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Article Dans Une Revue European Physical Journal C: Particles and Fields Année : 2003

Dispersion relations and Omnès representations for $K \to \pi\pi$ decay amplitudes

Résumé

We derive dispersion relations for $K\to\pi\pi$ decay, using the Lehmann-Symanzik-Zimmermann formalism, which allows the analytic continuation of the amplitudes with respect to the momenta of the external particles. No off-shell extrapolation of the field operators is assumed. We obtain generalized Omnès representations, which incorporate the $\pi\pi$ and $\pi K$ $S$-wave phase shifts in the elastic region of the direct and crossed channels, according to Watson theorem. The contribution of the inelastic final-state and initial-state interactions is parametrized by the technique of conformal mappings. We compare our results with previous dispersive treatments and indicate how the formalism can be combined with lattice calculations to yield physical predictions.
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Dates et versions

hal-00127165 , version 1 (29-01-2007)

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  • HAL Id : hal-00127165 , version 1

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Claude Bourrely, Irinel Caprini, Liliana Micu. Dispersion relations and Omnès representations for $K \to \pi\pi$ decay amplitudes. European Physical Journal C: Particles and Fields, 2003, 27, pp.439-446. ⟨hal-00127165⟩
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