Bootstrap and the physical values of πN\pi N resonance parameters

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 figure

Renormalization programme for effective theories

We summarize our latest developments in perturbative treating the effective theories of strong interactions. We discuss the principles of constructing the mathematically correct expressions for the S-matrix elements at a given loop order and briefly review the renormalization procedure. This talk shall provide the philosophical basement as well as serve as an introduction for the material presented at this conference by A. Vereshagin and K. Semenov-Tian-Shansky.Comment: 6 pages, talk given at HSQCD 2004, Russia, May 2004, to be published in Proceeding

Bootstrap and the Parameters of Pion-Nucleon Resonances

In this talk we demonstrate the results of application of the perturbative effective theory formalism developed in recent papers to the calculation of $\pi N$ elastic scattering amplitude. Restrictions on the contributing resonance parameters are obtained and the low energy coefficients are calculated.Comment: 6 pages, talk given at the X. International Conference On Hadron Spectroscopy (HADRON'03), August 31 - September 6, 2003, Aschaffenburg, Germany; to appear in Proceeding

A note on inequalities for the masses of the lightest pi-pi resonances in large N_c QCD

We derive and analyse inequalities relating masses of the lightest pi-pi resonances (rho and sigma) to low energy couplings of the effective chiral Lagrangian in the limit of large number of colours.Comment: 8 pages, discussion of the hybrid component is correcte

Localizable Effective Theories, Bootstrap and the Parameters of Hadron Resonances

We discuss the basic principles of constructing a meaningful perturbative scheme for effective theory. The main goal of this talk is to explain the approach and to present recent results obtained with the help of the method of Cauchy forms in several complex variables.Comment: 6 pages, Talk given at the X. International Conference On Hadron spectroscopy (HADRON'03), August 31 - September 6, 2003, Aschaffenburg, Germany; to appear in Proceeding