We study the $\rho \pi$ and $b_1\pi$ decay modes of the $1^{-+}$ light hybrid state within the framework of light-cone QCD sum rules. We use both the tensor current $\overline{\psi }{\sigma }_{\mu \nu }\psi$ and the derivative current $\overline{\psi }{\overleftrightarrow{D}}_{\mu }{\gamma }_5\psi$ as interpolating currents to calculate the partial decay width of the $b_1\pi$ decay mode. Comparing the sum rules obtained by using different currents, we obtain $\mathrm{\Gamma }({\pi }_1\to b_1\pi )=8–23$, 32–86 and 52–151 MeV for $m_{1^{-+}}=1.6$, 1.8 and 2.0 GeV respectively, which favor the results from the flux tube models and lattice simulations. We also use the tensor current to study the $\rho \pi$ decay mode, and although an extended stability criterion is needed, our results suggest a small partial decay width.

• Received 11 August 2016

DOI:https://doi.org/10.1103/PhysRevD.94.054037