Abstract: I will describe a method based on chiral susceptibility, which enables one to draw a phase diagram in the chemical-potential--temperature plane for strongly interacting quarks whose interactions are described by any reasonable gap equation, even if the diagrammatic content of the quark-gluon vertex is unknown. At temperatures above but near that for which chiral symmetry is restored, I found that in addition to the normal and plasmino modes the dressed-quark spectral function also exhibits an essentially nonperturbative zero mode. This long-wavelength mode gives a hint that the system may fairly be described as a strongly-coupled state of matter.
In addition, I will explain a form for the rainbow-ladder kernel whose momentum-dependence is consonant with modern DSE- and lattice-QCD results, and assess its capability as a tool in hadron physics. Using it, ground-state, radially-excited and exotic scalar-, vector- and flavoured-pseudoscalar-mesons are studied. Although the inability of this truncation to provide realistic predictions for the masses of excited- and exotic-states is confirmed and explained, it is potentially useful in proceeding beyond this leading-order truncation and also able to highlight and illustrate some features of hadron observables that do not depend on details of the dynamics.
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