Derivation and implications of rigorous absolute bounds for ππ partial waves up to 1 GeV

Generalized dispersion relations and axiomatic results are used to derive absolute upper bounds for the ππ partial waves in a complex energy domain containing the physical region up to 1 GeV. As applications, a new lower bound for the π⁰π⁰ S-wave scattering length is given and some ambiguities in the connection between resonances and second sheet poles are removed.