Low-lying Scalars in an extended Linear $\sigma$ Model

Abstract

We formulate an extended linear $\sigma$ model of a quarkonia nonet and a tetraquark nonet as well as a complex iso-singlet (glueball) by virtue of chiral symmetry $S{U}_L(3)\times S{U}_R(3)$ and $U_A(1)$ symmetry. In the linear realization formalism, we study the mass spectra and components of the low-lying scalars and pseudo scalars in this model. The mass matrices for physical staes are obtained and the glueball candidates are examined. We find that the model can accommodate the mass spectra of low-lying states quite well. Our fits indicate that the most glueball like scalar should be 2 GeV or higher while the glueball pseudoscalar is $\eta (1756)$. We also examine the parameter region where the lightest iso-scalar $f_0(600)$ can be the glueball and quarkonia dominant but find such a parameter region may be confronted with the problem of the unbounded vacuum from below.

14 pages, 2 figures

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• Light scalar mesons in QCD
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Cited by in corpus (11)

• Is f0(1710) a glueball?
• Excited Scalar and Pseudoscalar Mesons in the Extended Linear Sigma Model
• Two-gluon and trigluon glueballs from dynamical holography QCD
• The role of the next-to-leading order triangle-shaped diagram in two-body hadronic decays
• Probing the substructure of $f_0(1370)$
• How tetraquarks can generate a second chiral phase transition
• Inverse Mass Hierarchy of Light Scalar Mesons Driven by Anomaly-Induced Flavor Breaking
• Chiral symmetry breaking patterns in the U_L(n)xU_R(n) meson model
• Phenomenology of a pseudoscalar glueball and charmed mesons
• Chiral phase transition with mixing between scalar quarkonium and tetraquark
• Baryon octet and decuplet phenomenology in a three-flavor extended linear sigma model