Tetraquark mixing framework for isoscalar resonances in light mesons

Kim, H.*; Kim, K. S.*; Cheoun, M.-K.*; Oka, Makoto   

A tetraquark mixing framework has been applied successfully to the isoscalar resonances, , , and . Tetraquarks in this framework can have two spin configurations containing either spin-0 diquark or spin-1 diquark and each configuration forms a nonet in flavor space. The two spin configurations are found to mix strongly through the color-spin interactions. Their mixtures, which diagonalize the hyperfine masses, can generate the physical resonances constituting two nonets, which, in fact, coincide roughly with the experimental observation. We identify that , are the isoscalar members in the light nonet, and , are the similar members in the heavy nonet. The complication arises because the isoscalar members of each nonet are subject to an additional flavor mixing known as Okubo-Zweig-Iizuka rule. The tetraquark mixing framework including the flavor mixing is tested for the isoscalar resonances in terms of the mass splitting and the fall-apart decay modes. The mass splitting among the isoscalar resonances is found to be consistent qualitatively with their hyperfine mass splitting strongly driven by the spin configuration mixing, which suggests that the tetraquark mixing framework works. The fall-apart modes from our tetraquarks also seem to be consistent with the experimental modes. We also discuss possible existence of the spin-1 tetraquarks that can be constructed by the spin-1 diquark.