We revisit the masses of heavy quarkonium double-gluon hybrid mesons with exotic quantum numbers JPC = 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 JPC = 1−+ and five independent currents with JPC = 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 αs, 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.
We revisit the masses of heavy quarkonium double-gluon hybrid mesons with exotic quantum numbers JPC = 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 JPC = 1−+ and five independent currents with JPC = 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 αs, 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.
A model of light hybrid mesons and their strong decays is developed. The model employs a gluonic quasiparticle to describe low energy gluodynamics and uses the QCD Hamiltonian in Coulomb gauge to guide the construction of states and decay amplitudes. We compute the partial widths of the twelve low lying isovector and vector hybrids. Implications of these results on hybrid searches are also made, with the chief conclusions being that direct observation of the vector states will be difficult, that a hybrid π(1800) has distinctive decay characteristics, a narrow η(1900) hybrid should exist, an η1(1750) should be sought, and that the exotic nature of JPC=2−+ hybrid mesons should be discernible with sufficient data. We argue that the isovector π2 hybrid has been discovered, giving a total of four possible hybrid mesons, π1(1600), η1(1855), π(1800), and π2(2360), which appear to be filling out the low lying hybrid supermultiplet in the expected fashion.
Published by the American Physical Society
2024
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