NLO QCD sum rules analysis of $1^{-+}$ tetraquark states

Abstract: We present an NLO QCD sum rules analysis of $J^{PC}=1^{-+}$ light four-quark states, investigated several compact tetraquark and four-quark molecule states, we obtain $1^{-+}$ light four-quark states masses,. Crucially, we have not find four-quark states with mass $\sim 1.4\,\text{GeV}$, which is the interpreted to be $π_1(1400)$ exotic state in previous leading-order studies. This result do not support the existence of $π_1(1400)$ state, agrees with the current experimental observation.