In this paper (second in the series) we study the properties of tree-level binary amplitudes of the infinite-component effective field theory of strong interaction obeying the requirements of quark-hadron duality and maximal analyticity. In contrast to 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 string-like structure of a theory. Next, we derive the full set of bootstrap constraints for the resonance parameters in (π, K) system. Numerical test shows: (1) those constraints are consistent with data on well established vector resonances; (2) two light broad resonances -σ and κ -are needed to saturate sum rules following from Chiral symmetry and analyticity. As a by-product we obtain expressions for the parameters of Chiral expansions and give corresponding estimates.

This is the fourth paper in a series devoted to a systematic study of the problem of a mathematically correct formulation of the rules needed to manage an effective field theory. Here we consider the problem of constructing the full set of essential parameters in the case of the most general effective scattering theory containing no massless particles with spin JϾ1/2. We perform a detailed classification of combinations of the Hamiltonian coupling constants and select those which appear in the expressions for renormalized S-matrix elements at a given loop order.

This is the 5-th paper in the series devoted to explicit formulating of the rules needed to manage an effective field theory of strong interactions in S-matrix sector. We discuss the principles of constructing the meaningful perturbation series and formulate two basic ones: uniformity and summability. Relying on these principles one obtains the bootstrap conditions which restrict the allowed values of the physical (observable) parameters appearing in the extended perturbation scheme built for a given localizable effective theory. The renormalization prescriptions needed to fix the finite parts of counterterms in such a scheme can be divided into two subsets: minimal -needed to fix the S-matrix, and non-minimal -for eventual calculation of Green functions; in this paper we consider only the minimal one. In particular, it is shown that in theories with the amplitudes which asymptotic behavior is governed by known Regge intercepts, the system of independent renormalization conditions only contains those fixing the counterterm vertices with n ≤ 3 lines, while other prescriptions are determined by self-consistency requirements. Moreover, the prescriptions for n ≤ 3 cannot be taken arbitrary: an infinite number of bootstrap conditions should be respected. The concept of localizability, introduced and explained in this article, is closely connected with the notion of resonance in the framework of perturbative QFT. We discuss this point and, finally, compare the corner stones of our approach with the philosophy known as "analytic S-matrix".