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Pole trajectories from $S$ - and $P$ -wave $D {\bar{D}}^{*}$ interactions

Xiao-Xiao Chen , Zuo-Ming Ding , and Jun He ^*

School of Physics and Technology, Nanjing Normal University, Nanjing 210097, China

^*Contact author: junhe@njnu.edu.cn

Phys. Rev. D 111, 114008 – Published 10 June, 2025

DOI: https://doi.org/10.1103/36vy-r2z8

Abstract

In this work, we investigate the $S$ - and $P$ -wave interactions of the $D {\bar{D}}^{*}$ system within the framework of the quasipotential Bethe-Salpeter equation, with the aim of exploring possible molecular states and their corresponding pole trajectories. The interaction potentials are constructed using the one-boson-exchange model, incorporating the exchanges of $π$ , $η$ , $ρ$ , $ω$ , $σ$ , and $J / ψ$ mesons, based on heavy quark effective Lagrangians. The poles of the scattering amplitude are analyzed and their evolution on two Riemann sheets is systematically traced as the cutoff parameter increases up to 5 GeV. We identify four molecular states arising from the $S$ -wave $D {\bar{D}}^{*}$ interaction. Among them, the bound state with quantum numbers $I^{G} (J^{P C}) = 0^{+} (1^{+ +})$ corresponds well to the experimentally observed $X (3872)$ , while its isovector partner with $I^{G} (J^{P C}) = 1^{-} (1^{+ +})$ is found to exist only as a virtual state. Additionally, a $0^{-} (1^{+ -})$ state appears as a bound state. The isovector $1^{+ -}$ state, which may be associated with the $Z_{c} (3900)$ , is observed to evolve from a bound state to a virtual state as the interaction strength decreases. For the $P$ -wave $D {\bar{D}}^{*}$ interaction, the structure $G (3900)$ recently observed at BESIII is likely connected to a $0^{-} (1^{- -})$ state. A $0^{+} (0^{- +})$ state is also predicted in this channel. Both can appear as either resonance or bound/virtual state depending on the interaction strength.

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Phys. Rev. D 111, 114008– Published 10 June, 2025

Vol. 111, Iss. 11 — 1 June 2025

Received 21 April 2025
Accepted 28 May 2025

DOI: https://doi.org/10.1103/36vy-r2z8

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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Pole trajectories from $S$ - and $P$ -wave $D {\bar{D}}^{*}$ interactions

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Pole trajectories from S- and P-wave DD¯* interactions

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References (67)

Pole trajectories from $S$ - and $P$ -wave $D {\bar{D}}^{*}$ interactions