Meson-Hybrid Mixing in $J^{PC}=1^{++}$ Heavy Quarkonium from QCD Sum-Rules

Abstract

We explore conventional meson-hybrid mixing in $J^{PC}=1^{++}$ heavy quarkonium using QCD Laplace sum-rules. We calculate the cross-correlator between a heavy conventional meson current and heavy hybrid current within the operator product expansion, including terms proportional to the four- and six-dimensional gluon condensates and the six-dimensional quark condensate. Using experimentally determined hadron masses, we construct models of the $1^{++}$ charmonium and bottomonium mass spectra. These models are used to investigate which resonances couple to both currents and thus exhibit conventional meson-hybrid mixing. In the charmonium sector, we find almost no conventional meson-hybrid mixing in the ${\chi }_{c1}(1P)$, minimal mixing in the $X(3872)$, and significant mixing in both the $X(4140)$ and $X(4274)$. In the bottomonium sector, we find minimal conventional meson-hybrid mixing in the ${\chi }_{b1}(1P)$ and significant mixing in both the ${\chi }_{b1}(2P)$ and ${\chi }_{b1}(3P)$.

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• Heavy-light hybrid mesons with different spin-parities
• Predictions of the hybrid mesons with exotic quantum numbers $J^{PC}=2^{+-}$
• Mass spectrum of the hidden-charm hybrid states via the QCD sum rules
• Mixing of X and Y states from QCD Sum Rules analysis
• Probing Axial-Vector Charmonia ${\chi }_{c1}(1P)$ and ${\chi }_{c1}(2P)$
• Revisit the heavy quarkonium double-gluon hybrid mesons with exotic quantum numbers
• Vector and Scalar Mesons' Mixing from QCD Sum Rules
• Study of the ${\Omega }_{ccc}{\Omega }_{ccc}$ and ${\Omega }_{bbb}{\Omega }_{bbb}$ dibaryons in QCD Sum Rules