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Search for signals of the $D \bar{D}$ bound state $X (3700)$ from study of the $B^{+} \to D^{+} D^{-} K^{+}$ , $B^{0} \to D^{+} D^{-} K^{0}$ and $Λ_{b} \to D^{+} D^{-} Λ$ reactions

Xiu-Lei Ren ^1,*, Hai-Peng Li ^2,†, Wei-Hong Liang ^3,4,‡, Chu-Wen Xiao ^3,4, and Eulogio Oset ^3,5,§

¹Shandong Provincial Key Laboratory of Nuclear Science, Nuclear Energy Technology and Comprehensive Utilization, and School of Nuclear Science, Energy and Power Engineering, Shandong University, 250061 Jinan, China
²School of Physics and Electronics, Nanning Normal University, Nanning 530100, China
³Department of Physics, Guangxi Normal University, Guilin 541004, China
⁴Guangxi Key Laboratory of Nuclear Physics and Technology, Guangxi Normal University, Guilin 541004, China
⁵Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC Institutos de Investigación de Paterna, Apartado 22085, 46071 Valencia, Spain

^*Contact author: xiulei.ren@sdu.edu.cn
^†Contact author: haipeng@nnnu.edu.cn
^‡Contact author: liangwh@gxnu.edu.cn
^§Contact author: Oset@ific.uv.es

Phys. Rev. D 114, 074020 – Published 9 October, 2026

DOI: https://doi.org/10.1103/6w2t-tpmv

Abstract

We perform a theoretical study of the $B^{+} \to D^{+} D^{-} K^{+}$ , $B^{0} \to D^{+} D^{-} K^{0}$ and $Λ_{b} \to D^{+} D^{-} Λ$ reactions by looking at the production mechanisms, with special emphasis in the final state interaction of the charmed mesons, which gives rise to the $X (3930)$ , coupling strongly to $D_{s} {\bar{D}}_{s}$ , and another state that we call $X (3700)$ , coupling strongly to $D \bar{D}$ that qualifies as a $D \bar{D}$ bound state. The combined study of all these reactions shows that the final state interaction responsible for the production of these resonances is more important in the $B^{+} \to D^{+} D^{-} K^{+}$ reaction than in the $Λ_{b} \to D^{+} D^{-} Λ$ one. We have taken this into account and shown that normalizing the $D^{+} D^{-}$ mass distributions to the same value at the peak of the $ψ (3770)$ production, the two mass distributions are quite different in a range of 10 MeV above the $D^{+} D^{-}$ threshold, with a value about an order of magnitude bigger for the $B^{+} \to D^{+} D^{-} K^{+}$ reaction than for the $Λ_{b} \to D^{+} D^{-} Λ$ one. The $D^{+} D^{-}$ mass distribution by itself also shows an enhancement of about one order of magnitude in the presence of the $X (3700)$ with respect to a calculation where this resonance is absent. We make a call to measure these magnitudes in the coming LHCb upgrades, which would bring great support to the existence of the bound $D^{+} D^{-}$ state.

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Phys. Rev. D 114, 074020– Published 9 October, 2026

Vol. 114, Iss. 7 — 1 October 2026

Received 19 June 2026
Accepted 3 September 2026

DOI: https://doi.org/10.1103/6w2t-tpmv

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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Search for signals of the $D \bar{D}$ bound state $X (3700)$ from study of the $B^{+} \to D^{+} D^{-} K^{+}$ , $B^{0} \to D^{+} D^{-} K^{0}$ and $Λ_{b} \to D^{+} D^{-} Λ$ reactions

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Search for signals of the DD¯ bound state X(3700) from study of the B+→D+D−K+, B0→D+D−K0 and Λb→D+D−Λ reactions

Abstract

Physics Subject Headings (PhySH)

Article Text

References (57)

Search for signals of the $D \bar{D}$ bound state $X (3700)$ from study of the $B^{+} \to D^{+} D^{-} K^{+}$ , $B^{0} \to D^{+} D^{-} K^{0}$ and $Λ_{b} \to D^{+} D^{-} Λ$ reactions