Molecular Interpretation of $X(3960)$ as $D_s^+ D_s^-$ State

TL;DR

This paper investigates the $X(3960)$ as a hadronic molecule composed of $D_s^+ D_s^-$, using QCD sum rules to predict its mass and decay constant, aligning with recent experimental findings.

Contribution

It provides the first QCD sum rule analysis of the $D_s^+ D_s^-$ molecular state, predicting its mass and decay constant consistent with experimental data.

Findings

Predicted mass of $D_s^+ D_s^-$ state matches LHCb observation.

Supports the molecular interpretation and quantum number assignment.

Suggests observing $D ar D$ state could confirm a four-quark state in charmonium sector.

Abstract

We study $D_s^+ D_s^-$ and $D \bar D$ states assuming that they are hadronic molecules with $J^{PC}=0^{++}$ quantum number. We use two-point QCD sum rule formalism and extract the mass and decay constant values of these states. We take into account contributions of various quark, gluon, and mixed vacuum condensates up to dimension eight. The extracted mass and decay constant values of $D \bar D$ and $D_s^+ D_s^-$ states read as $M_{D \bar D} = 3795^{+85}_{-82} ~\mathrm{MeV} $, $f_{D \bar D} = 1.70^{+0.33}_{-0.29} \times 10^{-2} ~\mathrm{GeV}^5$, and $M_{D_s^+ D_s^-} = 3983^{+93}_{-88} ~\mathrm{MeV}$, $f_{D_s^+ D_s^-} = 2.52^{+0.64}_{-0.54} \times 10^{-2} ~\mathrm{GeV}^5$, respectively. The predicted mass of $D_s^+ D_s^-$ state is in good agreement with the recent LHCb observation and supports quantum number and molecular picture assignments. A possible observation of $D \bar D$ state would help for establishing the lowest four-quark state in charmonium sector.