Current algebra and π-π scattering lengths. A dispersion relation approach

Abstract

The usual simple linear expansion of the scattering amplitude ins, t andu is used to continue on to the mass shell but not to physical values ofs. The continuation to physicals. values is made using a linear combination of the partial-wave dispersion relations on the first and second Riemann sheets, into which any desired effects of the unitarity cut may easily be inserted. A complicated spectrum ofT=0 andT=2 scattering lengths is obtained. Many of the qualitative features of the solution are in agreement with other calculations in which some account has been taken of the unitarity cut.