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Three-body final state interactions in $B^{+} \to D \bar{D} K^{+}$ decays

Xin-Yue Hu ^1,2,3,*, Jiahao He ^2,4,*, Pengyu Niu ^1,3,†, Qian Wang ^1,3,5,6,‡, and Yupeng Yan^7,§

¹Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Guangdong Provincial Key Laboratory of Nuclear Science, Guangzhou 510006, China
²Key Laboratory of Atomic and Subatomic Structure and Quantum Control (MOE), Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Guangzhou 510006, China
³State Key Laboratory of Nuclear Physics and Technology, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China
⁴School of Physics, South China Normal University, Guangzhou 510006, China
⁵Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, Huizhou 516000, Guangdong Province, China
⁶Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047, Japan
⁷School of Physics and Center of Excellence in High Energy Physics & Astrophysics, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand

^*These authors contributed equally to this work.
^†Contact author: niupy@m.scnu.edu.cn
^‡Contact author: qianwang@m.scnu.edu.cn
^§Contact author: yupeng@sut.ac.th

Phys. Rev. D 113, 054003 – Published 2 March, 2026

DOI: https://doi.org/10.1103/whyt-cx47

Abstract

This paper presents a detailed analysis of the three-body final state interactions in the $B^{+} \to D \bar{D} K^{+}$ process, whose phase space is sufficient small. To precisely extract the resonance parameters, for instance the $χ_{c 0 / 2} (3930)$ in the $D \bar{D}$ invariant mass distributions, in this process, one has to take into account final state interaction, especially the three-body final state interaction. We employ the dispersive Khuri-Treiman formalism, combined with a parametrization of the $D \bar{D}$ interaction based on heavy quark spin symmetry. By performing a simultaneous fit to the experimental data from LHCb, BABAR, and Belle collaborations, the scheme with three-body interaction successfully describes the invariant mass distributions of the three two-body subsystems. We precisely extract the pole structures of $χ_{c 0} (3930)$ and $ψ (3770)$ as $3.913 - 0.016 i GeV$ and $3.761 - 0.006 i GeV$ in $B^{+}$ decay. By performing the pole trajectory analysis on a uniformized complex plane, we find that both of them stem from the input bare state.

Physics Subject Headings (PhySH)

Particle interactions

Article Text

References (63)

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Phys. Rev. D 113, 054003– Published 2 March, 2026

Vol. 113, Iss. 5 — 1 March 2026

Received 22 September 2025
Accepted 6 February 2026

DOI: https://doi.org/10.1103/whyt-cx47

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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Three-body final state interactions in $B^{+} \to D \bar{D} K^{+}$ decays

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Three-body final state interactions in B+→DD¯K+ decays

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Physics Subject Headings (PhySH)

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References (63)

Three-body final state interactions in $B^{+} \to D \bar{D} K^{+}$ decays