A new method for deriving rigorous results on ππ scattering

A new approach to the problem of constraining the pi pi scattering amplitudes by means of the axiomatically proved properties of unitarity, analyticity, and crossing symmetry is developed. The method is based on the solution of an extremal problem on a convex set of analytic functions and provides a global description of the domain of values taken by any finite number of partial waves at an arbitrary set of unphysical energies, compatible with unitarity, the bounds at complex energies derived from generalised dispersion relations and the crossing integral relations. From this domain the authors obtain new absolute bounds for the amplitudes as well as rigorous correlations between the values of various partial waves.