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

TL;DR

This paper uses QCD sum rules to analyze specific tetraquark states, proposing assignments for observed particles and exploring their internal structure, with minimal flavor symmetry breaking effects.

Contribution

Introduces an explicit P-wave diquark construction and local four-quark currents to study hidden-charm tetraquarks with various quantum numbers.

Findings

Supports assigning $X(4475)$ and $X(4500)$ as specific tetraquark states.

Supports assigning $Z_c(4600)$ and $Z_{ar{c}ar{s}}(4600)$ as specific tetraquark states.

Rules out $X(4710)$ and $X(4700)$ as tetraquark states.

Abstract

In this work, we introduce an explicit P-wave to construct the diquarks $[qc]_{\widehat{V}}$, 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 $[uc]_{\widehat{V}}[\overline{uc}]_{\widehat{V}}-[dc]_{\widehat{V}}[\overline{dc}]_{\widehat{V}}$ and $[sc]_{\widehat{V}}[\overline{sc}]_{\widehat{V}}$ tetraquark states with the $J^{PC}=0^{++}$ respectively, and assigning the $Z_{c}(4600)$ and $Z_{\bar{c}\bar{s}}(4600)$ as the $[uc]_{\widehat{V}}[\overline{dc}]_{\widehat{V}}$ and $[qc]_{\widehat{V}}[\overline{sc}]_{\widehat{V}}$ 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 $\widehat{V}\widehat{V}$ type components.