Abstract
We study the mass of the state $Y(2175)$ of ${J}^{PC}={1}^{--}$ in the QCD sum rule. We construct both the diquark-antidiquark currents $(ss)(\overline{s}\overline{s})$ and the meson-meson currents $(\overline{s}s)(\overline{s}s)$. We find that there are two independent currents for both cases and derive the relations between them. The operator product expansion convergence of these two currents is sufficiently fast, which enables us to perform good sum rule analysis. Both the SVZ (Shifman-Vainshtein-Zakharov) sum rule and the finite energy sum rule lead to a mass around $2.3\ifmmode\pm\else\textpm\fi{}0.4\text{ }\text{ }\mathrm{GeV}$, which is consistent with the observed mass within the uncertainties of the present QCD sum rule. The coupling of the four-quark currents to lower lying states such as $\ensuremath{\phi}(1020)$ turns out to be rather small. We also discuss possible decay properties of $Y(2175)$ if it is a tetraquark state.
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