K to \pi\pi decays and the K to \sigma weak amplitude

Understand

We use a twice-subtracted partial-wave dispersion relation in the elastic unitarity approximation for final-state interactions to study the amplitude for the delta I = 1/2 CP-conserving weak process K+spurion->pi+pi.

• We use a simple parameterization to approximate the low energy I = 0 S-wave pipi->pipi scattering phase shift and extract the residue of the sigma pole in the weak amplitude obtained from the dispersion relation.
• Using this residue, we relate the K->pipi decay amplitude, the weak amplitude at the soft pion point and the K->sigma weak amplitude.