High-Energy Large-Momentum Processes: Ladder Diagrams in PHI(3) Theory

Relativistic quantum field theories may help us to understand high-energy, large-momentum-transfer processes, where the center-of-mass energy is much larger than the transverse momentum transfers, which are in turn much larger than the masses of the participating particles. With this possibility in mind, we study ladder diagrams in varphi^3 theory. We show that in the limit s gg | t| gg m^2, the scattering amplitude for the N-rung ladder diagram takes the form s^{-1}| t|^{-N+1} times a homogeneous polynomial of degree 2N - 2 in ln s and ln | t|. This polynomial takes different forms depending on the relation of ln | t| to ln s. More precisely, the asymptotic formula for the N-rung ladder diagram has points of non-analyticity when ln | t | = gamma ln s for gamma = {1/2 }, {1/3}, ...,{1/{N-2}}.