The Linear Meson Model and Chiral Perturbation Theory

We compare the linear meson model and chiral perturbation theory in next to leading order in the quark mass expansion. In particular, we compute the couplings L_4--L_8 of chiral perturbation theory as functions of the parameters of the linear model. They are induced by the exchange of 0^{++} scalar mesons. We use a phenomenological analysis of the effective vertices of the linear model in terms of pseudoscalar meson masses and decay constants. Our results for the L_i agree with previous phenomenological estimates.Comment: 21 pages, LaTe

Effective linear meson model

The effective action of the linear meson model generates the mesonic n-point functions with all quantum effects included. Based on chiral symmetry and a systematic quark mass expansion we derive relations between meson masses and decay constants. The model ``predicts'' values for f_eta and f_eta' which are compatible with observation. This involves a large momentum dependent eta-eta' mixing angle which is different for the on--shell decays of the eta and the eta'. We also present relations for the masses of the 0^{++} octet. The parameters of the linear meson model are computed and related to cubic and quartic couplings among pseudoscalar and scalar mesons. We also discuss extensions for vector and axialvector fields. In a good approximation the exchange of these fields is responsible for the important nonminimal kinetic terms and the eta-eta' mixing encountered in the linear meson model.Comment: 79 pages, including 3 abstracts, 9 tables and 9 postscript figures, LaTeX, requires epsf.st

Quark and Nuclear Matter in the Linear Chiral Meson Model

We present an analytical description of the phase transitions from a nucleon gas to nuclear matter and from nuclear matter to quark matter within the same model. The equation of state for quark and nuclear matter is encoded in the effective potential of a linear sigma model. We exploit an exact differential equation for its dependence upon the chemical potential $\mu$ associated to conserved baryon number. An approximate solution for vanishing temperature is used to discuss possible phase transitions as the baryon density increases. For a nucleon gas and nuclear matter we find a substantial density enhancement as compared to quark models which neglect the confinement to baryons. The results point out that the latter models are not suitable to discuss the phase diagram at low temperature.Comment: 27 pages, Int.J.Mod.Phys.A versio

Signals of confinement in Green functions of SU(2) Yang-Mills theory

The vortex picture of confinement is employed to explore the signals of confinement in Yang-Mills Green functions. By using SU(2) lattice gauge theory, it has been well established that the removal of the center vortices from the lattice configurations results in the loss of confinement. The running coupling constant, the gluon and the ghost form factors are studied in Landau gauge for both cases, the full and the vortex removed theory. In the latter case, a strong suppression of the running coupling constant and the gluon form factor at low momenta is observed. At the same time, the singularity of the ghost form factor at vanishing momentum disappears. This observation establishes an intimate correlation between the ghost singularity and confinement. The result also shows that a removal of the vortices generates a theory for which Zwanziger's horizon condition for confinement is no longer satisfied.Comment: 4 pages, 4 figure