# The role of scalar mesons in extended perturbation scheme for effective field theory

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## Abstract

The Role of Scalar Mesons in Extended Perturbation Scheme for Effective Field Theory Kirill Semenov-Tian-Shansky∗, Alexander Vereshagin† and Vladimir Vereshagin∗∗ ∗Institut für Theoretische Physik II, Ruhr-Universität Bochum, Bochum, Germany †Department of Physics and Technology, University of Bergen, Bergen, Norway ∗∗Department of High Energy Physics, Saint-Petersburg State University, Saint-Petersburg, Russia Abstract. We argue how it is possible to apply the general scheme of the effective scattering theory (EST) to the description of the hadronic processes. The results of the numerical tests of sum rules for piN spectrum parameters that follow from the bootstrap system allow us to claim the consistency of the predictions obtained in the framework of our approach with the known phenomenology. We also demonstrate that the tree-level low energy expansion coefficients computed in the framework of our approach show nice agreement with known experimental data. Keywords: Effective field theories, renormalizability PACS: 02.30.Lt, 11.15.Bt, 13.75.Gx, 14.20.Gk INTRODUCTION In papers [3, 4, 5, 6] we started the systematic study of the special class of effective theories of strong interaction. Our principle goal is to develop a self consistent Dyson perturbation technique for the infinite component effective scattering theory of strong interaction. It is quite reasonable to start from the definition of such a theory. We use a slightly modified version of the definition first given in [1]. The field theory is called ef- fective if the quantum interaction Hamiltonian (in the interaction picture) contains all the monomials consistent with a given algebraic (linear) symmetry. The effective theories are as renormalizable as the ordinary renormalizable ones. The only difference is that one needs to formulate an infinite number of renormalization prescriptions (RPs) fixing the finite part of counterterms. Effective theories are intrinsically quantum constructions since we relay upon Weinberg scheme o

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