Dispersion relations and Omnès representations for K decay amplitudes

We derive dispersion relations for K → ππ decay, using the LehmannSymanzik-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 ππ and πK 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 initialstate 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.