High-Energy Scattering Amplitude in Perturbation Theory

Abstract

The consequences of keeping terms in addition to the leading terms in each order of perturbation theory are investigated. The model is the $g{\ensuremath{\phi}}^{3}$ theory and the method is that of Bjorken and Wu. When the second-most dominant terms in each order of ladder graphs are summed, a second-order pole in the angular momentum plane is obtained and the contribution to the amplitude dominates the sum of leading terms at high energy. When the class of terms to be summed is further enlarged in a well-defined way, the simple Regge behavior is restored. The divergence at threshold in the trajectory function obtained by summing the leading terms is not present in the final result. The question of the high-energy behavior of the complete sum of the ladder graphs is still unsettled.