Revisit the heavy quarkonium double-gluon hybrid mesons with exotic quantum numbers

• Published in: The journal of high energy physics Vol. 2024; no. 6; pp. 173 - 33
• Main Authors: Lian, Ding-Kun, Wang, Qi-Nan, Chen, Xu-Liang, Yang, Peng-Fei, Chen, Wei, Chen, Hua-Xing
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 26.06.2024; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Correlation; Correlation Functions; Divergence; Elementary Particles; Feynman diagrams; Gluons; Hadronic Spectroscopy; Hypergeometric functions; Investigations; Mesons; Numerical analysis; Operators (mathematics); Physics; Physics and Astronomy; Properties of Hadrons; Quantum chromodynamics; Quantum Field Theories; Quantum Field Theory; Quantum numbers; Quantum Physics; Quarkonium; Quarks; Regular Article - Theoretical Physics; Relativity Theory; Spectrum analysis; String Theory; Structure and Interactions; Sum rules; Sums; Structure and Interactions; Properties of Hadrons; Hadronic Spectroscopy; Correlation Functions; Quarkonium
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP06(2024)173

A bstract We revisit the masses of heavy quarkonium double-gluon hybrid mesons with exotic quantum numbers J PC = 1 −+ and 2 +− in the framework of the QCD sum rules. Considering the double-gluon hybrid meson operators in the octet-octet color structure, we have constructed two independent interpolating currents with J PC = 1 −+ and five independent currents with J PC = 2 +− . For the interpolating currents with antisymmetric glueball operator, there exist non-local divergences in one kind of additional Feynman diagrams of the tri-gluon condensate, which will give important contributions to the sum rule stabilities and mass predictions. We use the diagrammatic renormalization to cancel out such divergences. At the leading order of α s , the two-point correlation functions and spectral densities can be expressed in the analytic form of the generalized hypergeometric functions and Meijer’s G-functions. After performing the numerical analysis, we predict the masses of the 1 −+ and 2 +− charmonium double-gluon hybrid mesons to be around 6 . 1 − 7 . 2 GeV and 6 . 3 − 6 . 4 GeV, respectively. For the bottomonium systems, their masses are predicted to be 13 . 7 − 14 . 3 GeV and 12 . 6 − 13 . 3 GeV for the 1 −+ and 2 +− channels, respectively. Besides, it is possible to hunt for these charmonium hybrids in the radiative decays of bottomonium mesons in BelleII experiment. Further investigations on these hybrid states in various theoretical and phenomenological methods are also anticipated in the future.