A tetraquark 81-plet with JPC=1⁻⁺ or a hybrid nonet

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 π ₁(1600) π 1 ( 1600 ) and η ₁(1855) η 1 ( 1855 ) as candidate tetraquark states with exotic quantum numbers JPC = 1⁻⁺ J PC = 1 - + . Within the hybrid framework, an $$ SU(3) $$ S U ( 3 ) flavor nonet is expected, featuring two isoscalar configurations, qq̄g q q ¯ g and ss̄g s s ¯ g , where $$q = u/d $$ q = u / d . Moreover, the decay width of the ss̄g s s ¯ g state into the K^* K̄^* K ∗ K ¯ ∗ channel ( VV ) is found to be two orders of magnitude smaller than that into the η η ^ η η ′ channel ( PP ) [1]. In contrast, the tetraquark scenario predicts an $$ SU(3) $$ S U