Dispersive Approach to Chiral Perturbation Theory

Abstract

We generalise the reconstruction theorem of Stern, Sazdjian, and Fuchs based on the dispersion relations to the case of the (2 -> 2) scattering of all the pseudoscalar octet mesons (pi, K, eta). We formulate it in a general way and include also a discussion of the assumptions of the theorem. It is used to obtain the amplitudes of all such processes in the isospin limit to the one-loop order (and can be straightforwardly extended to two loops) independently on the particular power-counting scheme of the chiral perturbation theory in question. The results in this general form are presented.

25 pages, 1 figure; added one appendix and correction of typos

References in corpus (8)

• Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
• The Low Energy $\pi \pi$ Amplitude to One and Two Loops
• A new measurement of K+(e4) decay and the s-wave pi-pi-scattering length a00
• What $\pi -\pi$ Scattering Tells Us About Chiral Perturbation Theory
• Chiral Perturbation Theory Beyond One Loop
• Comparison of Pion-Kaon Scattering in SU(3) Chiral Perturbation Theory and Dispersion Relations
• $\pi K$ sum rules and the SU(3) chiral expansion
• Dispersive representation of K -> 3 pi amplitudes and cusps

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• Convergence properties of $\eta \to 3\pi$ decays in chiral perturbation theory
• Constraints on low energy QCD parameters from $\eta \to 3\pi$ and $\pi \pi$ scattering
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