H. Reinhardt

Effective hadron theory of QCD

Abstract We review present path-integral attempts to derive effective meson-baryon Lagrangians out of QCD or QCD-motivated quark models. There exist two different approaches to the solution of this problem for mesons. In the first case mesons are treated as composite quark-antiquark objects, whereas in the second case they are introduced as chiral phase of quark fields and external sources in the QCD Lagrangian. Our main attention is devoted to a discussion of the more dynamical first approach. This includes the hadronization of the Nambu-Jona-Lasinio model and various physical applications of the resulting effective Lagrangian concerning strong, electromagnetic and weak interactions of mesons. There emerge basically two principally different types of effective hadron theories reflecting the alternative (but at the same time dual) pictures of baryons: baryons as chiral (topological) solitons of the meson fields and as bound states of quarks and diquarks. It is demonstrated that these two pictures describe only two sides of the same medal.

The Elusiveness of infrared critical exponents in Landau gauge Yang-Mills theories

We solve a truncated system of coupled Dyson-Schwinger equations for the gluon and ghost propagators in

Baryons as chiral solitons in the Nambu-Jona-Lasinio model

\mathrm{SU}{(N}_{c})

Variational solution of the Yang-Mills Schrödinger equation in Coulomb gauge

Yang-Mills theories in Faddeev-Popov quantization on a four-torus. This compact space-time manifold provides an efficient mean to solve the gluon and ghost Dyson-Schwinger equations without any angular approximations. We verify that analytically two powerlike solutions in the very far infrared seem possible. However, only one of these solutions can be matched to a numerical solution for nonvanishing momenta. For a bare ghost-gluon vertex this implies that the gluon propagator is only weakly infrared vanishing,

Deconfinement in SU(2) Yang-Mills theory as a center vortex percolation transition

{D}_{\mathrm{gl}}{(k}^{2})\ensuremath{\propto}{(k}^{2}{)}^{2\ensuremath{\kappa}\ensuremath{-}1},

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

\ensuremath{\kappa}\ensuremath{\approx}0.595,

Baryons as bound states of diquarks and quarks in the Nambu-Jona-Lasinio model

and the ghost propagator is infrared singular,

Gluon propagator and quark confinement

{D}_{\mathrm{gh}}{(k}^{2})\ensuremath{\propto}{(k}^{2}{)}^{\ensuremath{-}\ensuremath{\kappa}\ensuremath{-}1}.

Confinement and scaling of the vortex vacuum of SU(2) lattice gauge theory

For nonvanishing momenta our solutions are in agreement with the results of recent SU(2) Monte Carlo lattice calculations. The running coupling possesses an infrared fixed point. We obtain