Open Access

$Z_{c s}^{+}$ production in $B^{+}$ decays

Zhuo Yu^1,*, Qi Wu ^2,†, and Dian-Yong Chen ^1,3,‡

¹School of Physics, Southeast University, Nanjing 210094, China
²Institute of Particle and Nuclear Physics, Henan Normal University, Xinxiang 453007, China
³Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou 730000, China

^*Contact author: zhuo@seu.edu.cn
^†Contact author: wuqi@htu.edu.cn
^‡Contact author: chendy@seu.edu.cn

Phys. Rev. D 112, 094054 – Published 25 November, 2025

DOI: https://doi.org/10.1103/fjsv-fxpm

Abstract

In the present work, we study the $Z_{c s}^{+}$ exotic state production in the $B^{+}$ meson decays through the meson loop mechanism, where the $B^{+}$ meson decays into an anticharmed meson and a charmed-strange meson pair, and consequently couples to $Z_{c s}$ and a light meson ( $ϕ, ρ^{0}, ω, η, η^{'}$ , and $π^{0}$ ) via exchanging a proper charmed or charmed-strange meson. Using the effective Lagrangian approach, we estimate the branching fractions of different channels, finding them to be of the order of $10^{- 4}$ , and their ratios are almost independent of the model parameter. The fit fractions of $Z_{c s}^{+}$ in different $B^{+}$ decay processes are also estimated, and we propose searching for $Z_{c s}^{+}$ in the $B^{+} \to J / ψ K^{+} η^{'}$ process, which should be accessible to both Belle II and LHCb Collaborations.

Physics Subject Headings (PhySH)

Article Text

References (90)

S. K. Choi et al., Observation of a narrow charmonium-like state in exclusive $B^{\pm} \to K^{\pm} π^{+} π^{-} J / ψ$ decays, Phys. Rev. Lett. 91, 262001 (2003).
Hua-Xing Chen, Wei Chen, Xiang Liu, and Shi-Lin Zhu, The hidden-charm pentaquark and tetraquark states, Phys. Rep. 639, 1 (2016).
Atsushi Hosaka, Toru Iijima, Kenkichi Miyabayashi, Yoshihide Sakai, and Shigehiro Yasui, Exotic hadrons with heavy flavors: X, Y, Z, and related states, Prog. Theor. Exp. Phys. 2016, 062C01 (2016).
Richard F. Lebed, Ryan E. Mitchell, and Eric S. Swanson, Heavy-quark QCD exotica, Prog. Part. Nucl. Phys. 93, 143 (2017).
A. Esposito, A. Pilloni, and A. D. Polosa, Multiquark resonances, Phys. Rep. 668, 1 (2017).
Feng-Kun Guo, Christoph Hanhart, Ulf-G. Meißner, Qian Wang, Qiang Zhao, and Bing-Song Zou, Hadronic molecules, Rev. Mod. Phys. 90, 015004 (2018); 94, 029901(E) (2022).
Ahmed Ali, Jens Sören Lange, and Sheldon Stone, Exotics: Heavy pentaquarks and tetraquarks, Prog. Part. Nucl. Phys. 97, 123 (2017).
Stephen Lars Olsen, Tomasz Skwarnicki, and Daria Zieminska, Nonstandard heavy mesons and baryons: Experimental evidence, Rev. Mod. Phys. 90, 015003 (2018).
Marek Karliner, Jonathan L. Rosner, and Tomasz Skwarnicki, Multiquark states, Annu. Rev. Nucl. Part. Sci. 68, 17 (2018).
Chang-Zheng Yuan, The XYZ states revisited, Int. J. Mod. Phys. A 33, 1830018 (2018).
Yubing Dong, Amand Faessler, and Valery E. Lyubovitskij, Description of heavy exotic resonances as molecular states using phenomenological Lagrangians, Prog. Part. Nucl. Phys. 94, 282 (2017).
Yan-Rui Liu, Hua-Xing Chen, Wei Chen, Xiang Liu, and Shi-Lin Zhu, Pentaquark and tetraquark states, Prog. Part. Nucl. Phys. 107, 237 (2019).
Ming-Zhu Liu, Ya-Wen Pan, Zhi-Wei Liu, Tian-Wei Wu, Jun-Xu Lu, and Li-Sheng Geng, Can $Z_{c s} (3985)$ be a molecular state of ${\bar{D}}_{s}^{*} D$ and ${\bar{D}}_{s} D^{*}$ ? arXiv:2011.08720.
Zhi-Gang Wang, Review of the QCD sum rules for exotic states, Front. Phys. (Beijing) 21, 016300 (2026).
S. K. Choi et al., Observation of a resonance-like structure in the $p i^{\pm} ψ^{'}$ mass distribution in exclusive $B \to K π^{\pm} ψ^{'}$ decays, Phys. Rev. Lett. 100, 142001 (2008).
R. Mizuk et al., Dalitz analysis of $B \to K π^{+} ψ^{'}$ decays and the $Z (4430)^{+}$ , Phys. Rev. D 80, 031104 (2009).
K. Chilikin et al., Experimental constraints on the spin and parity of the $Z (4430)^{+}$ , Phys. Rev. D 88, 074026 (2013).
Roel Aaij et al., Observation of the resonant character of the $Z (4430)^{-}$ state, Phys. Rev. Lett. 112, 222002 (2014).
R. Mizuk et al., Observation of two resonance-like structures in the $π^{+} χ_{c 1}$ mass distribution in exclusive ${\bar{B}}_{0} \to K^{-} π^{+} χ_{c 1}$ decays, Phys. Rev. D 78, 072004 (2008).
M. Ablikim et al., Observation of a charged charmoniumlike structure in $e^{+} e^{-} \to π^{+} π^{-} J / ψ$ at $\sqrt{s} = 4.26 GeV$ , Phys. Rev. Lett. 110, 252001 (2013).
Z. Q. Liu et al., Study of $e^{+} e^{-} \to π^{+} π^{-} J / ψ$ and observation of a charged charmoniumlike state at Belle, Phys. Rev. Lett. 110, 252002 (2013); 111, 019901(E) (2013).
K. Chilikin et al., Observation of a new charged charmoniumlike state in ${\bar{B}}^{0} \to J / ψ K^{-} π^{+}$ decays, Phys. Rev. D 90, 112009 (2014).
Roel Aaij et al., Evidence for an $η_{c} (1 S) π^{-}$ resonance in $B^{0} \to η_{c} (1 S) K^{+} π^{-}$ decays, Eur. Phys. J. C 78, 1019 (2018).
M. Ablikim et al., Observation of a charged charmoniumlike structure $Z_{c} (4020)$ and search for the $Z_{c} (3900)$ in $e^{+} e^{-} \to π^{+} π^{-} h_{c}$ , Phys. Rev. Lett. 111, 242001 (2013).
T. Xiao, S. Dobbs, A. Tomaradze, and Kamal K. Seth, Observation of the charged hadron $Z_{c}^{\pm} (3900)$ and evidence for the neutral $Z_{c}^{0} (3900)$ in $e^{+} e^{-} \to π π J / ψ$ at $\sqrt{s} = 4170 MeV$ , Phys. Lett. B 727, 366 (2013).
M. Ablikim et al., Observation of a charged $(D {\bar{D}}^{*})^{\pm}$ mass peak in $e^{+} e^{-} \to π D {\bar{D}}^{*}$ at $\sqrt{s} = 4.26 GeV$ , Phys. Rev. Lett. 112, 022001 (2014).
M. Ablikim et al., Observation of a charged charmoniumlike structure in $e^{+} e^{-} \to (D^{*} {\bar{D}}^{*})^{\pm} π^{\mp}$ at $\sqrt{s} = 4.26 GeV$ , Phys. Rev. Lett. 112, 132001 (2014).
Zhi-Feng Sun, Zhi-Gang Luo, Jun He, Xiang Liu, and Shi-Lin Zhu, A note on the $B * \bar{B}, B * \bar{B} *, D * \bar{D}, D * \bar{D} *$ , molecular states, Chin. Phys. C 36, 194 (2012).
Jun He, Xiang Liu, Zhi-Feng Sun, and Shi-Lin Zhu, $Z_{c} (4025)$ as the hadronic molecule with hidden charm, Eur. Phys. J. C 73, 2635 (2013).
Wei Chen, T. G. Steele, Meng-Lin Du, and Shi-Lin Zhu, $D^{*} {\bar{D}}^{*}$ molecule interpretation of $Z_{c} (4025)$ , Eur. Phys. J. C 74, 2773 (2014).
Yubing Dong, Amand Faessler, Thomas Gutsche, and Valery E. Lyubovitskij, Strong decays of molecular states $Z_{c}^{+}$ and $Z_{c}^{' +}$ , Phys. Rev. D 88, 014030 (2013).
Qian Wang, Christoph Hanhart, and Qiang Zhao, Decoding the riddle of $Y (4260)$ and $Z_{c} (3900)$ , Phys. Rev. Lett. 111, 132003 (2013).
Gang Li, Hidden-charmonium decays of $Z_{c} (3900)$ and $Z_{c} (4025)$ in intermediate meson loops model, Eur. Phys. J. C 73, 2621 (2013).
Gang Li, Xiao Hai Liu, and Zhu Zhou, More hidden heavy quarkonium molecules and their discovery decay modes, Phys. Rev. D 90, 054006 (2014).
Cheng-Jian Xiao, Dian-Yong Chen, Yu-Bing Dong, Wei Zuo, and Takayuki Matsuki, Understanding the $η_{c} ρ$ decay mode of $Z_{c}^{(')}$ via the triangle loop mechanism, Phys. Rev. D 99, 074003 (2019).
Dian-Yong Chen, Yu-Bing Dong, Ming-Tao Li, and Wen-Ling Wang, Pionic transition from $Y (4260)$ to $Z_{c} (3900)$ in a hadronic molecular scenario, Eur. Phys. J. A 52, 310 (2016).
Dian-Yong Chen and Yu-Bing Dong, Radiative decays of the neutral $Z_{c} (3900)$ , Phys. Rev. D 93, 014003 (2016).
L. Maiani, V. Riquer, F. Piccinini, and A. D. Polosa, Four quark interpretation of $Y (4260)$ , Phys. Rev. D 72, 031502 (2005).
M. Nielsen, F. S. Navarra, and M. E. Bracco, Investigating the tetraquark structure of the new mesons, Braz. J. Phys. 37, 56 (2007).
Stanislav Dubnicka, Anna Z. Dubnickova, Mikhail A. Ivanov, and Juergen G. Korner, Quark model description of the tetraquark state $X (3872)$ in a relativistic constituent quark model with infrared confinement, Phys. Rev. D 81, 114007 (2010).
Chengrong Deng, Jialun Ping, and Fan Wang, Interpreting $Z_{c} (3900)$ and $Z_{c} (4025) / Z_{c} (4020)$ as charged tetraquark states, Phys. Rev. D 90, 054009 (2014).
Chengrong Deng, Jialun Ping, Hongxia Huang, and Fan Wang, Systematic study of $Z_{c}^{+}$ family from a multiquark color flux-tube model, Phys. Rev. D 92, 034027 (2015).
Stanley J. Brodsky, Dae Sung Hwang, and Richard F. Lebed, Dynamical picture for the formation and decay of the exotic $XYZ$ mesons, Phys. Rev. Lett. 113, 112001 (2014).
Richard F. Lebed, Spectroscopy of exotic hadrons formed from dynamical diquarks, Phys. Rev. D 96, 116003 (2017).
Dian-Yong Chen, Xiang Liu, and Takayuki Matsuki, Reproducing the $Z_{c} (3900)$ structure through the initial-single-pion-emission mechanism, Phys. Rev. D 88, 036008 (2013).
Dian-Yong Chen, Xiang Liu, and Takayuki Matsuki, Novel charged charmoniumlike structures in the hidden-charm dipion decays of $Y (4360)$ , Phys. Rev. D 88, 014034 (2013).
Xiao Wang, Yuan Sun, Dian-Yong Chen, Xiang Liu, and Takayuki Matsuki, Simulating the charged charmoniumlike structure $Z_{c} (4025)$ , Eur. Phys. J. C 74, 2761 (2014).
Dian-Yong Chen, Xiang Liu, and Takayuki Matsuki, Interpretation of $Z_{b} (10610)$ and $Z_{b} (10650)$ in the ISPE mechanism and the charmonium counterpart, Chin. Phys. C 38, 053102 (2014).
D. Ebert, R. N. Faustov, and V. O. Galkin, Excited heavy tetraquarks with hidden charm, Eur. Phys. J. C 58, 399 (2008).
J. Ferretti and E. Santopinto, Hidden-charm and bottom tetra- and pentaquarks with strangeness in the hadro-quarkonium and compact tetraquark models, J. High Energy Phys. 04 (2020) 119.
Su Houng Lee, Marina Nielsen, and Ulrich Wiedner, $D_{s} D^{*}$ molecule as an axial meson, J. Korean Phys. Soc. 55, 424 (2009).
Jorgivan M. Dias, Xiang Liu, and Marina Nielsen, Predicition for the decay width of a charged state near the $D_{s} {\bar{D}}^{*} / D_{s}^{*} \bar{D}$ threshold, Phys. Rev. D 88, 096014 (2013).
Dian-Yong Chen, Xiang Liu, and Takayuki Matsuki, Predictions of charged charmoniumlike structures with hidden-charm and open-strange channels, Phys. Rev. Lett. 110, 232001 (2013).
Medina Ablikim et al., Observation of a near-threshold structure in the $K^{+}$ recoil-mass spectra in $e^{+} e^{-} \to K^{+} (D_{s}^{-} D^{* 0} + D_{s}^{* -} D^{0}$ ), Phys. Rev. Lett. 126, 102001 (2021).
Roel Aaij et al., Observation of new resonances decaying to $J / ψ K^{+} +$ and $J / ψ ϕ$ , Phys. Rev. Lett. 127, 082001 (2021).
Zhi Yang, Xu Cao, Feng-Kun Guo, Juan Nieves, and Manuel Pavon Valderrama, Strange molecular partners of the $Z_{c} (3900)$ and $Z_{c} (4020)$ , Phys. Rev. D 103, 074029 (2021).
Pablo G. Ortega, David R. Entem, and F. Fernandez, The strange partner of the $Z_{c}$ structures in a coupled-channels model, Phys. Lett. B 818, 136382 (2021).
Qi Wu, Dian-Yong Chen, Wen-Hua Qin, and Gang Li, Production of $Z_{c s}$ in $B$ and $B_{s}$ decays, Eur. Phys. J. C 82, 520 (2022).
Qi-Nan Wang, Wei Chen, and Hua-Xing Chen, Exotic molecular states and tetraquark states with $J^{P} = 0^{+}, 1^{+}, 2^{+}$ , Chin. Phys. C 45, 093102 (2021).
U. Özdem and K. Azizi, Magnetic dipole moment of the $Z_{c s} (3985)$ state: Diquark–antidiquark and molecular pictures, Eur. Phys. J. Plus 136, 968 (2021).
Lu Meng, Bo Wang, and Shi-Lin Zhu, $Z_{c s} (3985)^{-}$ as the $U$ -spin partner of $Z_{c} (3900)^{-}$ and implication of other states in the ${SU (3)}_{F}$ symmetry and heavy quark symmetry, Phys. Rev. D 102, 111502 (2020).
Zhi-Feng Sun and Chu-Wen Xiao, Explanation of the newly obseaved $Z_{c s}^{-} (3985)$ as a $D_{s}^{(*) -} D^{(*) 0}$ molecular state, arXiv:2011.09404.
Bo Wang, Lu Meng, and Shi-Lin Zhu, Decoding the nature of $Z_{c s} (3985)$ and establishing the spectrum of charged heavy quarkoniumlike states in chiral effective field theory, Phys. Rev. D 103, L021501 (2021).
Xiang-Kun Dong, Feng-Kun Guo, and Bing-Song Zou, Explaining the many threshold structures in the heavy-quark hadron spectrum, Phys. Rev. Lett. 126, 152001 (2021).
Yong-Jiang Xu, Yong-Lu Liu, Chun-Yu Cui, and Ming-Qiu Huang, ${\bar{D}}_{s}^{(*)} D^{(*)}$ molecular state with $J^{P} = 1^{+}$ , Phys. Rev. D 104, 094028 (2021).
Mao-Jun Yan, Fang-Zheng Peng, Mario Sánchez Sánchez, and Manuel Pavon Valderrama, Axial meson exchange and the $Z_{c} (3900)$ and $Z_{c s} (3985)$ resonances as heavy hadron molecules, Phys. Rev. D 104, 114025 (2021).
Bing-Dong Wan and Cong-Feng Qiao, About the exotic structure of $Z_{c s}$ , Nucl. Phys. B968, 115450 (2021).
Zhi-Gang Wang, Analysis of $Z_{c s} (3985)$ as the axialvector tetraquark state, Chin. Phys. C 45, 073107 (2021).
Xin Jin, Yuheng Wu, Xuejie Liu, Hongxia Huang, Jialun Ping, and Bin Zhong, Strange hidden-charm tetraquarks in constituent quark model, Eur. Phys. J. C 81, 1108 (2021).
Jesse F. Giron, Richard F. Lebed, and Steven R. Martinez, Spectrum of hidden-charm, open-strange exotics in the dynamical diquark model, Phys. Rev. D 104, 054001 (2021).
Gang Yang, Jialun Ping, and Jorge Segovia, Hidden-charm tetraquarks with strangeness in the chiral quark model, Phys. Rev. D 104, 094035 (2021).
Jun-Zhang Wang, Qin-Song Zhou, Xiang Liu, and Takayuki Matsuki, Toward charged $Z_{c s} (3985)$ structure under a reflection mechanism, Eur. Phys. J. C 81, 51 (2021).
Natsumi Ikeno, Raquel Molina, and Eulogio Oset, The $Z_{c s} (3985)$ as a threshold effect from the ${\bar{D}}_{s}^{*} D + {\bar{D}}_{s} D^{*}$ interaction, Phys. Lett. B 814, 136120 (2021).
Rui Chen and Qi Huang, $Z_{c s} (3985)^{-}$ : A strange hidden-charm tetraquark resonance or not? Phys. Rev. D 103, 034008 (2021).
R. L. Workman et al., Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
Qi Wu and Dian-Yong Chen, Exploration of the hidden charm decays of $Z_{c s} (3985)^{-}$ , Phys. Rev. D 104, 074011 (2021).
Hai-Yang Cheng, Chun-Khiang Chua, and Chien-Wen Hwang, Covariant light front approach for $s$ wave and $p$ wave mesons: Its application to decay constants and form-factors, Phys. Rev. D 69, 074025 (2004).
Nakul R. Soni, Aidos Issadykov, Akshay N. Gadaria, Zhomart Tyulemissov, Janaki J. Patel, and Jignesh N. Pandya, Form factors and branching fraction calculations for $B_{s} \to D_{s}^{(*)} ℓ^{+} ν_{ℓ}$ in view of LHCb observation, Eur. Phys. J. Plus 138, 163 (2023).
Manfred Bauer, B. Stech, and M. Wirbel, Exclusive nonleptonic decays of $D$ , $D_{s}$ , and $B$ mesons, Z. Phys. C 34, 103 (1987).
P. A. Zyla et al., Review of particle physics, Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
Ahmed Ali, G. Kramer, and Cai-Dian Lu, Experimental tests of factorization in charmless nonleptonic two-body $B$ decays, Phys. Rev. D 58, 094009 (1998).
Mikhail A. Ivanov, Jurgen G. Korner, and Pietro Santorelli, Exclusive semileptonic and nonleptonic decays of the $B_{c}$ meson, Phys. Rev. D 73, 054024 (2006).
D. Coffman et al., Measurements of $J / ψ$ decays into a vector and a pseudoscalar meson, Phys. Rev. D 38, 2695 (1988); 40, 3788(E) (1989).
J. Jousset et al., The $J / ψ \to vector + pseudoscalar$ decays and the $η$ , $η^{'}$ quark content, Phys. Rev. D 41, 1389 (1990).
Hai-Yang Cheng, Chun-Khiang Chua, and Amarjit Soni, Final state interactions in hadronic $B$ decays, Phys. Rev. D 71, 014030 (2005).
S. Aoki et al., FLAG review 2019: Flavour Lattice Averaging Group (FLAG), Eur. Phys. J. C 80, 113 (2020).
Dae Sung Hwang and Do-Won Kim, Decay constants of ${D *}_{sJ} (2317)$ and $D_{sJ} (2460)$ , Phys. Lett. B 606, 116 (2005).
Claudia Isola, Massimo Ladisa, Giuseppe Nardulli, and Pietro Santorelli, Charming penguins in $B \to K^{*} π, K (ρ, ω, ϕ)$ decays, Phys. Rev. D 68, 114001 (2003).
Adam F. Falk and Michael E. Luke, Strong decays of excited heavy mesons in chiral perturbation theory, Phys. Lett. B 292, 119 (1992).
R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, Raoul Gatto, F. Feruglio, and G. Nardulli, Phenomenology of heavy meson chiral Lagrangians, Phys. Rep. 281, 145 (1997).

Phys. Rev. D 112, 094054– Published 25 November, 2025

Vol. 112, Iss. 9 — 1 November 2025

Received 11 June 2025
Accepted 6 November 2025

DOI: https://doi.org/10.1103/fjsv-fxpm

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.

Published by the American Physical Society

Physical Review D

Reuse & Permissions

Export citation

Export citation

$Z_{c s}^{+}$ production in $B^{+}$ decays

Abstract

Physics Subject Headings (PhySH)

Article Text

References (90)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Zcs+ production in B+ decays

Abstract

Physics Subject Headings (PhySH)

Article Text

References (90)

$Z_{c s}^{+}$ production in $B^{+}$ decays