Complex Regge Trajectories

Conditions are explored which require the presence of leading positive- or negative-signature trajectories of the form α(t)=1+const√t+O(t). General forms of continued partial-wave amplitudes with such trajectories are given, and their implications for high-energy limits are evaluated. The restrictions on the character of the complex singular surfaces are discussed. Explicit examples are given for amplitudes with complex Regge trajectories.