Eikonal Estimates and Cancellations at High Energies

Using functional methods and the eikonal model, the leading $s$ dependence of elastic scattering in a modified ${\phi }^3$ theory is discussed. An approximate evaluation of ladder or tower graphs and certain nonplanar graphs reveals strong cancellations. The net contribution falls as a power of the energy rather than saturating the Froissart bound, as found in less complete treatments of multiperipheral models.