On the Optimality of Axiomatic Constraints for Pion Pion Scattering: The Case of the Lower Bounds

摘要

A nine parameter family of pion-pion yields pion-pion amplitudes F(s,t) is constructed such that (1) all the analytic and unitary conditions used in the derivation of rigorous absolute bounds are satisfied and (2) F(s,t) can assume negative values in the unphysical region. Within this set the values of F(4/3,4/3) and of the scattering length a (00) = F(4,0) are minimized. Best results realized are F(4/3,4/3) = -1.69 and a (00) = -0.88, whereas the best present lower bounds are F(4/3,4/3) -8.2 and a(00) -1.65.