Study of kaon decay to two pions

Abstract

The weak decay of the kaon to two pions is studied within the model of Nambu and Jona-Lasinio. Using the standard effective weak Hamiltonian, both the decay amplitude arising from an intermediate state sigma meson and the direct decay amplitude are calculated. The effect of final state interactions is also included. When the matching scale is chosen such that the decay amplitude with isospin I = 2 is close to its experimental value, our model including the sigma meson contributes up to 80% of the total I = 0 amplitude. This supports recent suggestions that the sigma meson should play a vital role in explaining the Delta I = 1/2 rule in this system.