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This is the revised version of Sect. I - IV of the paper https://doi.org/10.1103/PhysRevD.89.125022 originally published in 2014. The thing is that in https://doi.org/10.1103/PhysRevD.89.125022 the text was insufficiently clear and, in addition, it contained (through my fault) a few typos. This is the reason why I decided to offer a revised version. Original abstract: This is the eighth paper in the series devoted to the systematic study of effective theories. Below, I discuss the renormalization of the one-loop two-leg functions in multicomponent effective scalar theory. It is shown that only a part of numerous contributions that appear in the general expression for a two-leg graph can be considered as the true self-energy function. This part is completely fixed by the values of minimal coupling constants; it is the only one that should be taken into account in the conventional process of the summation of Dyson's chain that results in explicit expression for the full propagator. The other parts provide the well-defined finite corrections for the graphs with the number of legs n > 2. It is also shown that there is no need to attract the renormalization prescriptions for the higher derivatives of the two-leg function on the mass shell; the requirements of finiteness and diagonability turn out to be quite sufficient., Comment: 8 pages, 2 figures

This is the 6th paper in the series developing the formalism to manage the effective scattering theory of strong interactions. Relying on the theoretical scheme suggested in our previous publications we concentrate here on the practical aspect and apply our technique to the elastic pion-nucleon scattering amplitude. We test numerically the pion-nucleon spectrum sum rules that follow from the tree level bootstrap constraints. We show how these constraints can be used to estimate the tensor and vector $NN\rho$ coupling constants. At last, we demonstrate that the tree-level low energy expansion coefficients computed in the framework of our approach show nice agreement with known experimental data. These results allow us to claim that the extended perturbation scheme is quite reasonable from the computational point of view., Comment: 41 pages, 7 figures

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 (\pi,K) system. Numerical test shows: (1) those constraints are consistent with data on well established vector resonances; (2) two light broad resonances -- sigma- and kappa-mesons -- 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., Comment: 33 pages, 2 figures, 1 table, LATEX

We consider the tree-level amplitude, describing all 3 channels of the binary (pi ,K)-reaction, as a meromorphic polynomially bounded function of 3 dependent complex variables. Relying systematically on the Mittag-Leffler theorem, we construct 3 convergent partial fraction expansions, each one being applied in the corresponding domain. Noting, that the mutual intersections of those domains are nonempty, we realize the analytical continuation. It is shown that the necessary conditions to make such a continuation feasible, are the following: 1) The only parameters completely determining the amplitude are the on-shell couplings and masses; 2) These parameters are restricted by a certain (infinite) system of bootstrap equations; 3) The full cross-symmetric amplitude takes the typically dual form, the Pomeron contribution being taken into account; 4)This latter contribution corresponds to a nonresonant background, which, in turn, is expressed in terms of cross-channel resonances parameters. It is demonstrated also, that the Chiral Symmetry provides a unique scale for the mentioned parameters, the resonance saturation effect appearing as a direct consequence of the above results.