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, $a_0(980),a_0(1450)$, as well as to the isodoublet resonances, $K_0^{\ast }(800),K_0^{\ast }(1430)$. In this work, we present a more extensive view on the mixing framework and extend this to the isoscalar resonances, $f_0(500)$, $f_0(980)$, $f_0(1370)$, $f_0(1500)$. 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 the two nonets, which, in fact, coincide roughly with the experimental observation. We identify that $f_0(500)$, $f_0(980)$ are the isoscalar members in the light nonet, and $f_0(1370)$, $f_0(1500)$ 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 $f_0(500),f_0(1370)$ among the members in light mass, and $f_0(980),f_0(1500)$ in heavy mass. The complication arises because the isoscalar members of each nonet are subject to an additional flavor mixing known as OZI rule so that $f_0(500),f_0(980)$, and similarly $f_0(1370),f_0(1500)$, are the mixture of two isoscalar members belonging to an octet and a singlet in SU${}_f$(3). 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.

16 pages, 2 figures, slightly modified, 2 references added

References in corpus (5)

• A low-lying scalar meson nonet in a unitarized meson model
• Mixing of scalar tetraquark and quarkonia states in a chiral approach
• Positive Parity Scalar Mesons in the 1-2 GeV Mass Range
• Testing confining potentials through meson/baryon hyperfine splitting ratio
• Four-quark structure of the excited states of heavy mesons

Cited by in corpus (15)

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• Nature of the vector resonance $Y(2175)$
• Hexaquark picture for $d^{\ast }(2380)$
• Resonance $Y(4660)$ as a vector tetraquark and its strong decay channels
• The Scalar Hexaquark $uuddss$: a Candidate to Dark Matter?
• Further signatures to support the tetraquark mixing framework for the two light-meson nonets
• Light axial-vector and vector resonances $X(2100)$ and $X(2239)$
• Fragmentation functions for axial-vector heavy tetraquarks: A TQ4Q1.1 update
• Testing the tetraquark mixing framework from QCD sum rules for $a_0(980)$
• Fragmentation of fully heavy tetraquarks: The TQ4Q1.1 functions as a case study
• The strong decays of the light scalar mesons $f_0(500)$ and $f_0(980)$
• Tetraquark-Jet Systems at the High-Luminosity LHC
• Tetraquark mixing supported by the partial decay widths of two light-meson nonets
• On the decay widths of radially excited scalar meson $K_0^{\ast }(1430)$ in view of new experimental data