Reggeized Short-Range Potential Using the Veneziano Representation

In order to calculate the scattering amplitude at low energy, usualy one has used only the long-range potential due to the exchange o£ particles observed. In contrast with the long-range potential, one defines the short-range potential as a potential due to the exchange of the massive particle. In cases that one investigates the position of 3-3 resonance, s-wave scattering lengths and baryon 1\.egge trajectory around u = 0, it is important to introduce this short-range potential in addition to the ordinary long-range potential. Recently some authorsl' l have attempted, using the strip approximation, to introduce this short-range potential into the formalism which satisfies the requirements of analyticity, elastic unitarity, crossing symmetry and also self-consistency. In such a formalism, the long-range potential is defined by the following term arising from the exchange of the crossed channel absorptive parts in the flnite strip: