Predicting the existence of a 2.9 GeV $Df_0(980)$ molecular state

TL;DR

This paper predicts a 2.9 GeV $Df_0(980)$ molecular state using two independent models, one based on QCD sum rules and the other on few-body equations, providing strong evidence for its existence.

Contribution

The study introduces a combined theoretical approach using QCD sum rules and few-body equations to predict a new $Df_0(980)$ molecular state around 2.9 GeV.

Findings

A resonance at 2.926 GeV from QCD sum rules.

A dynamically generated $D$-like meson at 2.890 GeV from few-body equations.

Strong evidence supporting the $Df_0(980)$ molecular state.

Abstract

A $D$-like meson resonance with mass around 2.9 GeV has been found in the $DK\bar K$ system using two independent and different model calculations based on: (1) QCD sum rules and (2) solution of Fadeev equations with input interactions obtained from effective field theories built by considering both chiral and heavy quark symmetries. The QCD sum rules have been used to study the $D_{s^*0}(2317) \bar{K}$ and $D f_0(980)$ molecular currents. A resonance of mass 2.926 GeV is found with the $D f_0(980)$ current. Although a state in the $D_{s^*0}(2317) \bar{K}$ current is also obtained, with mass around 2.9 GeV, the coupling of this state is found to be two times weaker than the one formed in $D f_0(980)$. On the other hand, few-body equations are solved for the $D K \bar{K}$ system and its coupled channels with the input $t$-matrices obtained by solving Bethe-Salpeter equations for the $D K$, $D\bar{K}$ and $K \bar{K}$ subsystems. In this study a $D$-like meson with mass 2.890 GeV and full width $\sim$ 55 MeV is found to get dynamically generated when $D K \bar{K}$ gets reorganized as $D f_0(980)$. However, no clear signal appears for the $D_{s^*0}(2317) \bar{K}$ configuration. The striking similarity between the results obtained in the two different models indicates strongly towards the existence of a $D f_0 (980)$ molecule with mass nearly 2.9 GeV.