Analysis of the $X(4475/4710)$, $X(4500/4700)$, $Z_c(4600)$, $Z_{\bar{c}\bar{s}}(4600)$ and related tetraquark states with the QCD sum rules

Abstract

In this work, we introduce an explicit P-wave to construct the diquarks $[qc{]}_{\hat{V}}$, then construct the local four-quark currents to explore the hidden-charm tetraquark states with the $J^{PC}=0^{++}$, $1^{+-}$ and $2^{++}$ in the framework of the QCD sum rules at length. Our calculations indicate that the light-flavor $SU(3)$ breaking effects on the tetraquark masses are tiny. The predictions support assigning the $X(4475)$ and $X(4500)$ as the $[uc{]}_{\hat{V}}[\overline{uc}{]}_{\hat{V}}-[dc{]}_{\hat{V}}[\overline{dc}{]}_{\hat{V}}$ and $[sc{]}_{\hat{V}}[\overline{sc}{]}_{\hat{V}}$ tetraquark states with the $J^{PC}=0^{++}$ respectively, and assigning the $Z_c(4600)$ and $Z_{\bar{c}\bar{s}}(4600)$ as the $[uc{]}_{\hat{V}}[\overline{dc}{]}_{\hat{V}}$ and $[qc{]}_{\hat{V}}[\overline{sc}{]}_{\hat{V}}$ tetraquark states with the $J^{PC}=1^{+-}$ respectively. On the other hand, there is no room for the $X(4710)$ and $X(4700)$. Combined with previous works, the $X(4475)$, $X(4500)$, $Z_c(4600)$ and $Z_{\bar{c}\bar{s}}(4600)$ might have other important Fock components besides the $\hat{V}\hat{V}$ type components.

14 pages, 2 figures

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