Model for light scalars in QCD

Abstract

We propose a systematic procedure to study a generalized linear sigma model which can give a physical picture of possible mixing between $q\bar{q}$ and $qq\bar{q}\bar{q}$ low lying spin zero states. In the limit of zero quark masses, we derive the model independent results for the properties of the Nambu Goldstone pseudoscalar particles. For getting information on the scalars it is necessary to make a specific choice of terms. We impose two plausible physical criteria - the modeling of the axial anomaly and the suppression of effective vertices representing too many fermion lines - for limiting the large number of terms which are allowed on general grounds. We calculate the tree-level spectrum based on the leading terms in our approach and find that it prominently exhibits a very low mass isosinglet scalar state. Finally we point out that the low energy result for scattering of pions continues to hold in the general version of the model.

4 pages, 1 figure

References in corpus (16)

• Big-Bang nucleosynthesis (Particle Data Group mini-review)
• The Cosmological Parameters 2006
• Scalar mesons above and below 1 GeV
• Mechanism for a next-to-lowest lying scalar meson nonet
• Toy model for two chiral nonets
• Unitarized pseudoscalar meson scattering amplitudes in three flavor linear sigma models
• Scalar meson and glueball decays within a effective chiral approach
• A chiral model for bar{q}q and bar{q}bar{q}qq$ mesons
• QCD Tests of the Puzzling Scalar Mesons
• Isosinglet Scalar Mesons Below 2 GeV and the Scalar Glueball Mass
• Nature of the light scalar mesons
• Mass Uncertainties of f0(600) and f0(1370) and their Effects on Determination of the Quark and Glueball Admixtures of the I=0 Scalar Mesons
• Mixing among light scalar mesons and L=1 q\bar{q} scalar mesons
• Effects to Scalar Meson Decays of Strong Mixing between Low and High Mass Scalar Mesons
• Positive Parity Scalar Mesons in the 1-2 GeV Mass Range
• Anomaly induced QCD potential and Quark Decoupling

Cited by in corpus (28)

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• Global aspects of the scalar meson puzzle
• Note on a sigma model connection with instanton dynamics
• Conformal anomaly and the vector coupling in dense matter
• f0(980) meson as a K bar K molecule in a phenomenological Lagrangian approach
• Two chiral nonet model with massless quarks
• Strong and radiative decays of the scalars f0(980) and a0(980) in a hadronic molecule approach
• Chiral Nonet Mixing in pi pi Scattering
• Excited Scalar and Pseudoscalar Mesons in the Extended Linear Sigma Model
• Elementarity of composite systems
• The non-ordinary Regge behavior of the K*0(800) or Kappa-meson versus the ordinary K*0(1430)
• Chiral Nonet Mixing in ${\eta }^{\prime }\to \eta \pi \pi$ Decay
• Semi-leptonic $D_s^{+}$(1968) decays as a scalar meson probe
• Are three flavors special?
• Probing the substructure of $f_0(1370)$
• How tetraquarks can generate a second chiral phase transition
• Proximity of $f_0(1500)$ and $f_0(1710)$ to the scalar glueball
• Low-lying Scalars in an extended Linear $\sigma$ Model
• Generalized linear sigma model with two glueballs
• Chiral Nonet Mixing in $\pi K$ Scattering
• Probing scalar mesons in semi-leptonic decays of $D_s^{+}$, $D^{+}$ and $D^0$
• Spinless mesons and glueballs mixing patterns in SU(3) flavor limit
• Quark and glue spectroscopy of scalars and pseudoscalars in SU(3) flavor limit
• Two-body decay widths of lowest lying and next-to-lowest lying scalar and pseudoscalar mesons in generalized linear sigma model
• Two or Four: A Hint from Scalar Mesons in Radiative phi Decays ?
• Baryon octet and decuplet phenomenology in a three-flavor extended linear sigma model
• Examining a possible cascade effect in chiral symmetry breaking