Positivity and geometric function theory constraints on pion scattering

A bstract This paper presents the fascinating correspondence between geometric function theory and scattering amplitudes with O ( N ) global symmetry. crucial ingredient to show such is a fully crossing symmetric dispersion relation in z -variable, rather than fixed channel relation. We have written down for model -variable three independent combinations of isospin amplitudes. presented sum rules or locality constraints arising from relations. derived sets positivity conditions. obtained two-sided bounds on Taylor coefficients physical Pion around point (for example, π + − → 0 applying conditions Bieberbach-Rogosinski inequalities theory.