arXiv subjects

J. Berges

Publications and source records attributed to J. Berges.

87 records · Page 5Linked to original sources

arXiv1999

Magnetic fields within color superconducting neutron star cores

We discuss the Meissner effect for a color superconductor formed by cold dense quark matter. Though color and ordinary electromagnetism are broken in a color superconductor, there is a linear combination of the photon and a gluon that remains massless. Consequently, a color superconducting region may be penetrated by an external magnetic field. We show that at most a small fraction of the magnetic field is expelled, and if the screening distance is the smallest length scale in the problem there is no expulsion at all. We calculate the behavior of the magnetic field for a spherical geometry relevant for compact stars. If a neutron star contains a quark matter core, this core is a color superconductor. Our results demonstrate that such cores admit magnetic fields without restricting them to quantized flux tubes. Such magnetic fields within color superconducting neutron star cores are stable on time scales longer than the age of the universe, even if the spin period of the neutron star is changing.

hep-ph↗

arXiv1999

Gapless Color Superconductivity

We present the dispersion relations for quasiparticle excitations about the color-flavor locked ground state of QCD at high baryon density. In the presence of condensates which pair light and strange quarks there need not be an energy gap in the quasiparticle spectrum. This raises the possibility of gapless color superconductivity, with a Meissner effect but no minimum excitation energy. Analysis within a toy model suggests that gapless color superconductivity may occur only as a metastable phase.

hep-ph↗

arXiv1999

Unlocking Color and Flavor in Superconducting Strange Quark Matter

We explore the phase diagram of strongly interacting matter with massless u and d quarks as a function of the strange quark mass m_s and the chemical potential mu for baryon number. Neglecting electromagnetism, we describe the different baryonic and quark matter phases at zero temperature. For quark matter, we support our model-independent arguments with a quantitative analysis of a model which uses a four-fermion interaction abstracted from single-gluon exchange. For any finite m_s, at sufficiently large mu we find quark matter in a color-flavor locked state which leaves a global vector-like SU(2)_{color+L+R} symmetry unbroken. As a consequence, chiral symmetry is always broken in sufficiently dense quark matter. As the density is reduced, for sufficiently large m_s we observe a first order transition from the color-flavor locked phase to a color superconducting phase analogous to that in two flavor QCD. At this unlocking transition chiral symmetry is restored. For realistic values of m_s our analysis indicates that chiral symmetry breaking may be present for all densities down to those characteristic of baryonic matter. This supports the idea that quark matter and baryonic matter may be continuously connected in nature. We map the gaps at the quark Fermi surfaces in the high density color-flavor locked phase onto gaps at the baryon Fermi surfaces at low densities.

hep-ph↗

arXiv1999

QCD in Extreme Conditions and the Wilsonian `Exact Renormalization Group'

This is an introduction to the use of nonperturbative flow equations in strong interaction physics at nonzero temperature and baryon density. We investigate the QCD phase diagram as a function of temperature, chemical potential for baryon number and quark mass within the linear quark meson model for two flavors. Whereas the renormalization group flow leads to spontaneous chiral symmetry breaking in vacuum, the symmetry is restored in a second order phase transition at high temperature and vanishing quark mass. We explicitly connect the physics at zero temperature and realistic quark mass with the universal behavior near the critical temperature $T_c$ and the chiral limit. At high density we find a chiral symmetry restoring first order transition. The results imply the presence of a tricritical point with long-range correlations in the phase diagram. We end with an outlook to densities above the chiral transition, where QCD is expected to behave as a color superconductor at low temperature.

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

Color Superconductivity and Chiral Symmetry Restoration at Nonzero Baryon Density and Temperature

We explore the phase diagram of strongly interacting matter as a function of temperature and baryon number density, using a class of models for two-flavor QCD in which the interaction between quarks is modelled by that induced by instantons. Our treatment allows us to investigate the possible simultaneous formation of condensates in the conventional quark--anti-quark channel (breaking chiral symmetry) and in a quark--quark channel leading to color superconductivity: the spontaneous breaking of color symmetry via the formation of quark Cooper pairs. At low temperatures, chiral symmetry restoration occurs via a first order transition between a phase with low (or zero) baryon density and a high density color superconducting phase. We find color superconductivity in the high density phase for temperatures less than of order tens to 100 MeV, and find coexisting $ $ and $<\bar q q>$ condensates in this phase in the presence of a current quark mass. At high temperatures, the chiral phase transition is second order in the chiral limit and is a smooth crossover for nonzero current quark mass. A tricritical point separates the first order transition at high densities from the second order transition at high temperatures. In the presence of a current quark mass this tricritical point becomes a second order phase transition with Ising model exponents, suggesting that a long correlation length may develop in heavy ion collisions in which the phase transition is traversed at the appropriate density.

hep-ph↗

arXiv1998

QCD at high Baryon Density and Temperature: Competing Condensates and the Tricritical Point

The phase diagram of strongly interacting matter is explored as a function of temperature and baryon number density. We investigate the possible simultaneous formation of condensates in the conventional quark--anti-quark channel (breaking chiral symmetry) and in a quark--quark channel leading to color superconductivity: the spontaneous breaking of color symmetry via the formation of quark Cooper pairs. We point out that for two massless quark flavors a tricritical point in the phase diagram separates a chiral symmetry restoring first order transition at high densities from the second order transition at high temperatures. Away from the chiral limit this tricritical point becomes a second order phase transition with Ising model exponents, suggesting that a long correlation length may develop in heavy ion collisions in which the phase transition is traversed at the appropriate density.

hep-ph↗

arXiv1997

Universal Critical Equation of State and the Chiral Phase Transition in QCD

We employ non-perturbative 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. Our treatment covers both the chiral perturbation theory domain of validity and the domain of validity of universality associated with critical phenomena: We explicitly connect the physics at zero temperature and realistic quark mass with the universal behavior near the critical temperature $T_c$ and the chiral limit. For realistic quark masses the pion correlation length near $T_c$ turns out to be smaller than its zero temperature value. In the vicinity of $T_c$ and zero quark mass we obtain a precision estimate of the universal critical equation of state. It belongs to the universality class of the three dimensional O(4) symmetric Heisenberg model. We also investigate scalar field theories directly in three dimensions near second order and first order phase transitions. In particular, we obtain the universal equation of state for weak first order phase transitions in scalar matrix models. We also study the coarse grained free energy. Its dependence on the coarse graining scale gives a quantitative criterion for the validity of Langer's theory of spontaneous bubble nucleation.

hep-ph↗

arXiv1997

Chiral Phase Transition from Non-Perturbative Flow Equations

We employ non-perturbative flow equations to compute the equation of state for two flavor QCD within an effective quark meson model. Our treatment covers both the chiral perturbation theory domain of validity and the domain of validity of universality associated with critical phenomena. In the vicinity of $T_c$ and zero quark mass we obtain a precision estimate of the universal critical equation of state of the three dimensional O(4) symmetric Heisenberg model. For realistic quark masses the pion correlation length near $T_c$ turns out to be smaller than its zero temperature value.

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

Field theory near the critical temperature

Field theory at nonvanishing temperature beyond perturbation theory is discussed for the $N$-component $O(N)$-symmetric scalar theory. We compute the effective potential directly in three dimensions using an exact evolution equation for an effective action with an infrared cutoff. A suitable truncation is solved numerically. We obtain a detailed quantitative picture of the scaling form of the equation of state in the vicinity of the critical temperature of a second order phase transition.

hep-ph↗

arXiv1996

Coarse graining and first order phase transitions

We discuss the dependence of the coarse grained free energy and the classical interface tension on the coarse graining scale $k$. A stable range appears only if the renormalized dimensionless couplings at the critical temperature are small. This gives a quantitative criterion for the validity of computations within Langer's theory of spontaneous bubble nucleation.

hep-ph↗

arXiv1996

Equation of state and coarse grained free energy for matrix models

We investigate phase transitions in three dimensional scalar matrix models, with special emphasis on complex $2 \times 2$ matrices. The universal equation of state for weak first order phase transitions is computed. We also study the coarse grained free energy. Its dependence on the coarse graining scale gives a quantitative criterion for the validity of the standard treatment of bubble nucleation.

hep-th↗

arXiv1995

Critical equation of state from the average action

The scaling form of the critical equation of state is computed for $O(N)$-symmetric models. We employ a method based on an exact flow equation for a coarse grained free energy. A suitable truncation is solved numerically.

hep-th↗

arXiv1995

Solving non-perturbative flow equations

Non-perturbative exact flow equations describe the scale dependence of the effective average action. We present a numerical solution for an approximate form of the flow equation for the potential in a three-dimensional N-component scalar field theory. The critical behaviour, with associated critical exponents, can be inferred with good accuracy.

hep-th↗