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

Abstract

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.