Heavy Quarkonium ($1^{--}$) Meson-Hybrid Mixing from QCD Sum Rules

TL;DR

This paper investigates the mixing between conventional mesons and hybrid states in heavy quarkonium vector channels using QCD sum rules, revealing evidence of such mixing in charmonium and bottomonium states.

Contribution

It introduces a QCD sum-rule approach including gluon condensates to analyze meson-hybrid mixing in heavy quarkonium, providing new insights into their structure.

Findings

Evidence of meson-hybrid mixing in the $J/\psi$ and a 4.3 GeV resonance.

All examined bottomonium states ($\Upsilon(1S)$ to $\Upsilon(4S)$) show mixing.

The approach combines experimental masses with theoretical models for analysis.

Abstract

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.