Partial-Wave Dispersion Relations for Pion-Nucleon Scattering

Abstract
Partial-wave dispersion relations for pion-nucleon scattering are derived from the Mandelstam representation. The symmetry of the representation is used to obtain expressions for the discontinuities across the unphysical branch cuts. These expressions involve scattering amplitudes for pion-nucleon scattering and for the process π+πN+N¯. In the approximation of neglecting all but the nearest singularities it is shown that the Chew-Low effective-range formula is a solution to the equations.