Analysis of the $D{\overline{D}}^{⁎}K$ System with QCD Sum Rules

Wang, Zhi-Gang  (Department of Physics, North China Electric Power University, Baoding 071003, China) ; Di, Zun-Yan (Department of Physics, North China Electric Power University, Baoding 071003, China) (School of Nuclear Science and Engineering, North China Electric Power University, Beijing 102206, China)

09 April 2019

Abstract: In this article, we construct the color singlet-singlet-singlet interpolating current with $I\left({J}^{P}\right)=\left(\mathrm{3}/\mathrm{2}\right)\left({\mathrm{1}}^{-}\right)$ to study the $D{\overline{D}}^{⁎}K$ system through QCD sum rules approach. In calculations, we consider the contributions of the vacuum condensates up to dimension-16 and employ the formula $\mu =\sqrt{{M}_{X/Y/Z}^{\mathrm{2}}-{\left(\mathrm{2}{\mathbb{M}}_{c}\right)}^{\mathrm{2}}}$ to choose the optimal energy scale of the QCD spectral density. The numerical result ${M}_{Z}=\mathrm{4.7}{\mathrm{1}}_{-\mathrm{0.11}}^{+\mathrm{0.19}} \mathrm{G}\mathrm{e}\mathrm{V}$ indicates that there exists a resonance state $Z$ lying above the $D{\overline{D}}^{⁎}K$ threshold to saturate the QCD sum rules. This resonance state $Z$ may be found by focusing on the channel $J/\psi \pi K$ of the decay $B\to J/\psi \pi \pi K$ in the future.

Published in: Advances in High Energy Physics 2019 (2019) 8958079