- Open Access
Strangeonium spectrum with screening effects and interpretation of and observed by BESIII
Phys. Rev. D 112, 036006 – Published 13 August, 2025
DOI: https://doi.org/10.1103/yqxf-5scf
Abstract
Motivated by two new states and observed by BESIII, we have investigated the mass spectrum and the strong decay properties of the strangeonium mesons within the modified Godfrey-Isgur model by considering the screening effects. We have determined the free parameters using the masses and widths of the well-established states , , , , and . According to our results, and could be well explained as and states, respectively. Meanwhile, the possible assignments of , , and as , , and are also discussed. Furthermore, the masses and widths of the , , , , , , and states are also given and compared with various theoretical predictions, which will be helpful for the observations and confirmations of these states in the future.
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References (90)
- Pei-Lian Liu, Shuang-Shi Fang, and Xin-Chou Lou, Strange quarkonium states at BESIII, Chin. Phys. C 39, 082001 (2015).
- Bernhard Ketzer, Boris Grube, and Dmitry Ryabchikov, Light-meson spectroscopy with COMPASS, Prog. Part. Nucl. Phys. 113, 103755 (2020).
- Nora Brambilla, Simon Eidelman, Christoph Hanhart, Alexey Nefediev, Cheng-Ping Shen, Christopher E. Thomas, Antonio Vairo, and Chang-Zheng Yuan, The states: Experimental and theoretical status and perspectives, Phys. Rep. 873, 1 (2020).
- Eef van Beveren and George Rupp, Modern meson spectroscopy: The fundamental role of unitarity, Prog. Part. Nucl. Phys. 117, 103845 (2021).
- Qi Li, Long-Cheng Gui, Ming-Sheng Liu, Qi-Fang Lü, and Xian-Hui Zhong, Mass spectrum and strong decays of strangeonium in a constituent quark model, Chin. Phys. C 45, 023116 (2021).
- S. Godfrey and Nathan Isgur, Mesons in a relativized quark model with chromodynamics, Phys. Rev. D 32, 189 (1985).
- L. Burakovsky and J. Terrance Goldman, Constraint on axial-vector meson mixing angle from nonrelativistic constituent quark model, Phys. Rev. D 56, R1368 (1997).
- Cheng-Qun Pang, Excited states of meson, Phys. Rev. D 99, 074015 (2019).
- Ya Gao, Yateng Zhang, Bo Zheng, Zhen-Hua Zhang, Wenbiao Yan, and Xiaohua Li, Evaluation of the and the mixing angle , arXiv:1911.06967.
- Hai-Yang Cheng, Revisiting axial-vector meson mixing, Phys. Lett. B 707, 116 (2012).
- L. Burakovsky and J. Terrance Goldman, Towards resolution of the enigmas of wave meson spectroscopy, Phys. Rev. D 57, 2879 (1998).
- De-Min Li, Bing Ma, and Hong Yu, Regarding the axial-vector mesons, Eur. Phys. J. A 26, 141 (2005).
- M. Ablikim et al., Study of the decay , Phys. Rev. D 110, 112014 (2024).
- Medina Ablikim et al., Observation and study of the decay , Phys. Rev. D 99, 112008 (2019).
- Medina Ablikim et al., Observation of an axial-vector state in the study of decay, arXiv:2410.05736.
- Lowell S. Brown and William I. Weisberger, Remarks on the static potential in quantum chromodynamics, Phys. Rev. D 20, 3239 (1979).
- E. Eichten and F. Feinberg, Spin dependent forces in QCD, Phys. Rev. D 23, 2724 (1981).
- S. N. Gupta and S. F. Radford, Quark quark and quark–anti-quark potentials, Phys. Rev. D 24, 2309 (1981).
- James T. Pantaleone, S. H. Henry Tye, and Yee Jack Ng, Spin splittings in heavy quarkonia, Phys. Rev. D 33, 777 (1986).
- Olga Lakhina and Eric S. Swanson, A canonical ?, Phys. Lett. B 650, 159 (2007).
- Yu Lu, Muhammad Naeem Anwar, and Bing-Song Zou, Coupled-channel effects for the bottomonium with realistic wave functions, Phys. Rev. D 94, 034021 (2016).
- J. Ferretti, G. Galata, E. Santopinto, and A. Vassallo, Bottomonium self-energies due to the coupling to the meson-meson continuum, Phys. Rev. C 86, 015204 (2012).
- J. Ferretti, G. Galatà, and E. Santopinto, Interpretation of the as a charmonium state plus an extra component due to the coupling to the meson-meson continuum, Phys. Rev. C 88, 015207 (2013).
- Pablo G. Ortega, Jorge Segovia, David R. Entem, and Francisco Fernandez, Molecular components in -wave charmed-strange mesons, Phys. Rev. D 94, 074037 (2016).
- Wei Hao, Yu Lu, and Bing-Song Zou, Coupled channel effects for the charmed-strange mesons, Phys. Rev. D 106, 074014 (2022).
- Jing-Jing Yang, Wei Hao, Xiaoyu Wang, De-Min Li, Yu-Xiao Li, and En Wang, The mass spectrum and strong decay properties of the charmed-strange mesons within Godfrey–Isgur model considering the coupled-channel effects, Eur. Phys. J. C 83, 1098 (2023).
- Wei Hao and Ruilin Zhu, Beauty-charm meson family with coupled channel effects and their strong decays, Chin. Phys. C 48, 123101 (2024).
- Wei Hao, M. Atif Sultan, and En Wang, Spectrum and decay properties of the charmed mesons involving the coupled channel effects, Phys. Rev. D 111, 094024 (2025).
- E. Laermann, F. Langhammer, I. Schmitt, and P. M. Zerwas, The interquark potential: color gauge theory with fermions, Phys. Lett. B 173, 437 (1986).
- K. D. Born, E. Laermann, N. Pirch, T. F. Walsh, and P. M. Zerwas, Hadron properties in lattice QCD with dynamical fermions, Phys. Rev. D 40, 1653 (1989).
- Adi Armoni, Beyond the quenched (or probe brane) approximation in lattice (or holographic) QCD, Phys. Rev. D 78, 065017 (2008).
- Bai-Qing Li, Ce Meng, and Kuang-Ta Chao, Coupled-channel and screening effects in charmonium spectrum, Phys. Rev. D 80, 014012 (2009).
- Wei Hao, Guan-Ying Wang, En Wang, Guan-Nan Li, and De-Min Li, Canonical interpretation of the state within the model, Eur. Phys. J. C 80, 626 (2020).
- Xue-Chao Feng, Wei Hao, and li-Juan Liu, The assignments of the bottom mesons within the screened potential model and model, Int. J. Mod. Phys. E 31, 2250066 (2022).
- Wei Hao, Yu Lu, and En Wang, The assignments of the mesons within the screened potential model and model, Eur. Phys. J. C 83, 520 (2023).
- Qin-Tao Song, Dian-Yong Chen, Xiang Liu, and Takayuki Matsuki, Higher radial and orbital excitations in the charmed meson family, Phys. Rev. D 92, 074011 (2015).
- Qin-Tao Song, Dian-Yong Chen, Xiang Liu, and Takayuki Matsuki, Charmed-strange mesons revisited: Mass spectra and strong decays, Phys. Rev. D 91, 054031 (2015).
- Jun-Zhang Wang, Dian-Yong Chen, Xiang Liu, and Takayuki Matsuki, Constructing family with updated data of charmoniumlike states, Phys. Rev. D 99, 114003 (2019).
- Jun-Zhang Wang, Zhi-Feng Sun, Xiang Liu, and Takayuki Matsuki, Higher bottomonium zoo, Eur. Phys. J. C 78, 915 (2018).
- Ya-Rong Wang, Xiao-Hai Liu, Cheng-Qun Pang, and Hao Chen, New states and and higher light excited mesons, Phys. Rev. D 111, 054005 (2025).
- Zheng-Ya Li, De-Min Li, En Wang, Wen-Cheng Yan, and Qin-Tao Song, Assignments of the , (1900), and in the quark model, Phys. Rev. D 104, 034013 (2021).
- Xue-Chao Feng, Zheng-Ya Li, De-Min Li, Qin-Tao Song, En Wang, and Wen-Cheng Yan, Mass spectra and decay properties of the higher excited mesons, Phys. Rev. D 106, 076012 (2022).
- L. Micu, Decay rates of meson resonances in a quark model, Nucl. Phys. B10, 521 (1969).
- A. Le Yaouanc, L. Oliver, O. Pene, and J. C. Raynal, Naive quark pair creation model of strong interaction vertices, Phys. Rev. D 8, 2223 (1973).
- A. Le Yaouanc, L. Oliver, O. Pene, and J. C. Raynal, Naive quark pair creation model and baryon decays, Phys. Rev. D 9, 1415 (1974).
- De-Min Li and En Wang, Canonical interpretation of the , Eur. Phys. J. C 63, 297 (2009).
- Ting-Ting Pan, Qi-Fang Lü, En Wang, and De-Min Li, Strong decays of the newly observed by the BESIII Collaboration, Phys. Rev. D 94, 054030 (2016).
- Qi-Fang Lü, Ting-Ting Pan, Yan-Yan Wang, En Wang, and De-Min Li, Excited bottom and bottom-strange mesons in the quark model, Phys. Rev. D 94, 074012 (2016).
- Guan-Ying Wang, Shi-Chen Xue, Guan-Nan Li, En Wang, and De-Min Li, Strong decays of the higher isovector scalar mesons, Phys. Rev. D 97, 034030 (2018).
- Shi-Chen Xue, Guan-Ying Wang, Guan-Nan Li, En Wang, and De-Min Li, The possible members of the meson nonet, Eur. Phys. J. C 78, 479 (2018).
- J. Ferretti and E. Santopinto, Higher mass bottomonia, Phys. Rev. D 90, 094022 (2014).
- M. Jacob and G. C. Wick, On the general theory of collisions for particles with spin, Ann. Phys. (N.Y.) 7, 404 (1959).
- Cameron Hayne and Nathan Isgur, Beyond the wave function at the origin: Some momentum dependent effects in the nonrelativistic quark model, Phys. Rev. D 25, 1944 (1982).
- J. Vijande, F. Fernandez, and A. Valcarce, Constituent quark model study of the meson spectra, J. Phys. G 31, 481 (2005).
- Stephen Godfrey, K. Moats, and E. S. Swanson, and meson spectroscopy, Phys. Rev. D 94, 054025 (2016).
- S. Navas et al., Review of particle physics, Phys. Rev. D 110, 030001 (2024).
- Li-Ye Xiao, Xin-Zhen Weng, Xian-Hui Zhong, and Shi-Lin Zhu, A possible explanation of the threshold enhancement in the process , Chin. Phys. C 43, 113105 (2019).
- D. Ebert, R. N. Faustov, and V. O. Galkin, Mass spectra and Regge trajectories of light mesons in the relativistic quark model, Phys. Rev. D 79, 114029 (2009).
- Shin Ishida and Kenji Yamada, Light quark meson spectrum in the covariant oscillator quark model with one gluon exchange effects, Phys. Rev. D 35, 265 (1987).
- L. Bertanza et al., Possible resonances in the and systems, Phys. Rev. Lett. 9, 180 (1962).
- F. Mane, D. Bisello, J. C. Bizot, J. Buon, A. Cordier, and B. Delcourt, Study of in the 1.4-GeV to 2.18-GeV energy range: A new observation of an isoscalar vector meson (1.65-GeV), Phys. Lett. B 112, 178 (1982).
- M. Ablikim et al., Amplitude analysis of the system produced in radiative decays, Phys. Rev. D 98, 072003 (2018).
- M. Albrecht et al., Coupled channel analysis of , and at and of -scattering data, Eur. Phys. J. C 80, 453 (2020).
- A. V. Sarantsev, I. Denisenko, U. Thoma, and E. Klempt, Scalar isoscalar mesons and the scalar glueball from radiative decays, Phys. Lett. B 816, 136227 (2021).
- Medina Ablikim et al., Observation of in the decay, Phys. Rev. D 98, 072005 (2018).
- M. Ablikim et al., Partial wave analysis of , Phys. Rev. D 105, 072002 (2022).
- Sheng-Juan Jiang, S. Sakai, Wei-Hong Liang, and E. Oset, The decay to testing the nature of axial vector meson resonances, Phys. Lett. B 797, 134831 (2019).
- L. Roca, E. Oset, and J. Singh, Low lying axial-vector mesons as dynamically generated resonances, Phys. Rev. D 72, 014002 (2005).
- Shin Ishida, Masuho Oda, Haruhiko Sawazaki, and Kenji Yamada, Is the our first hybrid meson?, Prog. Theor. Phys. 82, 119 (1989).
- Ronald S. Longacre, The meson as a molecule, Phys. Rev. D 42, 874 (1990).
- V. R. Debastiani, F. Aceti, Wei-Hong Liang, and E. Oset, Revising the resonance, Phys. Rev. D 95, 034015 (2017).
- J. Abdallah et al., Measurement of inclusive and production in decays with the DELPHI detector, Phys. Lett. B 569, 129 (2003).
- T. Barnes, N. Black, and P. R. Page, Strong decays of strange quarkonia, Phys. Rev. D 68, 054014 (2003).
- W. Roberts and B. Silvestre-Brac, Meson decays in a quark model, Phys. Rev. D 57, 1694 (1998).
- L. S. Geng and E. Oset, Vector meson-vector meson interaction in a hidden gauge unitary approach, Phys. Rev. D 79, 074009 (2009).
- Lianrong Dai and Eulogio Oset, Tests on the molecular structure of , from and decays, Eur. Phys. J. A 49, 130 (2013).
- Ju-Jun Xie and E. Oset, and decays into and , Phys. Rev. D 90, 094006 (2014).
- H. Nagahiro, L. Roca, E. Oset, and B. S. Zou, Role of meson loops in the , , and decays into , Phys. Rev. D 78, 014012 (2008).
- Luciano M. Abreu, Lianrong Dai, and Eulogio Oset, decay to ,,, , , , and : Role of the -wave for tensor production, Phys. Lett. B 843, 137999 (2023).
- K. Karch et al., Analysis of the final state in photon-photon collisions, Z. Phys. C 54, 33 (1992).
- S. Al-Harran et al., Observation of a enhancement at 1.85-GeV in the reaction at 8.25-GeV/c, Phys. Lett. B 101, 357 (1981).
- D. Aston et al., Spin parity determination of the from interactions at 11-GeV/c, Phys. Lett. B 208, 324 (1988).
- Bernard Aubert et al., A structure at 2175-MeV in observed via initial-state radiation, Phys. Rev. D 74, 091103 (2006).
- Medina Ablikim et al., Measurement of cross sections at center-of-mass energies from 2.00 to 3.08 GeV, Phys. Rev. D 108, 032011 (2023).
- Chen-Guang Zhao, Guan-Ying Wang, Guan-Nan Li, En Wang, and De-Min Li, production in the process , Phys. Rev. D 99, 114014 (2019).
- Yi-Wei Jiang, Wei-Han Tan, Hua-Xing Chen, and Er-Liang Cui, Strong decays of the as a fully strange tetraquark state, Symmetry 16, 1021 (2024).
- Brenda B. Malabarba, K. P. Khemchandani, and A. Martinez Torres, decaying to and ’, Phys. Rev. D 108, 036010 (2023).
- Brenda B. Malabarba, Xiu-Lei Ren, K. P. Khemchandani, and A. Martinez Torres, Partial decay widths of to kaonic resonances, Phys. Rev. D 103, 016018 (2021).
- A. Martinez Torres, K. P. Khemchandani, L. S. Geng, M. Napsuciale, and E. Oset, The as a resonant state of the system, Phys. Rev. D 78, 074031 (2008).
- L. Alvarez-Ruso, J. A. Oller, and J. M. Alarcon, On the -wave scattering and the Y(2175) resonance, Phys. Rev. D 80, 054011 (2009).