- Open Access
Electromagnetic properties of the , , and their bottom partners in a molecular configuration
Phys. Rev. D 112, 114013 – Published 4 December, 2025
DOI: https://doi.org/10.1103/y77p-ch1k
Abstract
We investigate the electromagnetic properties of the axial-vector molecular states , , , and , which are used to model the charmed states , , and their bottom partners with quantum numbers . To our knowledge, this presents the first comprehensive calculation of the magnetic and quadrupole moments for these specific molecular configurations. Employing the QCD light-cone sum rule method with molecular-type interpolating currents, we compute these moments and perform a detailed flavor decomposition to reveal the internal distribution of the electromagnetic charge and spin. Our results demonstrate that the light up and down quarks dominate the electromagnetic response, with negligible contributions from the heavy quarks. The and states exhibit negative quadrupole moments and slightly oblate charge distributions, whereas the and states possess positive quadrupole moments and prolate distributions, with significant contributions from the strange quark. The predicted moments provide benchmarks for lattice QCD calculations and are testable through their influence on radiative transitions and photo- and electroproduction observables at high-luminosity facilities, offering crucial insights into the internal structure and nature of these axial-vector states.
Physics Subject Headings (PhySH)
Article Text
References (96)
- B. Aubert et al., Observation of a narrow meson decaying to at a mass of , Phys. Rev. Lett. 90, 242001 (2003).
- D. Besson et al., Observation of a narrow resonance of mass decaying to and confirmation of the state, Phys. Rev. D 68, 032002 (2003); 75, 119908(E) (2007).
- P. Krokovny et al., Observation of the and in B decays, Phys. Rev. Lett. 91, 262002 (2003).
- B. Aubert et al., Study of decays, Phys. Rev. Lett. 93, 181801 (2004).
- B. Aubert et al., A study of the and mesons in inclusive c anti-c production near , Phys. Rev. D 74, 032007 (2006).
- H. Albrecht et al., Observation of a new charmed—Strange meson, Phys. Lett. B 230, 162 (1989).
- Y. Mikami et al., Measurements of the resonance properties, Phys. Rev. Lett. 92, 012002 (2004).
- B. Aubert et al., Measurement of the and + properties in production, in 32nd International Conference on High Energy Physics (2004).
- B. Aubert et al., Observation of a narrow meson decaying to at a mass of 2.458-, Phys. Rev. D 69, 031101 (2004).
- E. K. Akhmedov and M. Frigerio, Duality in left-right symmetric Seesaw mechanism, Phys. Rev. Lett. 96, 061802 (2006).
- M. Nielsen, R. D. Matheus, F. S. Navarra, M. E. Bracco, and A. Lozea, Diquark-antidiquark with open charm in QCD sum rules, Nucl. Phys. B, Proc. Suppl. 161, 193 (2006).
- Z.-G. Wang and S.-L. Wan, as a tetraquark state with QCD sum rules in heavy quark limit, Nucl. Phys. A778, 22 (2006).
- Y.-Q. Chen and X.-Q. Li, A Comprehensive four-quark interpretation of , and , Phys. Rev. Lett. 93, 232001 (2004).
- V. Dmitrasinovic, mass difference as evidence for tetraquarks, Phys. Rev. Lett. 94, 162002 (2005).
- H.-Y. Cheng and W.-S. Hou, B decays as spectroscope for charmed four quark states, Phys. Lett. B 566, 193 (2003).
- K. Terasaki, BABAR resonance as a new window of hadron physics, Phys. Rev. D 68, 011501 (2003).
- V. Dmitrasinovic, and : Tetraquarks bound by the t Hooft instanton-induced interaction?, Phys. Rev. D 70, 096011 (2004).
- H. Kim and Y. Oh, as a four-quark state in QCD sum rules, Phys. Rev. D 72, 074012 (2005).
- J.-R. Zhang, Revisiting as a tetraquark state from QCD sum rules, Phys. Lett. B 789, 432 (2019).
- E. van Beveren and G. Rupp, Observed and tentative as the charmed cousins of the light scalar nonet, Phys. Rev. Lett. 91, 012003 (2003).
- L. Liu, K. Orginos, F.-K. Guo, C. Hanhart, and U.-G. Meissner, Interactions of charmed mesons with light pseudoscalar mesons from lattice QCD and implications on the nature of the , Phys. Rev. D 87, 014508 (2013).
- T. Barnes, F. E. Close, and H. J. Lipkin, Implications of a DK molecule at 2.32-GeV, Phys. Rev. D 68, 054006 (2003).
- L. Roca, J. M. Dias, and E. Oset, The decay from a molecular perspective, Eur. Phys. J. C 85, 808 (2025).
- S.-Y. Kong, J.-T. Zhu, D. Song, and J. He, Heavy-strange meson molecules and possible candidates , , and , Phys. Rev. D 104, 094012 (2021).
- E. E. Kolomeitsev and M. F. M. Lutz, On heavy light meson resonances and chiral symmetry, Phys. Lett. B 582, 39 (2004).
- A. P. Szczepaniak, Description of the resonance as the atom, Phys. Lett. B 567, 23 (2003).
- J. Hofmann and M. F. M. Lutz, Open charm meson resonances with negative strangeness, Nucl. Phys. A733, 142 (2004).
- D. Gamermann, E. Oset, D. Strottman, and M. J. Vicente Vacas, Dynamically generated open and hidden charm meson systems, Phys. Rev. D 76, 074016 (2007).
- J. M. Flynn and J. Nieves, Elastic -wave , , and scattering from lattice calculations of scalar form-factors in semileptonic decays, Phys. Rev. D 75, 074024 (2007).
- A. Faessler, T. Gutsche, V. E. Lyubovitskij, and Y.-L. Ma, Strong and radiative decays of the meson in the -molecule picture, Phys. Rev. D 76, 014005 (2007).
- F.-K. Guo, C. Hanhart, and U.-G. Meissner, Interactions between heavy mesons and Goldstone bosons from chiral dynamics, Eur. Phys. J. A 40, 171 (2009).
- Z.-X. Xie, G.-Q. Feng, and X.-H. Guo, Analyzing in the molecule picture in the Beth-Salpeter approach, Phys. Rev. D 81, 036014 (2010).
- M. Cleven, F.-K. Guo, C. Hanhart, and U.-G. Meissner, Light meson mass dependence of the positive parity heavy-strange mesons, Eur. Phys. J. A 47, 19 (2011).
- X.-G. Wu and Q. Zhao, The mixing of and , Phys. Rev. D 85, 034040 (2012).
- Z.-H. Guo, U.-G. Meißner, and D.-L. Yao, New insights into the and other charm scalar mesons, Phys. Rev. D 92, 094008 (2015).
- M. Albaladejo, D. Jido, J. Nieves, and E. Oset, and scattering in B decays from BABAR and LHCb data, Eur. Phys. J. C 76, 300 (2016).
- M.-L. Du, F.-K. Guo, U.-G. Meißner, and D.-L. Yao, Study of open-charm states in unitarized chiral effective theory with one-loop potentials, Eur. Phys. J. C 77, 728 (2017).
- Z.-H. Guo, L. Liu, U.-G. Meißner, J. A. Oller, and A. Rusetsky, Towards a precise determination of the scattering amplitudes of the charmed and light-flavor pseudoscalar mesons, Eur. Phys. J. C 79, 13 (2019).
- M. Albaladejo, P. Fernandez-Soler, J. Nieves, and P. G. Ortega, Contribution of constituent quark model states to the dynamics of the and resonances, Eur. Phys. J. C 78, 722 (2018).
- T.-W. Wu, M.-Z. Liu, L.-S. Geng, E. Hiyama, and M. P. Valderrama, , , and molecules–understanding the nature of the , Phys. Rev. D 100, 034029 (2019).
- E. B. Gregory, F.-K. Guo, C. Hanhart, S. Krieg, and T. Luu, Confirmation of the existence of an exotic state in the system, arXiv:2106.15391.
- P. Wang and X. G. Wang, Study on states with open charm in unitarized heavy meson chiral approach, Phys. Rev. D 86, 014030 (2012).
- B.-L. Huang, Z.-Y. Lin, and S.-L. Zhu, Light pseudoscalar meson and heavy meson scattering lengths to in heavy meson chiral perturbation theory, Phys. Rev. D 105, 036016 (2022).
- H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu, and S.-L. Zhu, A review of the open charm and open bottom systems, Rep. Prog. Phys. 80, 076201 (2017).
- Y.-R. Liu, H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Pentaquark and tetraquark states, Prog. Part. Nucl. Phys. 107, 237 (2019).
- Z. Zhou, G.-L. Yu, Z.-G. Wang, and J. Lu, Analysis of the hadronic molecules , , and their bottom analogs with QCD sum rules, arXiv:2508.00402.
- Z. Zhou, G.-L. Yu, Z.-G. Wang, and J. Lu, Analysis of the strong vertices of hadronic molecules , , and their bottom analogs, arXiv:2510.13706.
- W. A. Bardeen, E. J. Eichten, and C. T. Hill, Chiral multiplets of heavy—light mesons, Phys. Rev. D 68, 054024 (2003).
- A. Deandrea, G. Nardulli, and A. D. Polosa, On the mass of the system, Phys. Rev. D 68, 097501 (2003).
- Y.-B. Dai, C.-S. Huang, C. Liu, and S.-L. Zhu, Understanding the and with sum rules in HQET, Phys. Rev. D 68, 114011 (2003).
- M. Sadzikowski, The Masses of and in the MIT bag model, Phys. Lett. B 579, 39 (2004).
- R. N. Cahn and J. D. Jackson, Spin orbit and tensor forces in heavy quark light quark mesons: Implications of the new state at 2.32-GeV, Phys. Rev. D 68, 037502 (2003).
- D. S. Hwang and D.-W. Kim, Mass of and coupled channel effect, Phys. Lett. B 601, 137 (2004).
- Y. A. Simonov and J. A. Tjon, The coupled-channel analysis of the and mesons, Phys. Rev. D 70, 114013 (2004).
- H.-Y. Cheng and F.-S. Yu, Near mass degeneracy in the scalar meson sector: Implications for and mesons, Phys. Rev. D 89, 114017 (2014).
- Q.-T. Song, D.-Y. Chen, X. Liu, and T. Matsuki, Charmed-strange mesons revisited: Mass spectra and strong decays, Phys. Rev. D 91, 054031 (2015).
- H.-Y. Cheng and F.-S. Yu, Masses of scalar and axial-vector B mesons revisited, Eur. Phys. J. C 77, 668 (2017).
- S.-Q. Luo, B. Chen, X. Liu, and T. Matsuki, Predicting a new resonance as charmed-strange baryonic analog of , Phys. Rev. D 103, 074027 (2021).
- Z.-Y. Zhou and Z. Xiao, Two-pole structures in a relativistic Friedrichs–Lee-QPC scheme, Eur. Phys. J. C 81, 551 (2021).
- M. H. Alhakami, Mass spectra of heavy-light mesons in heavy hadron chiral perturbation theory, Phys. Rev. D 93, 094007 (2016).
- J. Vijande, F. Fernandez, and A. Valcarce, Open-charm meson spectroscopy, Phys. Rev. D 73, 034002 (2006); 74, 059903(E) (2006).
- L. Maiani, F. Piccinini, A. D. Polosa, and V. Riquer, Diquark-antidiquarks with hidden or open charm and the nature of X(3872), Phys. Rev. D 71, 014028 (2005).
- Y.-B. Dai, X.-Q. Li, S.-L. Zhu, and Y.-B. Zuo, Contribution of DK continuum in the QCD sum rule for (2317), Eur. Phys. J. C 55, 249 (2008).
- T. E. Browder, S. Pakvasa, and A. A. Petrov, Comment on the new resonances, Phys. Lett. B 578, 365 (2004).
- J.-X. Lin, H.-X. Chen, W.-H. Liang, C.-W. Xiao, and E. Oset, and the nature of the two resonances, Eur. Phys. J. C 84, 439 (2024).
- D. Gamermann and E. Oset, Axial resonances in the open and hidden charm sectors, Eur. Phys. J. A 33, 119 (2007).
- F.-K. Guo, P.-N. Shen, H.-C. Chiang, R.-G. Ping, and B.-S. Zou, Dynamically generated heavy mesons in a heavy chiral unitary approach, Phys. Lett. B 641, 278 (2006).
- F.-K. Guo, P.-N. Shen, and H.-C. Chiang, Dynamically generated heavy mesons, Phys. Lett. B 647, 133 (2007).
- A. Faessler, T. Gutsche, V. E. Lyubovitskij, and Y.-L. Ma, Molecular structure of the and bottom-strange mesons, Phys. Rev. D 77, 114013 (2008).
- R. Aaij et al., Observation of new excited states, Eur. Phys. J. C 81, 601 (2021).
- U. Özdem, and molecular states: Probing their electromagnetic fingerprints, Phys. Rev. D 112, 014011 (2025).
- V. L. Chernyak and I. R. Zhitnitsky, B meson exclusive decays into baryons, Nucl. Phys. B345, 137 (1990).
- V. M. Braun and I. E. Filyanov, QCD sum rules in exclusive kinematics and pion wave function, Z. Phys. C 44, 157 (1989).
- I. I. Balitsky, V. M. Braun, and A. V. Kolesnichenko, Radiative decay in quantum chromodynamics, Nucl. Phys. B312, 509 (1989).
- U. Özdem, Analysis of the molecular pentaquark state by its electromagnetic properties, Eur. Phys. J. C 84, 765 (2024).
- U. Özdem, Electromagnetic properties of resonances via light-cone QCD, Eur. Phys. J. Plus 139, 978 (2024).
- U. Özdem, Analysis of the state through its electromagnetic properties, Eur. Phys. J. C 84, 359 (2024).
- U. Özdem, Magnetic dipole moments of the and states from molecular perspective, Phys. Lett. B 849, 138432 (2024).
- U. Ozdem, Electromagnetic properties of the and states via light-cone QCD, Eur. Phys. J. C 83, 1077 (2023).
- U. Özdem and K. Azizi, Magnetic moment of the state in the diquark–antidiquark picture, Eur. Phys. J. A 58, 171 (2022).
- U. Özdem, Magnetic moment of the as a molecular pentaquark state, Eur. Phys. J. Plus 137, 103. (2022).
- K. Azizi and U. Özdem, Magnetic dipole moments of the and tetraquark states, Phys. Rev. D 104, 114002 (2021).
- K. Azizi and U. Özdem, The electromagnetic multipole moments of the possible charm-strange pentaquarks in light-cone QCD, Eur. Phys. J. C 78, 698 (2018).
- K. Azizi and U. Özdem, The electromagnetic multipole moments of the charged open-flavor states, J. Phys. G 45, 055003 (2018).
- S. J. Brodsky and J. R. Hiller, Universal properties of the electromagnetic interactions of spin one systems, Phys. Rev. D 46, 2141 (1992).
- I. I. Balitsky and V. M. Braun, Evolution equations for QCD string operators, Nucl. Phys. B311, 541 (1989).
- V. M. Belyaev and B. Y. Blok, Charmed baryons in quantum chromodynamics, Z. Phys. C 30, 151 (1986).
- P. Ball, V. M. Braun, and N. Kivel, Photon distribution amplitudes in QCD, Nucl. Phys. B649, 263 (2003).
- D. Antonov and J. E. F. T. Ribeiro, Quark condensate for various heavy flavors, Eur. Phys. J. C 72, 2179 (2012).
- U. Özdem, Electromagnetic properties of doubly heavy pentaquark states, Eur. Phys. J. Plus 137, 936 (2022).
- U. Özdem, Insight into the nature of the and related pentaquarks, Eur. Phys. J. C 85, 624 (2025).
- U. Özdem, Electromagnetic form factors of the Bc-like tetraquarks: Molecular and diquark-antidiquark pictures, Phys. Lett. B 838, 137750 (2023).
- S. Navas et al., Review of particle physics, Phys. Rev. D 110, 030001 (2024).
- B. L. Ioffe, QCD at low energies, Prog. Part. Nucl. Phys. 56, 232 (2006).
- J. Rohrwild, Determination of the magnetic susceptibility of the quark condensate using radiative heavy meson decays, J. High Energy Phys. 09 (2007) 073.
- S. Narison, and from heavy quarkonia, Nucl. Part. Phys. Proc. 300–302, 153 (2018).