$\{Q\bar{s}\}\{\bar{Q}^{(')}s\}$ molecular states in QCD sum rules

TL;DR

This paper uses QCD sum rules to systematically study the mass spectra of $ ext{Q}ar{s} ext{-}ar{ ext{Q}}^{(')}s$ molecular states, providing theoretical predictions that support interpreting the observed $X(4350)$ as a molecular state.

Contribution

The study proposes specific interpolating currents and includes operators up to dimension six in the OPE to calculate the masses of these molecular states.

Findings

Mass of $D_{s}^{*}ar{D}_{s0}^{*}$ molecular state is $4.36 ext{ GeV}$.

Predicted mass aligns with the observed $X(4350)$ mass.

Supports $X(4350)$ as a $D_{s}^{*}ar{D}_{s0}^{*}$ molecular state.

Abstract

We systematically investigate the mass spectra of $\{Q\bar{s}\}\{\bar{Q}^{(')}s\}$ molecular states in the framework of QCD sum rules. The interpolating currents representing the molecular states are proposed. Technically, contributions of the operators up to dimension six are included in operator product expansion (OPE). The masses for molecular states with various $\{Q\bar{s}\}\{\bar{Q}^{(')}s\}$ configurations are presented. The result $4.36\pm0.08 GeV$ for the $D_{s}^{*}\bar{D}_{s0}^{*}$ molecular state is consistent with the mass $4350^{+4.6}_{-5.1}\pm0.7 MeV$ of the newly observed $X(4350)$, which could support $X(4350)$ interpreted as a $D_{s}^{*}\bar{D}_{s0}^{*}$ molecular state.