# Color halo scenario of charmonium-like hybrids

• The internal structures of $J^{PC} = 1^{--}, (0,1,2)^{-+}$ charmonium-like hybrids are investigated under lattice QCD in the quenched approximation. We define the Bethe-Salpeter wave function ($\Phi_n(r)$) in the Coulomb gauge as the matrix element of a spatially extended hybrid-like operator ($\bar{c}{c}g$) between the vacuum and n-th state for each $J^{PC}$, with r being the spatial separation between a localized $\bar{c}c$ component and the chromomagnetic strength tensor. These wave functions exhibit some similarities for states with the aforementioned different quantum numbers, and their r-behaviors (no node for the ground states and one node for the first excited states) imply that r can be a meaningful dynamical variable for these states. Additionally, the mass splittings of the ground states and first excited states of charmonium-like hybrids in these channels are obtained for the first time to be approximately 1.2-1.4 GeV. These results do not support the flux-tube description of heavy-quarkonium-like hybrids in the Born-Oppenheimer approximation. In contrast, a charmonium-like hybrid can be viewed as a “color halo” charmonium for which a relatively localized color octet $\bar{c}c$ is surrounded by gluonic degrees of freedom, which can readily decay into a charmonium state along with one or more light hadrons. The color halo picture is compatible with the decay properties of $Y(4260)$ and suggests LHCb and BelleII to search for $(0,1,2)^{-+}$ charmonium-like hybrids in $\chi_{c0,1,2}\eta$ and $J/\psi \omega (\phi)$ final states.
PCAS:
•  [1] K. Juge, J. Kuti, and C. Morningstar, Nucl. Phys. B Proc. Suppl. 63, 326 (1998), arXiv:hep-lat/9709131 doi: 10.1016/S0920-5632(97)00759-7 [2] K. Juge, J. Kuti, and C. Morningstar, Phys. Rev. Lett. 82, 4400 (1999), arXiv:hep-ph/9902336 doi: 10.1103/PhysRevLett.82.4400 [3] A. P. Szczepaniak and P. Krupinski, Physical Review D 73, 034022 (2006) doi: 10.1103/physrevd.73.034022 [4] A. P. Szczepaniak and P. Krupinski, Physical Review D 73, 116002 (2006) doi: 10.1103/physrevd.73.116002 [5] E. Braaten, C. Langmack, and D. H. Smith, Phys. Rev. D 90, 014044 (2014), arXiv:1402.0438 [hep-ph doi: 10.1103/PhysRevD.90.014044 [6] N. Akbar and S. Noor, (2020), arXiv: 2005.02626 [hepph] [7] P. Lacock, C. Michael, P. Boyle et al. (UKQCD), Phys. Rev. D 54, 6997 (1996), arXiv:heplat/9605025 [hep-lat [8] C. W. Bernard et al., Phys. Rev. D 56, 7039 (1997), arXiv:hep-lat/9707008 [hep-lat [9] X. Liao and T. Manke, (2002), arXiv: hep-lat/0210030 [hep-lat] [10] C. Bernard, T. Burch, E. B. Gregory et al., Phys. Rev. D 68, 074505 (2003), arXiv:heplat/0301024 [hep-lat [11] Z.-H. Mei and X.-Q. Luo, Int. J. Mod. Phys. A 18, 5713 (2003), arXiv:hep-lat/0206012 [hep-lat [12] J. J. Dudek, R. G. Edwards, M. J. Peardon et al., Phys. Rev. Lett. 103, 262001 (2009), arXiv:0909.0200 [hep-ph doi: 10.1103/PhysRevLett.103.262001 [13] Y.-B. Yang, Y. Chen, G. Li et al., Phys. Rev. D 86, 094511 (2012), arXiv:1202.2205 [hep-ph [14] J. J. Dudek and E. Rrapaj, Phys. Rev. D 78, 094504 (2008), arXiv:0809.2582 [hep-ph [15] J. J. Dudek, R. Edwards, and C. E. Thomas, Phys. Rev. D 79, 094504 (2009), arXiv:0902.2241 [hep-ph [16] L. Liu, G. Moir, M. Peardon et al. (Hadron Spectrum), JHEP 07, 126 (2012), arXiv:1204.5425 [hep-ph [17] N. Brambilla, S. Eidelman, C. Hanhart et al., (2019), arXiv: 1907.07583 [hep-ex] [18] M. Tanabashi et al., Phys. Rev. D 98, 030001 (2018) [19] S.-L. Zhu, Phys. Lett. B 625, 212 (2005), arXiv:hepph/0507025 [hep-ph [20] Y. Chen, W.-F. Chiu, M. Gong et al., Chin. Phys. C 40, 081002 (2016), arXiv:1604.03401 [heplat [21] X. Y. Gao, C. P. Shen, and C. Z. Yuan, Phys. Rev. D 95, 092007 (2017), arXiv:1703.10351 [hep-ex [22] C.-Z. Yuan, Int. J. Mod. Phys. A 33, 1830018 (2018), arXiv:1808.01570 [hep-ex [23] C. J. Morningstar and M. J. Peardon, Phys. Rev. D 60, 034509 (1999), arXiv:hep-lat/9901004 [hep-lat [24] Y. Chen et al., Phys. Rev. D 73, 014516 (2006), arXiv:hep-lat/0510074 [hep-lat [25] S.-q. Su, L.-m. Liu, X. Li et al., Int. J. Mod. Phys. A 21, 1015 (2006), arXiv:hep-lat/0412034 [hep-lat [26] L. Giusti, M. Paciello, C. Parrinello et al., Int. J. Mod. Phys. A 16, 3487 (2001), arXiv:hep-lat/0104012 doi: 10.1142/S0217751X01004281 [27] V. Bhardwaj et al., Phys. Rev. Lett. 111, 032001 (2013), arXiv:1304.3975 [hep-ex doi: 10.1103/PhysRevLett.111.032001 [28] M. Ablikim et al., Phys. Rev. Lett. 115, 011803 (2015), arXiv:1503.08203 [hep-ex doi: 10.1103/PhysRevLett.115.011803 [29] R. Aaij et al., JHEP 07, 035 (2019), arXiv:1903.12240 [hep-ex [30] Y.-B. Yang, Y. Chen, L.-C. Gui et al. (CLQCD), Phys. Rev. D 87, 014501 (2013), arXiv:1206.2086 [hep-lat [31] G. S. Bali, Phys. Rev. D 62, 114503 (2000), arXiv:heplat/0006022 [hep-lat [32] Y. Ma, Y. Chen, M. Gong et al., Chin. Phys. C 45, 013112 (2021), arXiv:2007.14893 [hep-lat doi: 10.1088/1674-1137/abc241 [33] N. Isgur and J. E. Paton, Phys. Rev. D 31, 2910 (1985)

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Yunheng Ma, Wei Sun, Ying Chen, Ming Gong and Zhaofeng Liu. A Color Halo Scenario of Charmonium-like Hybrids[J]. Chinese Physics C. doi: 10.1088/1674-1137/ac0ee2
Yunheng Ma, Wei Sun, Ying Chen, Ming Gong and Zhaofeng Liu. A Color Halo Scenario of Charmonium-like Hybrids[J]. Chinese Physics C.
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###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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## Color halo scenario of charmonium-like hybrids

• 1. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
• 2. School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China
• 3. Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, Newport News, VA 23606, USA

Abstract: The internal structures of $J^{PC} = 1^{--}, (0,1,2)^{-+}$ charmonium-like hybrids are investigated under lattice QCD in the quenched approximation. We define the Bethe-Salpeter wave function ($\Phi_n(r)$) in the Coulomb gauge as the matrix element of a spatially extended hybrid-like operator ($\bar{c}{c}g$) between the vacuum and n-th state for each $J^{PC}$, with r being the spatial separation between a localized $\bar{c}c$ component and the chromomagnetic strength tensor. These wave functions exhibit some similarities for states with the aforementioned different quantum numbers, and their r-behaviors (no node for the ground states and one node for the first excited states) imply that r can be a meaningful dynamical variable for these states. Additionally, the mass splittings of the ground states and first excited states of charmonium-like hybrids in these channels are obtained for the first time to be approximately 1.2-1.4 GeV. These results do not support the flux-tube description of heavy-quarkonium-like hybrids in the Born-Oppenheimer approximation. In contrast, a charmonium-like hybrid can be viewed as a “color halo” charmonium for which a relatively localized color octet $\bar{c}c$ is surrounded by gluonic degrees of freedom, which can readily decay into a charmonium state along with one or more light hadrons. The color halo picture is compatible with the decay properties of $Y(4260)$ and suggests LHCb and BelleII to search for $(0,1,2)^{-+}$ charmonium-like hybrids in $\chi_{c0,1,2}\eta$ and $J/\psi \omega (\phi)$ final states.

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