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Decoding $Z_{c} (4430)$ and $Z_{c} (4200)$ : The role of $P$ -wave charmed mesons

Jian-Bo Cheng ^1,2,*, Zi-Yang Lin ^2,†, Jun-Zhang Wang^3,‡, and Shi-Lin Zhu ^2,§

¹College of Science, China University of Petroleum, Qingdao, Shandong 266580, China
²School of Physics and Center of High Energy Physics, Peking University, Beijing 100871, China
³Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 401331, China

^*Contact author: jbcheng@pku.edu.cn
^†Contact author: lzy_15@pku.edu.cn
^‡Contact author: wangjzh@cqu.edu.cn
^§Contact author: zhusl@pku.edu.cn

Phys. Rev. D 113, 096001 – Published 5 May, 2026

DOI: https://doi.org/10.1103/v5jm-59g9

Abstract

In this work, we perform a systematic investigation of the hidden-charm tetraquark states with $I^{G} (J^{P C}) = 1^{+} (1^{+ -})$ 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 Schrödinger 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 Flatté-like parametrization with energy-dependent self-energy terms, providing predictions for its open-charm decay modes to guide future experimental searches.

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Phys. Rev. D 113, 096001– Published 5 May, 2026

Vol. 113, Iss. 9 — 1 May 2026

Received 29 January 2026
Accepted 19 March 2026

DOI: https://doi.org/10.1103/v5jm-59g9

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Decoding $Z_{c} (4430)$ and $Z_{c} (4200)$ : The role of $P$ -wave charmed mesons

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

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References (79)

Decoding $Z_{c} (4430)$ and $Z_{c} (4200)$ : The role of $P$ -wave charmed mesons