Geometrical restrictions on the pion-pion partial waves

Abstract

Various rigorous inequalities on pion-pion partial waves in the interval 0≤s≤4 are obtained from crossing symmetry and positivity properties due to unitarity. In particular, the position of the minimum of the π0π0 S-wave amplitude is located between close limits. The threshold behaviour of higher waves is established, with the help of some additional assumptions. The positivity of the T=0, l≥2 partial waves is used to prove the existence of an essential singularity at s=0 on the second sheet, or more precisely, that poles accumulate at s=0. © 1967 Società Italiana di Fisica.