QCD sum rules study of X(4350)

Abstract

The QCD sum rule approach is used to analyze the nature of the rencently observed new resonance $X(4350)$, which is assumed to be a diquark-antidiquark state $[cs][\bar{c}\bar{s}]$ with $J^{PC}=1^{-+}$. The interpolating current representing this state is proposed. In the calculation, contributions of operators up to dimension six are included in the operator product expansion (OPE), as well as terms which are linear in the strange quark mass $m_s$. We find $m_{1^{-+}}=(4.82\pm 0.19)\,\mbox{GeV}$, which is not compatible with the $X(4350)$ structure as a $1^{-+}$ tetraquark state. Finally, we also discuss the difference of a four-quark state's mass whether the state's interpolating current has a definite charge conjugation.