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

Abstract

In this article, we assume that there exist the pseudoscalar $D{\bar{D}}_{s0}^{\ast }(2317)$ and $D^{\ast }{\bar{D}}_{s1}^{\ast }(2460)$ 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 $D{\bar{D}}_{s0}^{\ast }(2317)$ and $D^{\ast }{\bar{D}}_{s1}^{\ast }(2460)$ thresholds respectively, indicate that the $D{\bar{D}}_{s0}^{\ast }(2317)$ and $D^{\ast }{\bar{D}}_{s1}^{\ast }(2460)$ are difficult to form bound state molecular states, the $Z_{1,2}$ are probably resonance states.

arXiv comment17 pages, 10 figures. arXiv admin note: text overlap with arXiv:1806.08703, arXiv:1901.05196, arXiv:1802.05354

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• Excited $K$ meson, $K_c(4180)$, with hidden charm as a $D\bar{D}K$ bound state
• ${\bar{D}}_s^{(\ast )}{D}^{(\ast )}$ molecular state with $J^P=1^{+}$
• Study of ${\Lambda }_c$${\Lambda }_c$ dibaryon and ${\Lambda }_c$${\bar{\Lambda }}_c$ baryonium states via QCD sum rules
• Faddeev fixed-center approximation to the $D\bar{D}K$ system and the hidden charm $K_{c\bar{c}}(4180)$ state
• Tetraquark molecular states in the $D_s{\bar{D}}_{s1}$ and $D_s^{\ast }{\bar{D}}_{s0}^{\ast }$ mass spectrum