K→ππ Decays in the K* Pole Model with Final-State Interactions : Particles and Fields

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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 ΔI=1/2 and ΔI=3/2 left-left operators but only constant contact amplitudes from ΔI=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 parametrization of the non-resonant portions of the final-state ππ 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 ΔI=3/2 K* pole amplitude enough to get agreement with the experimental ΔI=3/2 K→ππ decay amplitude and enhance the ΔI=1/2 K* pole amplitude to within 3/4 of the experimental ΔI=1/2 K→ππ decay amplitude. Although the purely ΔI=1/2 contact amplitude is numerically uncertain, it is of the wrong sign in our formalism to obtain further improvement of the calculated ΔI=1/2 K→ππ decay amplitude.
理論物理学刊行会の論文
1991-04-25

K→ππ Decays in the K* Pole Model with Final-State Interactions : Particles and Fields

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