A hybrid nonet with $J^{PC}=1^{-+}$ or a tetraquark 81-plet

TL;DR

This paper uses QCD sum rules to differentiate between hybrid mesons and tetraquark states with exotic quantum numbers, providing mass estimates and decay predictions to guide experimental identification.

Contribution

It systematically compares hybrid and tetraquark models for $J^{PC}=1^{-+}$ states, offering mass predictions and decay channels to distinguish their nature.

Findings

Mass of $ssar{s}ar{s}$ tetraquark estimated at 2.22 GeV

Tetraquark expected to decay into $ ext{phi} ext{phi}$ and $ ext{eta}f_1(1420)$

Experimental spectra analysis can differentiate hybrid from tetraquark states

Abstract

Confirming the existence of hybrid states remains challenging due to their experimental indistinguishability from tightly bound tetraquarks and loosely bound molecules. To address this issue, we employ QCD sum rules to systematically investigate the $\pi_1(1600)$ and $\eta_1(1855)$ as candidate tetraquark states with exotic quantum numbers $J^{PC} = 1^{-+}$. Within the hybrid framework, an $SU(3)$ flavor nonet is expected, featuring two isoscalar configurations, $q\bar{q}g$ and $s\bar{s}g$, where $q = u/d$. In contrast, the tetraquark scenario predicts an $SU(3)$ flavor 81-plet comprising three isoscalar states: $qq\bar{q}\bar{q}$, $qs\bar{q}\bar{s}$, and $ss\bar{s}\bar{s}$. Our analysis yields a mass of $2.22^{+0.18}_{-0.26}$ GeV for the $ss\bar{s}\bar{s}$ tetraquark state, which is expected to decay predominantly into the $\phi\phi$ and $\eta f_1(1420)$ final states. Therefore, experimental scrutiny of their invariant mass spectra is pivotal for distinguishing between hybrid and tetraquark interpretations.