# Parametrizations of three-body hadronic $B$- and $D$-decay amplitudes

## TL;DR

This paper reviews recent parametrizations of three-body hadronic weak decays of $B$ and $D$ mesons, emphasizing their derivation from a quasi-two-body approach and their utility in CP asymmetry analysis.

## Contribution

It introduces a new parametrization method for three-body decay amplitudes based on unitary form factors, offering an alternative to the isobar model.

## Key findings

- Provides a comprehensive framework for three-body decay amplitude analysis.
- Enhances interpretation of CP asymmetries in meson decays.
- Offers a practical tool for experimental data analysis.

## Abstract

A short review of our recent work on amplitude parametrizations of three-body hadronic weak $B$ and $D$ decays is presented. The final states are here composed of three light mesons, namely the various charge $\pi\pi\pi$, $K\pi\pi$ and $KK\bar K$ states. These parametrizations are derived from previous calculations based on a quasi-two-body factorization approach where the two-body hadronic final state interactions are fully taken into account in terms of unitary $S$- and $P$-wave $\pi\pi$, $\pi K$ and $K \bar K$ form factors. They are an alternative to the isobar-model description and can be useful in the interpretation of CP asymmetries.