Effective theories with maximal analyticity

Vereshagin, A.; Vereshagin, V.

doi:10.1103/physrevd.59.016002

Cited by 25 publications

(73 citation statements)

References 39 publications

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“…The results of these two Sections are generalized in Sec. VII, where phenomenological constraints are imposed and the renormalization prescriptions are explicitly written; besides, it is shown there that the bootstrap conditions obtained at any loop order can be treated as the relations between physical observables, which justify the legitimacy of our preceding analysis of experimental data [3,7,8].…”

Section: Introductionmentioning

confidence: 99%

“…We say that the field theory is effective if the interaction Hamiltonian in the interaction picture contains all the monomials consistent with a given algebraic (linear) symmetry 3 . Effective scattering theory is just the Hamiltonian density.…”

Section: Classification Of the Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Thus, in [4] (see also [7]) we suggest the notion of minimal parametrization and in [1] the corresponding reduction theorem is proven. This theorem explains why it is sufficient to consider only the minimal ("on-shell-surviving") vertices at each loop order of the perturbation theory -the fact implicitly used in [3] to parameterize amplitudes. Besides, in [4] we briefly discuss what we call the localizability requirement -the philosophy which, in particular, serves as background for the requirements of polynomial boundedness and meromorphy of tree level amplitudes.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the problems we have to do with include an infinite number of graphs to be summed up at each loop order and the problem of ordering the required renormalization conditions, since in such a theory one needs to fix an infinite number of parameters to be able to calculate amplitudes. In [3] it has been shown that already the requirement of summability of tree graphs -the existence of well-defined tree level amplitudes -leads to strong limitations on the possible values of coupling constants of a theory. However, in those articles some theoreti-cal statements, like meromorphy and polynomial boundedness of the tree level amplitude, were taken as postulates and only some general arguments in their favor were given.…”

Section: Introductionmentioning

confidence: 99%

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S-matrix renormalization in effective theories

Semenov-Tian-Shansky

Vereshagin²,

Vereshagin³

2006

Phys. Rev. D

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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".

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Section: Introductionmentioning

confidence: 99%

Section: Classification Of the Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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S-matrix renormalization in effective theories

Semenov-Tian-Shansky

Vereshagin²,

Vereshagin³

2006

Phys. Rev. D

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Testing the bootstrap constraints in the strange sector

Semenov-Tian-Shansky

Vereshagin

2013

J. High Energ. Phys.

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In this paper the bootstrap conditions that follow from the general postulates of effective scattering theory (EST) are checked in the strange sector. We construct the system of tree level bootstrap constraints for the renormalization prescriptions fixing the physical content of the theory. Then we perform the numerical testing of corresponding sum rules for the parameters of strange resonances. It is shown that, generally, the bootstrap constraints turn out consistent with presently known data on the strange resonance parameters. At the same time we point out few sum rules which cannot be saturated with modern data and discuss the possible reasons for such discrepancies.

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The light σ-meson

Anisovich

Nikonov

2000

Eur. Phys. J. A

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In the framework of the dispersion relation N/D-approach, we restore the low-energy ππ (IJ P C = 00 ++ )-wave amplitude sewing it with the previously obtained K-matrix solution for the region 450-1900 MeV. The restored N/D-amplitude has a pole on the second sheet of the complex-s plane near the ππ threshold, that is the light σ-meson.12.39. Mk, At present the understanding of scalar meson is one of the key problems for the Strong-QCD physics. The ππ low-mass data provide indications on the existence of a low-mass σ-meson. This state is beyond qq and gluonium systematics, which makes it necessary to confirm its existence as well as to study the possible mechanisms of its formation.Experimental data on meson spectra accumulated by the Crystal Barrel Collaboration [1], GAMS [2] and BNL [3] groups provided a good basis for setting up the qq/gluonium classification of the light scalars. For the (IJ P C = 00 ++ )-wave, the combined K-matrix analysis of the reactions ππ → ππ, KK, ηη, ηη ′ , ππππ has been carried out over the mass range 450-1900 MeV [4,5], then the K-matrix analysis was extended to the waves , thus making it possible to establish the qq systematics of scalars for 1 3 P 0 qq and 2 3 P 0 qq multiplets. The advantage of the K-matrix representation is that it allows us not only to determine the locations and partial widths of resonances but also to study characteristics of corresponding states with switched off decay channels: these "primary states", or "bare states" (i.e. states without a cloud of mesons produced by decay processes) are suitable objects for the qq/gluonium classification (see [7] for the details). The decay processes in the scalar/isoscalar sector cause a strong mixing which destroys the qq/gluonium classification. Another important effect generated by transitions (qq) 1 → real mesons → (qq) 2 is an accumulation of widths of neighbouring resonances by one of them, that results in appearance of a broad state.According to [4,5], five bare scalar/isoscalar states are located in the region 700-1800 MeV: f An important result of the article [4,5] is that the K-matrix 00 ++ -amplitude has no pole singularities in the region 500-800 MeV. Here the ππ-scattering phase δ 0 0 increases smoothly reaching 90• at 800-900 MeV. A straightforward explanation of such a behaviour of δ 0 0 might consist in the presence of a broad resonance, with a mass about 600-900 MeV and width Γ ∼ 500 MeV (for example, see Refs. [10,11] and references therein). However, according to the Kmatrix solution [4,5], the 00 ++ -amplitude does not contain pole singularities on the second sheet of the complex-M ππ plane inside the interval 450 ≤ Re M ππ ≤ 900 MeV: the K-matrix amplitude has a low-mass pole only, which is located on the second sheet either near the ππ threshold or even below it. In [4,5], the presence of this pole was not emphasized, for the left-hand cut, which is important for the reconstruction of analytic structure of the low-energy partial amplitude, was taken into account only indirectly; a proper way for the ...

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Effective theories with maximal analyticity

Cited by 25 publications

References 39 publications

S-matrix renormalization in effective theories

S-matrix renormalization in effective theories

Testing the bootstrap constraints in the strange sector

The light σ-meson

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