QCD Sum Rule Analysis of Heavy Quarkonium Hybrids

TL;DR

This paper uses QCD sum rules to analyze heavy quarkonium hybrid states, updating their mass spectra and identifying supermultiplet structures based on quantum numbers and parity.

Contribution

It provides the first reliable mass predictions for charmonium and bottomonium hybrids including dimension six condensates, confirming their role in stabilizing sum rules.

Findings

Negative-parity states form the lightest hybrid supermultiplet.

Positive-parity states belong to a heavier supermultiplet.

Dimension six condensates are crucial for stable sum rule analysis.

Abstract

We have studied the charmonium and bottomonium hybrid states with various $J^{PC}$ quantum numbers in QCD sum rules. At leading order in $\alpha_s$, the two-point correlation functions have been calculated up to dimension six including the tri-gluon condensate and four-quark condensate. After performing the QCD sum rule analysis, we have confirmed that the dimension six condensates can stabilize the hybrid sum rules and allow the reliable mass predictions. We have updated the mass spectra of the charmonium and bottomonium hybrid states and identified that the negative-parity states with $J^{PC}=(0, 1, 2)^{-+}, 1^{--}$ form the lightest hybrid supermultiplet while the positive-parity states with $J^{PC}=(0, 1)^{+-}, (0, 1, 2)^{++}$ belong to a heavier hybrid supermultiplet.