Tetraquark mixing framework for isoscalar resonances in light mesons

Kim, Hungchong (Research Institute of Basic Science, Korea Aerospace University, Goyang 412-791, Korea) ; Kim, K. S. (School of Liberal Arts and Science, Korea Aerospace University, Goyang 412-791, Korea) ; Cheoun, Myung-Ki (Department of Physics, Soongsil University, Seoul 156-743, Korea) ; Oka, Makoto (Department of Physics, Tokyo Institute of Technology, Meguro 152-8551, Japan) (Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan)

09 May 2018

Abstract: Recently, a tetraquark mixing framework has been proposed for light mesons and applied more or less successfully to the isovector resonances, ${a}_{0}\left(980\right)$, ${a}_{0}\left(1450\right)$, as well as to the isodoublet resonances, ${K}_{0}^{*}\left(800\right),{K}_{0}^{*}\left(1430\right)$. In this work, we present a more extensive view on the mixing framework and apply this framework to the isoscalar resonances, ${f}_{0}\left(500\right)$, ${f}_{0}\left(980\right)$, ${f}_{0}\left(1370\right)$, ${f}_{0}\left(1500\right)$. 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 ${f}_{0}\left(500\right)$, ${f}_{0}\left(980\right)$ are the isoscalar members in the light nonet, and ${f}_{0}\left(1370\right)$, ${f}_{0}\left(1500\right)$ are the similar members in the heavy nonet. This means that the spin configuration mixing, as it relates the corresponding members in the two nonets, can generate ${f}_{0}\left(500\right)$, ${f}_{0}\left(1370\right)$ among the members in light mass, and ${f}_{0}\left(980\right)$, ${f}_{0}\left(1500\right)$ in heavy mass. The complication arises because the isoscalar members of each nonet are subject to an additional flavor mixing known as Okubo-Zweig-Iizuka rule so that ${f}_{0}\left(500\right)$, ${f}_{0}\left(980\right)$, and similarly ${f}_{0}\left(1370\right)$, ${f}_{0}\left(1500\right)$, are the mixture of two isoscalar members belonging to an octet and a singlet in ${\mathrm{SU}}_{f}\left(3\right)$. 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.

Published in: Physical Review D 97 (2018)