Decoding $Z_c(4430)$ and $Z_c(4200)$: The role of $P$-wave charmed mesons

TL;DR

This paper investigates hidden-charm tetraquark states involving P-wave charmed mesons using a hadronic molecular approach, emphasizing three-body decay effects to explain experimental resonance properties.

Contribution

It introduces a comprehensive method incorporating three-body decay effects and complex scaling to accurately model broad resonances like Zc(4430) and Zc(4200).

Findings

Identifies broad resonances as candidates for Zc(4430) and Zc(4200).

Highlights the importance of three-body dynamics in resonance widths.

Provides line shape predictions for experimental searches.

Abstract

In this work, we perform a systematic investigation of the hidden-charm tetraquark states with $I^G(J^{PC})=1^+(1^{+-})$ within the hadronic molecular picture, placing particular emphasis on systems composed of an $S$-wave $(D, D^*)$ meson and a $P$-wave $(D_0^*(2300), D_1(2430), D_1(2420), D_2^*(2460))$ meson. Adopting the One-Boson Exchange potential, we solve the Schr\"odinger equation in momentum space via the Complex Scaling Method. A crucial feature of our approach is the rigorous treatment of the unstable nature of the $P$-wave constituents by incorporating three-body decay effects arising from self-energy corrections and the static limit approximation. Our results demonstrate that these three-body dynamics play a crucial role in determining the pole positions, specifically in reproducing the large decay widths observed experimentally. We identify several broad resonances in the $D^*\bar{D}_1(2420)$ and $D^*\bar{D}_2^*(2460)$ systems as candidates for the $Z_c(4430)$, while the significantly broader resonances in the $D\bar{D}_0^*(2300)$ and $D\bar{D}_1(2430)$ sectors are suggested as candidates for the $Z_c(4200)$. Focusing on the $D^*\bar{D}_2^*(2460)$ assignment as a specific case study, we further analyze the line shape of the $Z_c(4430)$ candidate using a Flatt\'e-like parametrization with energy-dependent self-energy terms, providing predictions for its open-charm decay modes to guide future experimental searches.