Physical pion-pion partial wave equations based on three-channel crossing symmetry

Abstract

We present a set of closed systems of partial-wave equations for pion-pion scattering valid for −28 m_π²≤s≤125.31m_π². These equations give the real part of a given partial-wave amplitude in terms of scattering lengths and a convergent series of integrals over the physical values of the absorptive parts of all partial waves. Our equations are extensions of relations previously derived from fixed-t dispersion relations. The new equations are rigorous consequences of axiomatic analyticity and three channel crossing symmetry. As an application, the effect of the f⁰-meson on the I=O S-wave is evaluated.