Takashi Obara

Analytic Properties of the Impact Parameter Amplitude

Analytic properties of the impact parameter amplitude H(s, b) are discussed in the b-plane. It is shown that H(s, b) has algebraic branch points at b=O and their orders depend on the Regge trajectory, if the amplitude is expressed by the Regge pole. As an example a detailed discussion is given for the Veneziano amplitude. It is also stressed that the s-plane analyticity of H(s, b) is much simpler than that of the partial wave amplitude.

Regge Pole Theory and Unitarity

Under the assumptions that are the case for non-relativistic theory, it is shown that the Regge pole theory is compatible with unitarity only if the Regge singularities are infinite in number. If we merely take account of a finite number of them, unitarity is justified in restricted regions such as t~oo and s~s0 • We also show that the double spectral function on which unitarity imposes some restrictions can be constructed by the use of an infinite set of the parallel daughter trajectories. Therefore introduction of these trajectories can remove the difficulties between the Regge pole theory and unitarity.