Tetraquark mixing framework for isoscalar resonances in light mesons

Abstract

Recently, a tetraquark mixing framework has been proposed for light mesons and applied more or less successfully to the isovector resonances, a 0 ð980Þ, a 0 ð1450Þ, as well as to the isodoublet resonances,. In this work, we present a more extensive view on the mixing framework and apply this framework to the isoscalar resonances, f 0 ð500Þ, f 0 ð980Þ, f 0 ð1370Þ, f 0 ð1500Þ. 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 ð500Þ, f 0 ð980Þ are the isoscalar members in the light nonet, and f 0 ð1370Þ, f 0 ð1500Þ 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 ð500Þ, f 0 ð1370Þ among the members in light mass, and f 0 ð980Þ, f 0 ð1500Þ 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 ð500Þ, f 0 ð980Þ, and similarly f 0 ð1370Þ, f 0 ð1500Þ, are the mixture of two isoscalar members belonging to an octet and a singlet in SU f ð3Þ. 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.

Testing the tetraquark mixing framework from QCD sum rules for a0(980)

“…But the QCD sum rule constructed from the spin-0 diquark configuration alone fails to predict the a 0 (980) mass. Our results therefore support the tetraquark mixing framework for the two light-meson nonets established in the constituent quark picture [19][20][21][22].…”

“…The second tetraquark type, |011 , which was suggested as another possibility in Refs. [19][20][21][22]32], is constructed by combining the spin-1 diquark in the structure of (6 c ,3 f ) and its antidiquark. By construction, the two tetraquark types differ by color and spin configurations but they have the same flavor structure, namely the nonet.…”

“…Here α, β are the mixing parameters determined in each isospin channel by the diagonalization process. But they are found to be almost independent of isospin [19][20][21][22] and their values are approximately close to α ≈ 2/3, β ≈ 1/3. This basically implies that the wave functions in Eqs.…”

“…The mixing parameters in this I = 1 channel are determined to be [19][20][21][22] α = 0.8167 , β = 0.5770 .…”

“…In practice, the QCD sum rule [24][25][26] or lattice QCD calculation [27] can be used for this purpose. One surprising result to test is the statement that the light nonet has more probability to stay in the second type tetraquark containing the spin-1 diquark rather than in the first type involving the spin-0 diquark [19][20][21][22]. This picture is very different from the common expectation that the light nonet has the structure of the first tetraquark type only [15-18, 28, 29].…”