Dyson-Schwinger equations: Density, temperature and continuum strong QCD

Masses of the ground state and the orbitally and radially excited states of quark-antiquark mesons composed of light $(u,d,s)$ quarks are calculated within the framework of the relativistic quark model based on the quasipotential approach. The relativistic treatment of the light quark dynamics results in mass spectra which agree well with available experimental data for the masses of the most well-established states. The Regge trajectories for angular and radial excitations are constructed, and their linearity, parallelism, and equidistance are verified. The assignment of experimentally observed light mesons to particular Regge trajectories is based on their masses and quantum numbers.

Mass spectra and Regge trajectories of light mesons in the relativistic quark model

Extended NJL model for light and heavy mesons without q-q thresholds

Baryons as chiral solitons in the nambu-jona-lasinio model

The historical development of the Nambu–Jona-Lasinio (NJL) model is briefly reviewed. The SU(2) × SU(2) and U(3) × U(3) local quark NJL models are considered. The mechanisms responsible for spontaneous breaking of chiral symmetry and vector dominance are exhibited. The local NJL model is adequate in describing the mass spectrum and the strong and electroweak decay modes of the four ground-state meson nonets: pseudoscalar, scalar, vector, and axial-vector. The applicability of the model to mesons in a hot dense medium is discussed. It is shown that solving problems related to the description of meson radial excitations and quark confinement requires the nonlocal extension of the NJL model. The primary emphasis of this review is on the methods that are used in various versions of the NJL model. The reader is referred to the cited works for what these models predict in low-energy hadron physics.

https://iopscience.iop.org/article/10.1070/PU2006v049n06ABEH005905/pdf

D. Ebert

Papers

Effective hadron theory of QCD