We study scalar, pseudoscalar, vector, and axial-vector mesons with non-strange and strange quantum numbers in the framework of a linear sigma model with global chiral U (N f )L × U (N f )R symmetry. We perform a global fit of meson masses, decay widths, as well as decay amplitudes. The quality of the fit is, for a hadronic model that does not consider isospin-breaking effects, surprisingly good. We also investigate the question whether the scalarqq states lie below or above 1 GeV and find the scalar states above 1 GeV to be preferred asqq states. Additionally, we also describe the axial-vector resonances asqq states.

We present a two-flavour linear sigma model with global chiral symmetry and vector and axialvector mesons. We calculate ππ scattering lengths and the decay widths of scalar, vector, and axial-vector mesons. It is demonstrated that vector and axial-vector meson degrees of freedom play an important role in these low-energy processes and that a reasonable theoretical description requires globally chirally invariant terms other than the vector meson mass term. An important question for meson vacuum phenomenology is the quark content of the physical scalar f0(600) and a0(980) mesons. We investigate this question by assigning the quark-antiquark σ and a0 states of our model with these physical mesons. We show via a detailed comparison with experimental data that this scenario can describe all vacuum properties studied here except for the decay width of the σ, which turns out to be too small. We also study the alternative assignment f0(1370) and a0(1450) for the scalar mesons. In this case the decay width agrees with the experimental value, but the ππ scattering length a 0 0 is too small. This indicates the necessity to extend our model by additional scalar degrees of freedom.

In the framework of the U (2) R × U (2) L symmetric linear sigma model with (axial)vector mesons generalized by including a dilaton field we study the phenomenology of the scalar-isoscalar resonances below 2 GeV. It turns out that, in our favoured scenario, the resonance f 0 (1370) is predominantly aqq state and f 0 (1500) is predominantly a glueball state. Additionally we are able to calculate the value of the gluon condensate, which is in agreement with lattice QCD results.

We revisit and extend previous calculations of glueball decay rates in the Sakai-Sugimoto model, a holographic top-down approach for QCD with chiral quarks based on D8-D8 probe branes in Witten's holographic model of nonsupersymmetric Yang-Mills theory. The rates for decays into two pions, two vector mesons, four pions, and the strongly suppressed decay into four π 0 are worked out quantitatively, using a range of the 't Hooft coupling which closely reproduces the decay rate of ρ and ω mesons and also leads to a gluon condensate consistent with QCD sum rule calculations. The lowest holographic glueball, which arises from a rather exotic polarization of gravitons in the supergravity background, turns out to have a significantly lower mass and larger width than the two widely discussed glueball candidates f 0 (1500) and f 0 (1710). The lowest nonexotic and predominantly dilatonic scalar mode, which has a mass of 1487 MeV in the Witten-Sakai-Sugimoto model, instead provides a narrow glueball state, and we conjecture that only this nonexotic mode should be identified with a scalar glueball component of f 0 (1500) or f 0 (1710). Moreover the decay pattern of the tensor glueball is determined, which is found to have a comparatively broad total width when its mass is adjusted to around or above 2 GeV.