Mass calculations of light quarkonium, exotic \(J^{PC} = 0^{+-}\) hybrid mesons from Gaussian sum rules

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 experimental importance, we identify the exotic \(J^{PC} = 0^{+-}\) channel as the most promising for detailed study. Using Gaussian sum rules constrained by the Hölder inequality, we calculate masses of light (nonstrange and strange) quarkonium hybrid mesons with \(J^{PC} = 0^{+-}\). A model-independent analysis of the hadronic spectral function indicates that there is distributed resonance strength in this channel. Hence, we study two hadronic models with distributed resonance strength: a single wide resonance model and a double narrow resonance model. The single wide resonance model is disfavored as it leads to an anomalously large resonance width (greater than 1 GeV). The double narrow resonance model yields excellent agreement between QCD and phenomenology: in both nonstrange and strange cases, we find hybrid masses of 2.60 GeV and 3.57 GeV