Effective theories with maximal analyticity

In this paper (the second in the series), we study the properties of the tree-level binary amplitudes of the infinite-component effective field theory of strong interactions obeying the requirements of quark-hadron duality and maximal analyticity. In contrast with the previous paper, here we derive the results following from less restrictive — Regge-like — boundedness conditions. We develop the technique of Cauchy’s forms in two variables and show the stringlike structure of the theory. Next, we derive the full set of bootstrap constraints for the resonance parameters in the $(\pi ,K)$ system. A numerical test shows (1) these constraints are consistent with data on well-established vector resonances, and (2) two light broad resonances — $\sigma$ and $\kappa$ — are needed to saturate the sum rules following from chiral symmetry and analyticity. This latter term is understood — in the customary field-theoretical sense — as meromorphy and polynomial boundedness of the tree-level amplitudes. As a by-product, we obtain expressions for the parameters of chiral expansions and give corresponding estimates.