# Further signatures to support the tetraquark mixing framework for the two light-meson nonets

Kim, Hungchong (Research Institute of Basic Science, Korea Aerospace University, Goyang, 412-791, Korea) (Center for Extreme Nuclear Matters, Korea University, Seoul 02841, 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) ; Jido, Daisuke (Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan) ; Oka, Makoto (Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan)

03 February 2019

Abstract: In this work, we investigate additional signatures to support the tetraquark mixing framework that has been recently proposed as a possible structure for the two nonets, namely ${a}_{0}\left(980\right)$, ${K}_{0}^{*}\left(800\right)$, ${f}_{0}\left(500\right)$, and ${f}_{0}\left(980\right)$ in the light nonet and ${a}_{0}\left(1450\right)$, ${K}_{0}^{*}\left(1430\right)$, ${f}_{0}\left(1370\right)$, and ${f}_{0}\left(1500\right)$ in the heavy nonet. First, we advocate that the two nonets form the flavor nonet approximately satisfying the Gell-Mann–Okubo mass relation. Then we reexamine the mass ordering generated from the tetraquark nonets and show that this mass ordering is satisfied by the two nonets although the ordering in the heavy nonet is marginal. The marginal mass ordering however can be regarded as another signature for tetraquarks because it can be explained partially by the hyperfine masses calculated from the tetraquark mixing framework. The tetraquark mixing parameters are found to be independent of isospins giving additional support for the formation of the flavor nonets. In addition, we discuss the other approaches like two-quark pictures or meson-meson bound states, and their possible limitations in explaining the two nonets. As a peculiar signature distinguished from other approaches, we investigate the fall-apart coupling strengths into two vector mesons from our tetraquarks. Coupling strengths into the two-vector modes are found to enhance strongly in the heavy nonet while they are suppressed in the light nonet. The coupling ratios, which depend on the isospin channel, are found to be huge around $\sim 15$. This trend in the two-vector modes, which is opposite to that in the two-pseudoscalar fall-apart modes, can provide another testing ground for the tetraquark mixing framework. Some experimental evidence related to the phenomena is discussed particularly from the resonances belonging to the heavy nonet.

Published in: Physical Review D 99 (2019)