Mass Spectrum of Heavy Quarkonium Hybrids

TL;DR

This paper refines the mass spectrum predictions of heavy quarkonium hybrids by including dimension six condensates in QCD sum-rule calculations, confirming supermultiplet structures and providing insights into exotic quantum states.

Contribution

It extends previous QCD sum-rule analyses by incorporating higher-dimension condensates, enabling more reliable mass predictions for heavy quarkonium hybrids with various quantum numbers.

Findings

Negative-parity states form the lightest hybrid supermultiplet.

Positive-parity states belong to a heavier supermultiplet.

The J^{PC}=0^{--} hybrid has a significantly higher mass.

Abstract

We have extended the calculation of the correlation functions of heavy quarkonium hybrid operators with various $J^{PC}$ quantum numbers to include QCD condensates up to dimension six. In contrast to previous analyses which were unable to optimize the QCD sum-rules for certain $J^{PC}$, recent work has shown that inclusion of dimension six condensates stabilizes the hybrid sum-rules and permits reliable mass predictions. In this work we have investigated the effects of the dimension six condensates on the remaining channels. After performing the QCD sum-rule analysis, we update the mass spectra of charmonium and bottomonium hybrids with exotic and non-exotic quantum numbers. We identify 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, confirming the supermultiplet structure found in other approaches. The hybrid with $J^{PC}=0^{--}$ has a much higher mass which may suggest a different excitation of the gluonic field compared to other channels. In agreement with previous results, we find that the $J^{PC}=1^{++}$ charmonium hybrid is substantially heavier than the X(3872), which seems to preclude a pure charmonium hybrid interpretation for this state.