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The weak decay of the kaon to two pions is studied within the NJL Model.Using the standard effective weak Hamiltonian, both the decay amplitude arisingfrom an intermediate state \sigma-meson and the direct decay amplitude arecalculated. The effect of final state interactions is also included. When thematching scale is chosen such that the decay amplitude with isospin I=2 isclose to its experimental value, the \sigma-meson contributes more than 85% ofthe total I=0 amplitude. This supports recent suggestions that the \sigma-mesonshould play a vital role in explaining the \Delta I= 1/2 rule in this system.

Study of Kaon Decay to Two Pions