HighEnergy Behavior near Threshold: ϕ^{3} Theory
Abstract
In this paper we study the twobody elastic scattering process in ϕ^{3} theory, in the limit s>∞ with t equal to or near the threshold value 4, where the mass of the scalar particle is taken to be unity. For the scattering amplitude corresponding to any laddertype diagram, we find that there is a promotion for the power of s by 1/2 . For example, the scattering amplitude for the ladder diagram of n+1 rungs is promoted from O(s^{1}ln^{n}s) away from threshold to O(s^{12}ln^{n1}s) at threshold. This means that, for small coupling constants, the leading Regge pole is promoted from the neighborhood of l=1 away from threshold to the neighborhood of l=12 at threshold. There are, in addition, infinitely many Regge trajectories approaching l=12 as t approaches 4. The scattering amplitude for the nrung diagram is explicitly given in the limit s>∞, with t at or near the threshold 4, and various scales for t4 are pointed out. The tworung and threerung diagrams are especially studied in detail.
 Publication:

Physical Review D
 Pub Date:
 November 1970
 DOI:
 10.1103/PhysRevD.2.2285
 Bibcode:
 1970PhRvD...2.2285C