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

TL;DR

This paper employs dispersion relations and phase shift analysis to connect K to pi pi decays with the sigma resonance, providing insights into the weak amplitude and final-state interactions.

Contribution

It introduces a method to extract the sigma pole residue from K to pi pi decay amplitudes using dispersion relations and phase shift parameterization.

Findings

Determined the sigma pole residue in the weak amplitude.

Linked K to pi pi decay amplitude with the sigma resonance.

Provided a framework for analyzing final-state interactions in weak decays.

Abstract

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.