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

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.