Physical-Region Discontinuity Equations for Many-Particle Scattering Amplitudes. II

Abstract

Discontinuity equations are derived for physical‐region normal thresholds in all direct and crossed channels. The discontinuity is given as a unitarity‐type integral with an integrand that contains, as factors, the two physical scattering functions corresponding to the two vertices of the Landau diagram associated with the normal threshold. There is also a third factor, which for the case of a leading normal threshold with any number of particles is the Hermitian conjugate of the elastic scattering matrix associated with the set of internal lines of the Landau diagram. For nonleading normal thresholds below the lowest 4‐particle threshold, the extra factor is defined by an integral equation that resembles unitarity, but has a restricted set of intermediate particles.