We argue that the low-lying scalar-meson nonet makes part of a subset of a family of infinitely many scalar-meson nonets, which in turn makes part of a family of infinitely many quark-antiquark bound states and resonances. We outline the properties of this subset.Comment: Talk presented at the workshop on "Scalar Mesons and Related Topics" honoring the 70th birthday of Michael Scadron, 11 pages, 7 figure

The quark-level linear σ model (LσM) is revisited, in particular concerning the identification of the f0(400–1200) (or σ(600)) scalar meson as the chiral partner of the pion. We demonstrate the predictive power of the LσM through the ππ and πNs-wave scattering lengths, as well as several electromagnetic, weak, and strong decays of pseudoscalar and vector mesons. The ease with which the data for these observables are reproduced in the LσM lends credit to the necessity to include the σ as a fundamental [Formula: see text] degree of freedom, to be contrasted with approaches like chiral perturbation theory or the confining NJL model of Shakin and Wang.

We report on a dispersion relation for the γγ → (ππ) I S-wave in isospin I emphasizing the low energy region. The f 0 (980) signal that emerges in γγ → ππ is also discussed. Our results could be used to distinguish between different ππ isoscalar S-wave parameterizations. We also calculate the width of the σ resonance to γγ and obtain the value Γ(σ → γγ) = (1.68 ± 0.15) KeV. Finally, we elaborate on the size of the f 0 (980) coupling to ππ and show that its smallness compared to the KK one is not related to the OZI rule.

By comparing SU (3)-breaking scales of linear mass formulae, it is shown that the lowest vector and scalar mesons all have aqq configuration, while the ground-state octet and decuplet baryons are qqq. Also, the quark-level linear σ model is employed to predict similarqq and qqq states. Furthermore, the approximate mass degeneracy of the scalar a0(985) and f0 (980) mesons is demonstrated to be accidental. Finally, it is shown that various strong, electromagnetic, and weak mesonic decay rates are successfully explained within the framework of the quark-level linear σ model.

On the basis of a new method for the derivation of the effective action the nonperturbative concept of "dynamical generation" is explained. A non-trivial, non-Hermitian and PT-symmetric solution for Wightman's scalar field theory in four dimensions is dynamically generated, rehabilitating Symanzik's precarious φ 4 -theory with a negative quartic coupling constant as a candidate for an asymptotically free theory of strong interactions. Finally it is shown making use of the dynamical generation that a Symanzik-like field theory with scalar confinement for the theory of strong interactions can be even suggested by experiment.