A new Regge representation for potential scattering

Abstract

For a superposition of Yukawa potentials such thatN Regge trajectories enter the right half of the angular-momentum plane we derive a decomposition of the scattering amplitude intoN+2 terms. These are, respectively, the Born term, a «background term», andN «Regge terms». A Regge term belongs to a specific trajectory and represents the effect of only that part of the trajectory, which lies in the right half of the angular momentum plane. Each Regge term satisfies a Mandelstam representation with a boundary curve for the spectral function as is usual for potential scattering. Moreover, the spectral function is nonvanishing only in a strip, parallel to thet-axis (t is momentum transfer), the width of which is determined by the energy interval for which the corresponding Regge trajectory is in the right half-plane. This corresponds exactly to the «new strip concept» ofChew, Frautschi andMandelstam. Contrary to other Regge representations a Regge term as defined in this paper has no unphysical left-hand cuts. A study of the contribution of a given Regge term to thel-th partial wave reveals that the Regge term describes all bound states and resonances that are being «caused» by the corresponding trajectory. It is shown that the partial-wave projection of a Regge term can be defined throughout the right half of the angular momentum plane.