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

TL;DR

This paper uses next-to-leading order QCD sum rules to analyze $1^{-+}$ light tetraquark states, identifying candidates around 2.0 GeV and excluding certain states like $ ext{pi}_1(1400)$ as tetraquarks.

Contribution

It provides a detailed NLO QCD sum rule analysis of $1^{-+}$ tetraquark states, clarifying their mass spectrum and challenging previous interpretations of specific resonances.

Findings

Excludes $ ext{pi}_1(1400)$ as a tetraquark or hybrid-tetraquark.

Identifies multiple $1^{-+}$ states around 2.0 GeV matching $ ext{pi}_1(2015)$.

Suggests $ ext{pi}_1(1600)$ is unlikely a tetraquark based on coupling tendencies.

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.