Fully-strange tetraquark states with the exotic quantum numbers $J^{PC}=0^{+-}$ and $2^{+-}$

Abstract

We study the fully-strange tetraquark states with the exotic quantum numbers $J^{PC}=0^{+-}$ and $2^{+-}$. We construct their corresponding diquark-antidiquark interpolating currents, and apply the QCD sum rule method to calculate both their diagonal and off-diagonal correlation functions. The obtained results are used to construct some mixing currents that are nearly non-correlated, from which we extract the masses of the lowest-lying states to be $M_{0^{+-}}=2.45_{-0.44}^{+0.33}$ GeV and $M_{2^{+-}}=3.07_{-0.33}^{+0.25}$ GeV. We apply the Fierz rearrangement to transform the diquark-antidiquark currents to be the combinations of meson-meson currents, and the obtained Fierz identities indicate that these two states may be searched for in the $P$-wave $\varphi (1020)f_0(1710)/\varphi (1020)f_2^{\prime }(1525)(\to \varphi K\bar{K}/\varphi \pi \pi )$ channels.

14 pages, 5 figures, 1 tables, revised version to be published in PRD

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