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

We present a next-to-leading order QCD sum rule analysis of $J^{PC}=1^{-+}$ light tetraquark states. By investigating various compact tetraquark and molecular configurations, we determine the mass spectrum of these states. Our calculations exclude the possibility that $\pi_{1}(1400)$ is a tetraquark or hybrid-tetraquark mixture. This suggests that it may not exist, which is consistent with recent experimental results. In contrast, we obtained multiple $1^{-+}$ states around $2.0\,\text{GeV}$ that match well with $\pi_{1}(2015)$, which makes us confident that $\pi_{1}(2015)$ is a tetraquark candidate. As for $\pi_{1}(1600)$, our results indicate that the tetraquark currents tend to couple to heavier states, reducing the possibility of it being a tetraquark, while earlier studies suggested the opposite.