Abstract
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 $\Upsilon(4S)$.
Highlights
Hybrids are hadrons containing explicit gluon degrees of freedom in addition to a constituent quark and antiquark
Compared to single resonance models that include only the ground state, we find that models that include excited states lead to significantly improved agreement between QCD and experiment
We focus on 1−− rather than some other JPC because more is known about the spectra of 1−− heavy quarkonium than is known about the spectra for the other quantum numbers [6]
Summary
Hybrids are hadrons containing explicit gluon degrees of freedom in addition to a constituent quark and antiquark They are color singlets and so should be allowed within QCD. The heavy quarkonium sectors have received considerable attention lately due primarily to the discovery of the XYZ resonances (see [2,3] for reviews and [4] for some recent developments). These XYZ resonances are a collection of hadrons many of whose properties (e.g., masses, widths, and decay rates) do not agree with quark model predictions [5]. We find evidence for meson-hybrid mixing in all of the Υð1SÞ, Υð2SÞ, Υð3SÞ, and Υð4SÞ
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