arXiv subjects

D. -U. Jungnickel

Publications and source records attributed to D. -U. Jungnickel.

11 recordsLinked to original sources

arXiv2003

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 $μ$ 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.

hep-ph↗

arXiv1999

Flow Equations for Phase Transitions in Statistical Physics and QCD

We review the formalism of the effective average action in quantum field theory which corresponds to a coarse grained free energy in statistical mechanics. The associated exact renormalization group equation and possible nonperturbative approximations for its solution are discussed. We describe in detail O(N)-symmetric scalar theories in two and three dimensions. These ideas are also applied to QCD where one observes the consecutive emergence of mesonic bound states and spontaneous chiral symmetry breaking as the coarse graining scale is lowered. We finally present a study of the chiral phase transition in two flavor QCD. A precision estimate of the universal critical equation of state for the three-dimensional O(4) Heisenberg model is presented. We explicitly connect the O(4) universal behavior near the critical temperature and zero quark mass with the physics at zero temperature and a realistic pion mass. For realistic quark masses the pion correlation length near T_c turns out to be smaller than its zero temperature value.

hep-ph↗

arXiv1998

The Chiral Phase Transition at High Baryon Density from Nonperturbative Flow Equations

We investigate the QCD chiral phase transition at high baryon number density within the linear quark meson model for two flavors. The method we employ is based on an exact renormalization group equation for the free energy. Truncated nonperturbative flow equations are derived at nonzero chemical potential and temperature. Whereas the renormalization group flow leads to spontaneous chiral symmetry breaking in vacuum, we find a chiral symmetry restoring first order transition at high density. Combined with previous investigations at nonzero temperature, the result implies the presence of a tricritical point with long--range correlations in the phase diagram.

hep-ph↗

arXiv1998

The chiral phase transition from the exact RG

A brief introduction is given to the concept of the effective average action. Its dependence on the averaging or coarse graining scale is governed by an exact RG equation for which nonperturbative approximation schemes are described. This formalism is applied to the computation of the equation of state for two flavor QCD within an effective linear quark meson model. Our results allow to derive the temperature and quark mass dependence of quantities like the chiral condensate or the pion mass. A precision estimate of the universal critical equation of state for the three--dimensional O(4) Heisenberg model is given. The exact RG formalism applied to the linear quark meson model is demonstrated to provide an explicit link between the O(4) universal behavior near the critical temperature and zero quark mass on one hand and the physics at low temperatures and realistic current quark masses, i.e., the domain of validity of chiral perturbation theory on the other hand.

hep-ph↗

arXiv1997

Two flavor chiral phase transition from nonperturbative flow equations

We employ nonperturbative flow equations to compute the equation of state for two flavor QCD within an effective quark meson model. This yields the temperature and quark mass dependence of quantities like the chiral condensate or the pion mass. A precision estimate of the universal critical equation of state for the three-dimensional O(4) Heisenberg model is presented. We explicitly connect the O(4) universal behavior near the critical temperature and zero quark mass with the physics at zero temperature and a realistic pion mass. For realistic quark masses the pion correlation length near T_c turns out to be smaller than its zero temperature value.

hep-ph↗

arXiv1996

Nonperturbative Flow Equations and Low--Energy QCD

hep-ph↗

arXiv1996

Quark masses from the linear meson model

Quark mass ratios are expressed within the linear meson model by universal relations involving only the masses and decay constants of the flavored pseudoscalars as well as their wave function renormalization. Quantitative results are in agreement with those obtained from chiral perturbation theory, with a tendency to a somewhat higher strange quark mass.

hep-ph↗

arXiv1996

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.

hep-ph↗

arXiv1995

Quarks, mesons and (exact) flow equations

Dynamical chiral symmetry breaking is described within the linear sigma model of QCD coupled to quarks. The main technical tool used for this intrinsically non--perturbative problem is an exact renormalization group equation for the quantum effective action. It is demonstrated that realistic values for phenomenological quantities like the pion decay constant, constituent quark masses or the chiral condensate are obtainable.

hep-ph↗

arXiv1995

Effective Action for the Quark-Meson Model

The scale dependence of an effective average action for mesons and quarks is described by a nonperturbative flow equation. The running couplings lead to spontaneous chiral symmetry breaking. We argue that for strong Yukawa coupling between quarks and mesons the low momentum physics is essentially determined by infrared fixed points. This allows us to establish relations between various parameters related to the meson potential. The results for $f_π$ and $\VEV{\olpsiψ}$ are not very sensitive to the poorly known details of the quark--meson effective action at scales where the mesonic bound states form. For realistic constituent quark masses we find $f_π$ around $100\MeV$.

hep-ph↗

arXiv1993

Chiral Hierarchies, Compositeness and the Renormalization Group

A wide class of models involve the fine--tuning of significant hierarchies between a strong--coupling ``compositeness'' scale, and a low energy dynamical symmetry breaking scale. We examine the issue of whether such hierarchies are generally endangered by Coleman--Weinberg instabilities. A careful study using perturbative two--loop renormalization group methods finds that consistent large hierarchies are not generally disallowed.

hep-th↗