On the Complete Unitarity Equations for Pion-Pion Scattering

Abstract

The off‐the‐mass‐shell equations for pion‐pion scattering in the lowest approximation of the complete unitarity formalism of Taylor are discussed. It is shown that if the vertex‐function renormalization constant is taken to be zero, the equations have no (nonzero) solution. These equations are equivalent to certain bootstrap equations, which thus also have no solution. Both systems are discussed in the case where the renormalization constant is not put equal to zero.