Theory of Pion-Pion Scattering

Abstract

Strong-interaction dynamics is formulated on two main assumptions. The first is similar to the one used in the Regge-pole-resonance interference model, and the other is that the potentials arising from the exchange of a few dominant particles and resonances in crossed channels can be accepted physically in the low-energy regions and that the convergent high-energy behavior of the potentials should be guaranteed by the Regge-pole theory. A long-range potential which satisfies both the low-energy and the high-energy boundary conditions stated above is introduced. The dynamical model with only Regge-pole exchange potentials (as in the new form of the strip approximation) does not produce low-energy resonance behavior as a dynamical output. We show that a potential which does produce the main low-energy resonance behavior as output can be constructed by an appropriate superposition of single-particle exchange potentials and Regge-pole exchange potentials according to our second assumption. Also, two other potentials arising from the large-$t$ parts of the Mandelstam double spectral functions are defined under the first assumption.