Existence of Complex Poles and Oscillatory Average Multiplicity in Multiperipheral Models

Using only the general factorization and nondegenerate threshold properties of multiperipheral models, we demonstrate the existence of damped oscillatory components for both the total cross section and the rate of growth of average multiplicity, with identical frequencies and relative amplitudes. For weak oscillation, however, they are shown to be 180^∘{} out of phase. Relevant experimental information on this fine structure is also discussed.