Mass Calculations of Light Quarkonium, Exotic $J^{PC}=0^{+-}$ Hybrid Mesons from Gaussian Sum-Rules

TL;DR

This paper improves QCD sum-rule calculations for light quarkonium hybrid mesons by including higher-dimensional condensates, identifying the $J^{PC}=0^{+-}$ channel as promising, and estimating hybrid masses around 2.60 GeV and 3.57 GeV.

Contribution

It extends previous sum-rule analyses by incorporating dimension five and six condensates, enhancing stability and accuracy in predicting hybrid meson masses.

Findings

Hybrid masses estimated at 2.60 GeV and 3.57 GeV.

Double narrow resonance model best fits QCD phenomenology.

Exotic $J^{PC}=0^{+-}$ channel identified as most promising for study.

Abstract

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 H\"older 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.