A low lying scalar meson nonet in a unitarized meson model

Abstract

A unitarized nonrelativistic meson model which is successful for the description of the heavy and light vector and pseudoscalar mesons yields, in its extension to the scalar mesons but for the same model parameters, a complete nonet below 1 GeV. In the unitarization scheme, real and virtual meson-meson decay channels are coupled to the quark-antiquark confinement channels. The flavor-dependent harmonic-oscillator confining potential itself has bound states ǫ(1.3 GeV), S(1.5 GeV), δ(1.3 GeV), κ(1.4 GeV), similar to the results of other bound-state qq models. However, the full coupled-channel equations show poles at ǫ(0.5 GeV), S(0.99 GeV), δ(0.97 GeV), κ(0.73 GeV). Not only can these pole positions be calculated in our model, but also cross sections and phase shifts in the meson-scattering channels, which are in reasonable agreement with the available data for ππ, ηπ and Kπ in S-wave scattering.

Are three flavors special?

“…As noted in the Appendix, the axial U(1) transformation properties of M and M (2) differ from each other and provide a measure of whether the state is of one quark-antiquark type, two quark -antiquark type etc. In the chiral Lagrangian there are terms which break the axial U(1) in a manner dictated by the QCD axial anomaly.…”

“…In fact it was shown in the first of [30] that the molecular form can be transformed using Fierz identities to a linear combination of the "diquark-antidiquark" forms. We thus assume that some unspecified linear combination of M (2) , M (3) and M (4) , denoted by M ′ , represents the qqqq chiral nonet which mixes with M . The decomposition into pseudoscalar and scalar fields is given by,…”

Diquark Correlations in Baryons: The Interacting Quark Diquark Model

“…of Ref. [66,67] in which the loop contributions are given by the hadronic intermediate states that each meson can access. It is via these hadronic loops that the bare states become "dressed" and the hadronic loop contributions totally dominate the dynamics of the process.…”

On the low energy end of the QCD spectrum

“…We are by no means the first to find a resonance in the vicinity of the above position. In the list of papers quoted by the Particle Data Group [40], the earliest one with a pole in this ball park appeared more than 20 years ago [41]. What is new is that we can perform an error calculation, because our method is free of the systematic theoretical uncertainties inherent in models and parametrizations.…”