Abstract
QCD Gaussian sum-rules are used to explore the vector ($J^{PC}=1^{--}$) strangeonium hybrid interpretation of the $Y(2175)$. Using a two-resonance model consisting of the $Y(2175)$ and an additional resonance, we find that the relative resonance strength of the $Y(2175)$ in the Gaussian sum-rules is less than 5\% that of a heavier 2.9 GeV state. This small relative strength presents a challenge to a dominantly-hybrid interpretation of the $Y(2175)$.
Highlights
The initial state radiation (ISR) process in eþe− annihilation is a very useful technique to search for vector states (i.e., JPC 1⁄4 1−−) in B-factories
To isolate the information in the Gaussian sum rules (GSRs) that is independent of the finite energy sum rule (FESR) constraint (27), we define normalized GSRs (NGSRs) [51], NQCDðs; τ; s0Þ ≡ R−∞∞GGQQCCDDðsðs;ˆ;τ;τ;ss0Þ0Þdsð28Þ
We choose the width of the Gaussian kernel to be τ 1⁄4 10 GeV4, in line with our previous GSRs analysis of light hybrids [41]
Summary
QCD Gaussian sum rules are used to explore the vector (JPC 1⁄4 1−−) strangeonium hybrid interpretation of the Yð2175Þ. Using a two-resonance model consisting of the Yð2175Þ and an additional resonance, we find that the relative resonance strength of the Yð2175Þ in the Gaussian sum rules is less than 5% that of a heavier 2.9 GeV state. This small relative strength presents a challenge to a dominantly hybrid interpretation of the Yð2175Þ
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