Open Access

$D^{()} {\bar{B}}^{()}$ dynamics in chiral effective field theory

Zhe Liu ^1,2,5,*, Hao Xu ^4,†, and Xiang Liu ^1,2,3,5,‡

¹School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
²Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China
³MoE Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, China
⁴Institute of Theoretical Physics, College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
⁵Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000, China

^*Contact author: zhliu20@lzu.edu.cn
^†Contact author: xuh2020@nwnu.edu.cn
^‡Contact author: xiangliu@lzu.edu.cn

Phys. Rev. D 112, 034007 – Published 13 August, 2025

DOI: https://doi.org/10.1103/l9pk-hqx1

Abstract

In this work, we systematically study the interactions of the $S$ -wave $D^{(*)} {\bar{B}}^{(*)}$ systems within the framework of chiral effective field theory in heavy hadron formalism. We calculate the $D^{(*)} {\bar{B}}^{(*)}$ effective potentials up to next-to-leading order, explore the bound state formations, and investigate the $D^{(*)} {\bar{B}}^{(*)}$ scattering properties, such as scattering rate, scattering length, and effective range. Our results show that all $I = 1$ $D^{(*)} {\bar{B}}^{(*)}$ potentials are repulsive, preventing the formation of bound states, while the $I = 0$ potentials are generally attractive. Specifically, we get two important observations: first, the shallow bound state is more likely to exist in the $D \bar{B} [I (J^{P}) = 0 (0^{+})]$ system than in the $D {\bar{B}}^{*} [I (J^{P}) = 0 (1^{+})]$ system; second, $D^{*} {\bar{B}}^{*} [I (J^{P}) = 0 (0^{+})]$ and $D^{*} {\bar{B}}^{*} [I (J^{P}) = 0 (1^{+})]$ systems possess relatively large binding energies and positive scattering lengths, which suggests strong bound state formations in these channels. So, the attractions in the $D^{*} {\bar{B}}^{*} [I = 0]$ systems are deeper than those in the $D {\bar{B}}^{(*)} [I = 0]$ systems, thus we strongly recommend the future experiment to search for the $D^{*} {\bar{B}}^{*} [I = 0]$ tetraquark systems. We also investigate the coupled-channel effects on the $J = 0, 1$ systems and conclude that the inclusion of the coupled channels introduces small but visible influences. In addition, we also investigate the dependencies of the $D {\bar{B}}^{(*)}$ binding energies on the contact low-energy coupling constants.

Physics Subject Headings (PhySH)

Strong interaction

Article Text

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Phys. Rev. D 112, 034007– Published 13 August, 2025

Vol. 112, Iss. 3 — 1 August 2025

Received 16 March 2025
Accepted 16 July 2025

DOI: https://doi.org/10.1103/l9pk-hqx1

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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$D^{()} {\bar{B}}^{()}$ dynamics in chiral effective field theory

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D(*)B¯(*) dynamics in chiral effective field theory

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$D^{()} {\bar{B}}^{()}$ dynamics in chiral effective field theory