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Particles and Fields
Eur. Phys. J. C 27, 439-446 (2003)
DOI: 10.1140/epjc/s2002-01120-4

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

C. Bourrely1, I. Caprini2 and L. Micu2

1  Centre de Physique Théorique (Unité Propre de Recherche 7061.) , CNRS-Luminy, Case 907, 13288 Marseille Cedex 9, France
2  National Institute of Physics and Nuclear Engineering, POB MG 6, Bucharest, 76900 Romania

(Received: 14 October 2002 / Published online: 14 February 2003 )

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$ and $\pi K$ S-wave phase shifts in the elastic region of the direct and crossed channels, according to the Watson theorem. The contribution of the inelastic final-state and initial-state interactions is parameterized 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.

© Società Italiana di Fisica, Springer-Verlag 2003