Abstract
Final-state interactions are incorporated into a K* vector meson pole model of parity-violating K →ππ decays which is based on a short-distance QCD corrected weak-interaction Lagrangian that yields explicit K* pole amplitudes from Δ I = 1/2 and Δ I = 3/2 left-left operators but only constant contact amplitudes from Δ I = 1/2 left-right operators. The resulting Muskhelishvili-Omnès singular integral equations are solved by resorting to an effective range approximation for the K* pole amplitudes, and this approximation is justified by appealing to the case of massless pions for which exact analytic solutions are obtained. A simple parametrization of the non-resonant portions of the final-state ππ scattering phase shifts is used to obtain analytic solutions for the Omnès functions which give the effects of final-state interactions on the K* pole amplitudes. Our results show that the non-resonant portions of the final-state interactions combined with the short-distance QCD corrections to the weak-interaction Lagrangian suppress the Δ I = 3/2 K* pole amplitude enough to get agreement with the experimental Δ I = 3/2 K →ππ decay amplitude and enhance the Δ I = 1/2 K* pole amplitude to within 3/4 of the experimental Δ I = 1/2 K →ππ decay amplitude. Although the purely Δ I = 1/2 contact amplitude is numerically uncertain, it is of the wrong sign in our formalism to obtain further improvement of the calculated Δ I = 1/2 K →ππ decay amplitude.
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