Geometrical restrictions on the pion-pion partial waves

• DOI: 10.1007/bf02818348
• Publication Date: 2008-02-01T11:43:51Z
• Authors: A. Martin
• Keywords: Unitarity; Position (finance); Crossing

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 theT=0,l≥2 partial waves is used to prove the existence of an essential singularity ats=0 on the second sheet, or more precisely, that poles accumulate ats=0.