Tree-level (pi, K)-amplitude and analyticity

Abstract

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.

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• Simple Description of Pion-Pion Scattering to 1 GeV
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• Two chiral nonet model with massless quarks
• Chiral Lagrangian treatment of pi eta scattering
• Large Nc and Chiral Dynamics
• Gauged linear sigma model and pion-pion scattering
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• Effects of light scalar mesons in $\eta \to 3\pi$ decay
• The Energy Momentum Tensor of Chiral Quark Models at Low Energies
• Effective theories with maximal analyticity
• Bootstrap and the physical values of $\pi N$ resonance parameters
• Comparing the Higgs Sector of Electroweak Theory with the Scalar Sector of Low Energy QCD
• The resultant parameters of effective theory
• On the S-matrix renormalization in effective theories
• High Energy Theorems at Large-N
• Pion-Pion Scattering in Two Dimensions