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

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 $\phi (1020)f_0(1710)\mathrm{/}\phi (1020)f_2^{\mathrm{\prime }}(1525)(\to \phi K\bar{K}\mathrm{/}\phi \pi \pi )$ channels.