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Register a new userMeson-Hybrid Mixing in $J^{PC}=1^{++}$ Heavy Quarkonium from QCD Sum-Rules
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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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We use QCD Laplace sum-rules to explore mixing between conventional mesons and hybrids in the heavy quarkonium vector $J^{PC}!=!1^{--}$ channel. Our cross-correlator includes perturbation theory and contributions proportional to the four-dimensional and six-dimensional gluon condensates. We input experimentally determined charmonium and bottomonium hadron masses into both single and multi-resonance models in order to test them for conventional meson and hybrid components. In the charmonium sector we find evidence for meson-hybrid mixing in the $J/psi$ and a $approx4.3$ GeV resonance. In the bottomonium sector, we find that the $Upsilon(1S)$, $Upsilon(2S)$, $Upsilon(3S)$, and $Upsilon(4S)$ all exhibit mixing.
QCD Laplace sum-rules are used to calculate axial vector $(J^{PC}=1^{++})$ charmonium and bottomonium hybrid masses. Previous sum-rule studies of axial vector heavy quark hybrids did not include the dimension-six gluon condensate, which has been shown to be important in the $1^{--}$ and $0^{-+}$ channels. An updated analysis of axial vector heavy quark hybrids is performed, including the effects of the dimension-six gluon condensate, yielding mass predictions of 5.13 GeV for hybrid charmonium and 11.32 GeV for hybrid bottomonium. The charmonium hybrid mass prediction disfavours a hybrid interpretation of the X(3872), if it has $J^{PC}=1^{++}$, in agreement with the findings of other theoretical approaches. It is noted that QCD sum-rule results for the $1^{--}$, $0^{-+}$ and $1^{++}$ channels are in qualitative agreement with the charmonium hybrid multiplet structure observed in recent lattice calculations.
We use QCD Laplace sum-rules to study meson-hybrid mixing in vector ($1^{--}$) heavy quarkonium. We compute the QCD cross-correlator between a heavy meson current and a heavy hybrid current within the operator product expansion. In addition to leading-order perturbation theory, we include four- and six-dimensional gluon condensate contributions as well as a six-dimensional quark condensate contribution. We construct several single and multi-resonance models that take known hadron masses as inputs. We investigate which resonances couple to both currents and so exhibit meson-hybrid mixing. Compared to single resonance models that include only the ground state, we find that models that also include excited states lead to significantly improved agreement between QCD and experiment. In the charmonium sector, we find that meson-hybrid mixing is consistent with a two-resonance model consisting of the $J/psi$ and a 4.3~GeV resonance. In the bottomonium sector, we find evidence for meson-hybrid mixing in the $Upsilon(1S)$, $Upsilon(2S)$, $Upsilon(3S)$, and $Upsilon(4S)$.
We extend previous calculations of leading-order correlation functions of spin-0 and spin-1 light quarkonium hybrids to include QCD condensates of dimensions five and six, with a view to improving the stability of QCD sum-rules analyses in previously unstable channels. Based on these calculations, prior analyses in the literature, and its phenomenological importance, we identify the exotic $J^{PC}=0^{+-}$ channel as the most promising for detailed study. Using Gaussian sum-rules constrained by the Holder inequality, we calculate masses of light (nonstrange and strange) quarkonium hybrid mesons with $J^{PC}=0^{+-}$. We consider single narrow, single wide, and double narrow resonance models, and find that the double narrow resonance model yields the best agreement between QCD and phenomenology. In both non-strange and strange cases, we find hybrid masses of $2.60$ GeV and $3.57$ GeV.
We investigate the hybrid exotic meson with $J^{PC}=1^{-+}$ within the framework of an AdS/QCD model. Introducing a holographic field dual to the operator for hybrid exotic meson, we obtain the eigen-value equation for its mass. Fixing all free parameters by QCD observables such as the $rho$-meson mass, we predict the masses of the hybrid exotic meson. The results turn out to be $1476 mathrm{MeV}$ for the ground state, and $2611 mathrm{MeV}$ for the first excited one. Being compared with the existing experimental data for the $pi_1(1400)$, which is known to be $m_{pi_1} = 1351pm30 mathrm{MeV}$, the present result seems to be qualitative in agreement with it. We also predict the decay constant of $pi_1$(1400): $F_{pi_1}= 10.6$ MeV.
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