K -> Decays in the K* Pole Model with Final-State Interactions

Abstract

Final-state interactions are incorporated into a K* vector meson pole model of parity-violating K -+ 7f7f decays which is based on a short-distance QCD corrected weak-interaction Lagrangian that yields explicit K* pole amplitudes from LlI=1/2 and LlI=3/2 left-left operators but only constant contact amplitudes from LlI=1/2.left-right operators. The resulting Muskhelishvili-Omnes 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 para'metrization of the non-resonant portions of the final-state 7f7f scattering phase shifts is used to obtain analytic solutions for the Omnes 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 LlI =3/2 K* pole amplitude enough to get agreement with the experimental LlI =3/2 K -+ 7f7f decay amplitude and enhance the LlI = 1/2 K* pole amplitude to within 3/4 of the experimental LlI=1/2 K-+7f7f decay amplitude. Although the purely LlI=1/2 contact amplitude is numerically uncertain, it is of the wrong sign in our formalism to obtain further improvement of the calculated LlI = 1/2 K -+ 7f7f decay amplitude.