Continuation of Scattering Amplitudes and Form Factors through Two-Particle Branch Lines

Abstract

It is shown that scattering amplitudes and form factors have two-particle branch lines which connect two Riemann sheets. For partial wave amplitudes and form factors the dispersive parts and, except for square root factors, the absorptive parts are regular functions in the cut energy plane except for isolated poles, physical inelastic cuts and left-hand branch lines. In order to show this it is assumed that, for particles without composite structure, the amplitudes have only such singularities in the physical sheet which correspond to absorptive processes. The analytic properties of absorptive parts are used for a general discussion of structure singularities (anomalous thresholds). It is shown that these structure cuts are extensions of left-hand branch lines in the second Riemann sheet. An example is given of a dispersion relation on the Riemann surface in which the integral over the two-particle branch line is eliminated.