Resonances and weak interactions in $D^+ \to\pi^+ \pi^- \pi^+$ decays

TL;DR

This paper models the $ ho ext{-} ext{wave}$ in $D^+ o ext{pi}^+ ext{pi}^- ext{pi}^+$ decays using a unitary approach to final state interactions, focusing on resonances and weak interactions.

Contribution

It introduces a unitary model for the $ ext{pi} ext{pi}$ S-wave in $D^+$ decays, incorporating a quasi two-body decay process with a resonance and pion at the weak vertex.

Findings

Provides a detailed description of the $ ext{pi} ext{pi}$ S-wave in $D^+$ decays.

Uses a unitarity-based model for final state interactions.

Analyzes the role of resonances in the decay process.

Abstract

We describe the $\pi\pi$ $S$-wave in $D^+ \to\pi^+ \pi^- \pi^+$ decays using a unitary model for the $\pi\pi$ Final State Interactions (FSI). The three body decay is treated as a quasi two-body process where, at the weak vertex, the D meson decays into a resonance and a pion. The weak part of the decay amplitude is evaluated using the effective weak Hamiltonian within the factorization approximation.