Open Access

Dynamically generated $h_{1}$ state by the $K^{} {\bar{K}}^{}$ interaction and its $K_{1} (1270) \bar{K}$ and $b_{1} (1235) π$ decays

Qing-Hua Shen ^1,2,3,*, Li-Sheng Geng ^{4,5,6,7,8,†}, Xiang Liu ^{2,9,10,11,‡}, and Ju-Jun Xie ^1,3,8,§

¹State Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
²School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
³School of Nuclear Sciences and Technology, University of Chinese Academy of Sciences, Beijing 101408, China
⁴School of Physics, Beihang University, Beijing 102206, China
⁵Sino-French Carbon Neutrality Research Center, Ecole Centrale de Pekin/School of General Engineering, Beihang University, Beijing 100191, China
⁶Peng Huanwu Collaborative Center for Research and Education, International Institute for Interdisciplinary and Frontiers, Beihang University, Beijing 100191, China
⁷Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, Beijing 102206, China
⁸Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, Huizhou 516000, China
⁹Lanzhou 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
¹⁰MoE Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, China
¹¹Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000, China

^*Contact author: shenqinghua@impcas.ac.cn
^†Contact author: lisheng.geng@buaa.edu.cn
^‡Contact author: xiangliu@lzu.edu.cn
^§Contact author: xiejujun@impcas.ac.cn

Phys. Rev. D 113, 114013 – Published 8 June, 2026

DOI: https://doi.org/10.1103/7h3x-hjxg

Abstract

We investigate the dynamically generated $h_{1}$ state with spin-parity $J^{P} = 1^{+}$ and a mass around 1790 MeV, arising from the $K^{*} {\bar{K}}^{*}$ interaction within the chiral unitary approach. The partial decay widths into the $K_{1} (1270) \bar{K}$ and $b_{1} (1235) π$ channels are calculated via a triangular-loop mechanism. In this mechanism, the $h_{1}$ state couples to $K^{*} {\bar{K}}^{*}$ , and final-state interactions between $K^{*}$ and ${\bar{K}}^{*}$ proceed through pseudoscalar-meson exchange, leading to the final states $\bar{K}$ (or $π$ ) and $K_{1} (1270)$ [or $b_{1} (1235)$ ]. We also present the invariant-mass distributions of a vector meson and a pseudoscalar meson originating from the decays of $K_{1} (1270)$ or $b_{1} (1235)$ , along with the corresponding decay widths. Our results show that these decay widths are all of the order of a few MeV. We hope that future experiments can test the predictions presented here, thereby helping to identify this $h_{1}$ state.

Physics Subject Headings (PhySH)

Article Text

References (66)

X. Liu, Chin. Sci. Bull. 59, 3815 (2014).
A. Hosaka, T. Iijima, K. Miyabayashi, Y. Sakai, and S. Yasui, Prog. Theor. Exp. Phys. 2016, 062C01 (2016).
H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Phys. Rep. 639, 1 (2016).
R. F. Lebed, R. E. Mitchell, and E. S. Swanson, Prog. Part. Nucl. Phys. 93, 143 (2017).
F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Rev. Mod. Phys. 90, 015004 (2018); 94, 029901(E) (2022).
S. L. Olsen, T. Skwarnicki, and D. Zieminska, Rev. Mod. Phys. 90, 015003 (2018).
N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. Shen, C. E. Thomas, A. Vairo, and C.-Z. Yuan, Phys. Rep. 873, 1 (2020).
J.-M. Richard, Few-Body Syst. 57, 1185 (2016).
L. Meng, B. Wang, G.-J. Wang, and S.-L. Zhu, Phys. Rep. 1019, 1 (2023).
H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu, and S.-L. Zhu, Rep. Prog. Phys. 86, 026201 (2023).
M.-Z. Liu, Y.-W. Pan, Z.-W. Liu, T.-W. Wu, J.-X. Lu, and L.-S. Geng, Phys. Rep. 1108, 1 (2025).
Y.-R. Liu, H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Prog. Part. Nucl. Phys. 107, 237 (2019).
J. A. Oller and E. Oset, Nucl. Phys. A620, 438 (1997); A652, 407(E) (1999).
E. Oset and A. Ramos, Nucl. Phys. A635, 99 (1998).
J. A. Oller, E. Oset, and J. R. Pelaez, Phys. Rev. D 59, 074001 (1999); 60, 099906(E) (1999); 75, 099903(E) (2007).
T. Inoue, E. Oset, and M. J. Vicente Vacas, Phys. Rev. C 65, 035204 (2002).
D. Jido, J. A. Oller, E. Oset, A. Ramos, and U. G. Meissner, Nucl. Phys. A725, 181 (2003).
L. Roca, E. Oset, and J. Singh, Phys. Rev. D 72, 014002 (2005).
F.-K. Guo, P.-N. Shen, H.-C. Chiang, R.-G. Ping, and B.-S. Zou, Phys. Lett. B 641, 278 (2006).
L. Roca, S. Sarkar, V. K. Magas, and E. Oset, Phys. Rev. C 73, 045208 (2006).
F.-K. Guo, P.-N. Shen, and H.-C. Chiang, Phys. Lett. B 647, 133 (2007).
L. S. Geng, E. Oset, L. Roca, and J. A. Oller, Phys. Rev. D 75, 014017 (2007).
D. Gamermann, E. Oset, D. Strottman, and M. J. Vicente Vacas, Phys. Rev. D 76, 074016 (2007).
D. Gamermann and E. Oset, Eur. Phys. J. A 33, 119 (2007).
R. Molina, D. Nicmorus, and E. Oset, Phys. Rev. D 78, 114018 (2008).
L. S. Geng and E. Oset, Phys. Rev. D 79, 074009 (2009).
S. Sarkar, B.-X. Sun, E. Oset, and M. J. Vicente Vacas, Eur. Phys. J. A 44, 431 (2010).
C. W. Xiao and E. Oset, Eur. Phys. J. A 49, 139 (2013).
W. H. Liang, T. Uchino, C. W. Xiao, and E. Oset, Eur. Phys. J. A 51, 16 (2015).
Y. Zhou, X.-L. Ren, H.-X. Chen, and L.-S. Geng, Phys. Rev. D 90, 014020 (2014).
J. M. Dias, V. R. Debastiani, J. J. Xie, and E. Oset, Phys. Rev. D 98, 094017 (2018).
Q.-X. Yu, J. M. Dias, W.-H. Liang, and E. Oset, Eur. Phys. J. C 79, 1025 (2019).
Z.-Y. Wang and Z.-F. Sun, Eur. Phys. J. C 83, 1106 (2023).
E. Oset and L. Roca, Eur. Phys. J. C 82, 882 (2022); 82, 1014(E) (2022).
Z.-F. Sun, J.-J. Xie, and E. Oset, Phys. Rev. D 97, 094031 (2018).
S. Sakai, L. Roca, and E. Oset, Phys. Rev. D 96, 054023 (2017).
J. M. Dias, F. Aceti, and E. Oset, Phys. Rev. D 91, 076001 (2015).
R. Molina, T. Branz, and E. Oset, Phys. Rev. D 82, 014010 (2010).
R. Molina and E. Oset, Phys. Rev. D 80, 114013 (2009).
E. Oset, A. Ramos, and C. Bennhold, Phys. Lett. B 527, 99 (2002); 530, 260(E) (2002).
S. Sarkar, E. Oset, and M. J. Vicente Vacas, Nucl. Phys. A750, 294 (2005); A780, 90(E) (2006).
M. Ablikim et al. (BES Collaboration), Phys. Lett. B 685, 27 (2010).
J.-J. Xie, M. Albaladejo, and E. Oset, Phys. Lett. B 728, 319 (2014).
X.-L. Ren, L.-S. Geng, E. Oset, and J. Meng, Eur. Phys. J. A 50, 133 (2014).
H. Nagahiro, L. Roca, A. Hosaka, and E. Oset, Phys. Rev. D 79, 014015 (2009).
X. Zhang and J.-J. Xie, Commun. Theor. Phys. 70, 060 (2018).
H. Albrecht et al. (ARGUS Collaboration), Z. Phys. C 58, 61 (1993).
J.-J. Xie, G. Li, and X.-H. Liu, Chin. Phys. C 44, 114104 (2020).
J.-M. Xie, J.-X. Lu, L.-S. Geng, and B.-S. Zou, Phys. Rev. D 108, L111502 (2023).
J.-M. Xie, Z.-W. Liu, J.-X. Lu, H. Liang, R. Molina, and L.-S. Geng, Phys. Rev. D 113, 074002 (2026).
L. Roca, A. Hosaka, and E. Oset, Phys. Lett. B 658, 17 (2007).
F. Aceti, J. M. Dias, and E. Oset, Eur. Phys. J. A 51, 48 (2015).
F. Aceti, J.-J. Xie, and E. Oset, Phys. Lett. B 750, 609 (2015).
J.-J. Xie, Phys. Rev. C 92, 065203 (2015).
R. Molina, M. Doering, W. H. Liang, and E. Oset, Eur. Phys. J. C 81, 782 (2021).
Q.-H. Shen, L.-S. Geng, and J.-J. Xie, Eur. Phys. J. A 61, 42 (2025).
D. Gülmez, U. G. Meißner, and J. A. Oller, Eur. Phys. J. C 77, 460 (2017).
Z.-L. Wang and B.-S. Zou, Phys. Rev. D 104, 114001 (2021).
Z.-L. Wang and B.-S. Zou, Eur. Phys. J. C 82, 509 (2022).
A. I. Titov, B. Kampfer, and B. L. Reznik, Eur. Phys. J. A 7, 543 (2000).
A. I. Titov, B. Kampfer, and B. L. Reznik, Phys. Rev. C 65, 065202 (2002).
L. R. Dai, L. Roca, and E. Oset, Eur. Phys. J. C 80, 673 (2020).
P.-L. Lü and J. He, Eur. Phys. J. A 52, 359 (2016).
L. R. Dai, L. Roca, and E. Oset, Phys. Rev. D 99, 096003 (2019).
C.-H. Zeng, J.-X. Lu, E. Wang, J.-J. Xie, and L.-S. Geng, Phys. Rev. D 102, 076009 (2020).
M. Bayar, F. Aceti, F.-K. Guo, and E. Oset, Phys. Rev. D 94, 074039 (2016).

Phys. Rev. D 113, 114013– Published 8 June, 2026

Vol. 113, Iss. 11 — 1 June 2026

Received 6 February 2026
Accepted 23 April 2026

DOI: https://doi.org/10.1103/7h3x-hjxg

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

Dynamically generated $h_{1}$ state by the $K^{} {\bar{K}}^{}$ interaction and its $K_{1} (1270) \bar{K}$ and $b_{1} (1235) π$ decays

Abstract

Physics Subject Headings (PhySH)

Article Text

References (66)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Dynamically generated h1 state by the K*K¯* interaction and its K1(1270)K¯ and b1(1235)π decays

Abstract

Physics Subject Headings (PhySH)

Article Text

References (66)

Dynamically generated $h_{1}$ state by the $K^{} {\bar{K}}^{}$ interaction and its $K_{1} (1270) \bar{K}$ and $b_{1} (1235) π$ decays