Understanding the internal structures of the $X(4140)$, $X(4274)$, $X(4500)$ and $X(4700)$

TL;DR

This paper uses QCD sum rules to analyze the internal structures of several exotic mesons, interpreting them as tetraquark states with specific configurations and predicting masses for related bottomonium states.

Contribution

It provides a novel interpretation of the $X(4500)$ and $X(4700)$ as D-wave tetraquark states and predicts their hidden-bottom partners around 10.64 GeV.

Findings

$X(4500)$ and $X(4700)$ are D-wave $csar{c}ar{s}$ tetraquarks with $J^P=0^+$.

Masses of hidden-bottom partners are predicted around 10.64 GeV.

Mass predictions depend on specific quark mass values.

Abstract

We investigate the newly observed $X(4500)$ and $X(4700)$ based on the diquark-antidiquark configuration within the framework of QCD sum rules. Both of them may be interpreted as the $D$-wave $cs\bar{c}\bar{s}$ tetraquark states of $J^P = 0^+$, but with opposite color structures, which is remarkably similar to the result obtained in Ref.~\cite{Chen:2010ze} that the $X(4140)$ and $X(4274)$ can be both interpreted as the $S$-wave $cs\bar{c}\bar{s}$ tetraquark states of $J^P = 1^+$, also with opposite color structures. However, the extracted masses and these suggested assignments to these $X$ states do depend on these running quark masses where $m_s (2 \mbox{ GeV}) = 95 \pm 5$ MeV and $m_c (m_c) = 1.23 \pm 0.09$ GeV. As a byproduct, the masses of the hidden-bottom partner states of the $X(4500)$ and $X(4700)$ are extracted to be both around 10.64 GeV, which can be searched for in the $\Upsilon \phi$ invariant mass distribution.