Partial-wave equations and analyticity domain of pion-pion scattering amplitudes

Abstract

We exploit the axiomatic analyticity domain obtained by A. Martin and three-channel crossing-symmetric representations of pion-pion scattering amplitudes to derive explicit analytic continuations of the partial waves. These continuations define the partial waves in terms of the S-wave scattering lengths and integrals involving physical region partial waves absorptive parts and known kernels. They exist in a domain extending from Re S=−28m_π² to +125.31m_π² and from Im S=−64.5m_π² to +64.5m_π² and excluding regions outside the previous Martin domain of analyticity (s=c.m. energy squared).