Model forπ−πScattering Satisfying Analyticity and Crossing Symmetry

Abstract

A crossing-symmetric model for $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ scattering is presented which satisfies the Mandelstam representation, has a finite number of resonances associated with an exchange-degenerate trajectory that turns over at high energies, and which has Regge asymptotic behavior in all channels. The Pomeranchukon amplitude is nonresonating and has background cuts. The total amplitude satisfies the Adler condition. Satellites are included that eliminate all the odd-daughter (ghost) resonances. The double-spectral functions are calculated and shown to have, except for the lack of curvature, the correct boundaries determined by elastic unitarity. The structure of the second-sheet singularities is briefly discussed. The $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ scattering lengths are calculated and found to be consistent with those obtained from current algebra, when terms of order ${{m}_{\ensuremath{\pi}}}^{2}$ and unitarity corrections are neglected.