Dispersion-Theoretic Approach to Hard-Pion Current-Algebra Results forρ−πandA1−πScattering

Abstract

Following recent attempts to explore possible connections between current algebra, dispersion relations, and Regge pole theory, we consider $\ensuremath{\rho}\ensuremath{-}\ensuremath{\pi}$ and ${A}_{1}\ensuremath{-}\ensuremath{\pi}$ scattering amplitudes, and calculate them both from the hard-pion current algebra for four-point functions and dispersion relations with saturation by single-particle intermediate states. The two are found to lead to mutually consistent results provided we introduce a subtraction in certain amplitudes. However, from Regge pole theory, many of these are found to require no subtractions. Thus, whereas the current algebra and the pole-dominated dispersion relations understandably give similar results, the Regge pole theory appears to give distinctly different results.