Analysis of the possible $D\bar{D}_{s0}^*(2317)$ and $D^*\bar{D}_{s1}^*(2460)$ molecules with QCD sum rules

TL;DR

This study uses QCD sum rules to analyze potential molecular states composed of D and D* mesons with strange partners, finding their masses suggest they are likely resonance states rather than bound molecules.

Contribution

It constructs and applies color singlet-singlet interpolating currents within QCD sum rules to estimate masses of these exotic molecular states, considering vacuum condensates up to dimension-10.

Findings

Masses of Z1 and Z2 are around 4.6 GeV.

Results suggest these states are likely resonances, not bound molecules.

Masses are above the respective thresholds.

Abstract

In this article, we assume that there exist the pseudoscalar $D\bar{D}_{s0}^*(2317)$ and $D^*\bar{D}_{s1}^*(2460)$ molecular states $Z_{1,2}$ and construct the color singlet-singlet molecule-type interpolating currents to study their masses with the QCD sum rules. In calculations, we consider the contributions of the vacuum condensates up to dimension-10 and use the formula $\mu=\sqrt{M_{X/Y/Z}^{2}-\left(2{\mathbb{M}}_{c}\right)^{2}}$ to determine the energy scales of the QCD spectral densities. The numerical results, $M_{Z_1}=4.61_{-0.08}^{+0.11}\,\text{GeV}$ and $M_{Z_2}=4.60_{-0.06}^{+0.07}\,\text{GeV}$, which lie above the $D\bar{D}_{s0}^*(2317)$ and $D^*\bar{D}_{s1}^*(2460)$ thresholds respectively, indicate that the $D\bar{D}_{s0}^*(2317)$ and $D^*\bar{D}_{s1}^*(2460)$ are difficult to form bound state molecular states, the $Z_{1,2}$ are probably resonance states.