High-Energy Behavior of Feynman Amplitudes

A method is developed for obtaining the asymptotic form of the Feynman integral associated with a general convergent $n\mathrm{th}$ order planar graph with two, three, or four external lines. Only graphs corresponding to the $\lambda {\phi }^3$ theory are considered explicitly. The Feynman integrals are shown to behave asymptotically like $s^{-\rho }{\left(\ln s\right)}^{\alpha }$, where $s$ is the large kinematical variable and $\rho$ and $\alpha$ are integers which can be read off from the topology of the graph according to a simple rule.