The Quark-Level Linear σ Model

Abstract

This review of the quark-level linear σmodel is based upon the dynamical realization of the pseudoscalar and scalar mesons as a linear representation of SU(2) x SU(2) chiral symmetry, with the symmetry weakly broken by current quark masses. In its simplest SU(2) incarnation, with two non-strange quark flavors and three colors, this nonperturbative theory, which can be selfconsistently bootstrapped in loop order, is shown to accurately reproduce a host of low-energy observables with only one parameter, namely the pion decay constant f_π. Extending the scheme to SU(3) by including the strange quark, equally good results are obtained for many strong, electromagnetic, and weak processes just with two extra constants, viz. f_K and $\langleπ|H_{\mbox{\scriptsize weak}}|K\rangle$. Links are made with the vector-meson-dominance model, the BCS theory of superconductivity, and chiral-symmetry restoration at high temperature. Finally, these ideas are cautiously generalized to the electroweak sector, including the W, Z, and Higgs bosons, and also to CP violation.

Review, 34 pages, 14 figures with 24 graphs, 1 table, version accepted for publication in Fortschritte der Physik; v2: typos and 3 references corrected, Ref. [175] updated

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Cited by in corpus (14)

• Inhomogeneous chiral condensates
• Inhomogeneous phases in the quark-meson model with vacuum fluctuations
• Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL${}_2$ model
• Excited Scalar and Pseudoscalar Mesons in the Extended Linear Sigma Model
• Modern meson spectroscopy: the fundamental role of unitarity
• The role of the next-to-leading order triangle-shaped diagram in two-body hadronic decays
• Proximity of $f_0(1500)$ and $f_0(1710)$ to the scalar glueball
• Role of a four-quark and a glueball state in pion-pion and pion-nucleon scattering
• Ordinary and exotic mesons in the extended Linear Sigma Model
• Quark-antiquark states of the lightest scalar mesons within the Nambu-Jona-Lasinio model with flavor-dependent coupling constants
• Nambu's Nobel Prize, the $\sigma$ meson and the mass of visible matter
• Chiral effective theory of scalar and vector diquarks revisited
• Understanding the $f_0(980)$ and $a_0(980)$ masses as well as their widths
• Dispersion theory of nucleon polarizabilities and outlook on chiral effective field theory