Multi-Meson Model for the $D^+\to K^+K^-K^+$ decay amplitude

TL;DR

This paper introduces a new chiral effective Lagrangian-based model for the $D^+ o K^+K^-K^+$ decay amplitude, enabling detailed analysis of $Kar{K}$ scattering and disentangling scalar contributions with different isospins.

Contribution

The novel approach combines nonresonant interactions and coupled-channel rescattering within a unitarized framework, surpassing the traditional isobar model by including chiral symmetry constraints.

Findings

The model effectively describes the decay amplitude with physical resonance parameters.

It allows extraction of $Kar{K}$ scattering information from decay data.

The nonresonant component is predicted by chiral symmetry, providing a new insight.

Abstract

We propose a novel approach to describe the $D^+\to K^+K^-K^+$ decay amplitude, based on chiral effective Lagrangians, which can be used to extract information about $K\bar{K}$ scattering. Our trial function is an alternative to the widely used isobar model and includes both nonresonant three-body interactions and two-body rescattering amplitudes, based on coupled channels and resonances, for S- and P-waves with isospin $0$ and $1$. The latter are unitarized in the $K$-matrix approximation and represent the only source of complex phases in the problem. Free parameters are just resonance masses and coupling constants, with transparent physical meanings. The nonresonant component, given by chiral symmetry as a real polynomium, is an important prediction of the model, which goes beyond the (2+1) approximation. Our approach allows one to disentangle the two-body scalar contributions with different isospins, associated with the $f_0(980)$ and $a_0(980)$ channels. We show how the $K\bar{K}$ amplitude can be obtained from the decay $D^+\to K^+K^-K^+$ and discuss extensions to other three-body final states.