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.
Categories: hep-ph