Dalitz-plot decomposition for the $e^+ e^- \to J/\psi \, \pi \, \pi \, (K \bar{K})$ and $e^+ e^- \to h_c \, \pi \, \pi$ processes

TL;DR

This paper introduces a Dalitz-plot decomposition method for analyzing specific electron-positron collision processes involving charmonium states, validating factorization and crossing symmetry, and employing dispersive techniques to model final state interactions.

Contribution

It develops a novel Dalitz-plot decomposition approach based on helicity formalism, validated with a toy model, and applies dispersive methods to accurately describe final state interactions in these processes.

Findings

Validated factorization of decay chains and spin alignments.

Successfully modeled $ ext{f}_0(500)$ and $ ext{f}_0(980)$ resonances.

Provided a framework to study exotic charged states $Z_c(3900)$ and $Z_c(4020)$.

Abstract

We present an analysis of the $e^+ e^- \to \gamma^* \to J/\psi \, \pi \, \pi \, (K \bar{K})$ and $e^+ e^- \to \gamma^* \to h_c \, \pi \, \pi$ processes employing the recently proposed Dalitz-plot decomposition approach, which is based on the helicity formalism for three-body decays. For the above reactions, we validate the factorization of the overall rotation for all decay chains and spin alignments, along with the crossing symmetry between final states, using a Lagrangian-based toy model. For the model-dependent factors that describe the subchannel dynamics, we employ the dispersive treatment of the $\pi \, \pi \, (K \bar{K})$ final state interaction, which accurately reproduces pole positions and couplings of the $f_0(500)$ and $f_0(980)$ resonances. The constructed amplitudes serve as an essential framework to further constrain the properties of the charged exotic states $Z_c(3900)$ and $Z_c(4020)$, produced in these reactions.