Dispersive representation of K -> 3 pi amplitudes and cusps

TL;DR

This paper develops a two-loop dispersive framework for K -> 3 pi decays, enabling precise analysis of cusp effects to extract pi-pi scattering lengths, accounting for isospin breaking.

Contribution

It introduces a novel two-loop dispersive approach to model K -> 3 pi amplitudes with isospin breaking effects, improving the theoretical understanding of cusp phenomena.

Findings

Demonstrates the effectiveness of the dispersive model in describing cusp structures.

Provides a method to extract pi-pi scattering lengths from experimental data.

Enhances the theoretical precision of K decay amplitude analyses.

Abstract

The NA48/2 collaboration has shown clear experimental evidence for a cusp in the data for K -> pi pi^0 pi^0. This effect can be used to extract information on the pi-pi scattering lengths. We address this issue using a two-loop dispersive construction of pi pi -> pi pi and K -> pi pi pi amplitudes in the presence of isospin breaking.