41 research outputs found
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
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
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 physical values of 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 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
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
The resultant parameters of effective theory
This is the 4-th paper in the series devoted to a systematic study of the
problem of 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 J > 1/2. We
perform the 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.Comment: 21 pages, 4 LaTeX figures, submitted to Phys. Rev.
On the S-matrix renormalization in effective theories
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
lines, while other prescriptions are determined by self-consistency
requirements. Moreover, the prescriptions for 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''.Comment: 28 pages, 10 Postscript figures, REVTeX4, submitted to Phys. Rev.