individual Feynman diagrams. This procedure is illustrated by the calculation of several examples, and is applied to the summation of several classes of diagrams in the high energy limit. Although all the examples dealt with concern spinless bosons and nonderivative coupling, the inclusion of spin and more complicated couplings does not alter the basic method.

The determination of the high energy behavior of physical scattering amplitudes in perturbation theory is an interesting problem, and apparently more difficult than the one occurring in renormalization theory, where all the momenta are spacelike (1). In this latter case the result is obtained by counting overall powers of the momenta, an essentially dimensional argument that has been proven rigorously correct (9). Of course, nonperturbative results can also be obtained under certain assumptions, for example by means of the renormalization group (3) and dispersion relations arguments (4). However, we are in terested in perturbation theory, and we are partially motivated by a recent suggestion of Gell-Mann and Goldberger (5) that conventional field theory may predict high energy behavior which is in agreement with the existence of Regge poles (6).

We shall present a method which is essentially calculational. For simplicity we have restricted ourselves to the case of no spin and trilinear nonderivative coupling, but aside from algebraic complications the same method may be used in the more interesting case of particles with spin and arbitrary couplings.