Can the X(4350) narrow structure be a $1^{-+}$ exotic state?

TL;DR

This study uses QCD sum rules to investigate whether the X(4350) structure can be a $1^{-+}$ exotic molecular state, concluding it is unlikely based on mass calculations.

Contribution

The paper provides the first QCD sum rule analysis of the X(4350) as a $1^{-+}$ molecular state, calculating its mass and testing its viability.

Findings

Mass of $D_s^*D_{s0}^*$ state is about 5.05 GeV.

Mass of $D^*D_0^*$ state is about 4.92 GeV.

X(4350) cannot be described as a $1^{-+}$ molecular state.

Abstract

Using the QCD sum rules we test if the new narrow structure, the X(4350) recently observed by the Belle Collaboration, can be described as a $J^{PC}=1^{-+}$ exotic $D_s^*D_{s0}^*$ molecular state. We consider the contributions of condensates up to dimension eight, we work at leading order in $\alpha_s$ and we keep terms which are linear in the strange quark mass $m_s$. The mass obtained for such state is $m_{D_s^*{D}_{s0}^*}=(5.05\pm 0.19)$ GeV. We also consider a molecular $1^{-+}, D^{*}{D}_0^{*}$ current and we obtain $m_{D^*{D}_0^*}=(4.92\pm 0.08)$ GeV. We conclude that it is not possible to describe the X(4350) structure as a $1^{-+} D_s^*{D}_{s0}^*$ molecular state.