Numerical solution of the color superconductivity gap in a weak coupling constant

We present the numerical solution of the full gap equation in a weak coupling constant $g$. It is found that the standard approximations to derive the gap equation to the leading order of coupling constant are essential for a secure numerical evaluation of the logarithmic singularity with a small coupling constant. The approximate integral gap equation with a very small $g$ should be inverted to a soft integral equation to smooth the logarithmic singularity near the Fermi surface. The full gap equation is solved for a rather large coupling constant $g\ge 2.0$. The approximate and soft integral gap equations are solved for small $g$ values. When their solutions are extrapolated to larger $g$ values, they coincide the full gap equation solution near the Fermi surface. Furthermore, the analytical solution matches the numerical one up to the order one O(1). Our results confirm the previous estimates that the gap energy is of the order tens to 100 MeV for the chemical potential $\mu\le 1000$ MeV. They also support the validity of leading approximations applied to the full gap equation to derive the soft integral gap equation and its analytical solution near the Fermi surface.Comment: 7 pages+ 6 figs, Stanford, Frankfurt and Bethlehe

Lifetime Effects in Color Superconductivity at Weak Coupling

Present computations of the gap of color superconductivity in weak coupling assume that the quarks which participate in the condensation process are infinitely long-lived. However, the quasiparticles in a plasma are characterized by having a finite lifetime. In this article we take into account this fact to evaluate its effect in the computation of the color gap. By first considering the Schwinger-Dyson equations in weak coupling, when one-loop self-energy corrections are included, a general gap equation is written in terms of the spectral densities of the quasiparticles. To evaluate lifetime effects, we then model the spectral density by a Lorentzian function. We argue that the decay of the quasiparticles limits their efficiency to condense. The value of the gap at the Fermi surface is then reduced. To leading order, these lifetime effects can be taken into account by replacing the coupling constant of the gap equation by a reduced effective one.Comment: 16 pages, 2 figures; explanations on the role of the Meissner effect added; 2 references added; accepted for publication in PR

The Ginzburg-Landau Free Energy Functional of Color Superconductivity at Weak Coupling

We derive the Ginzburg-Landau free energy functional of color superconductivity in terms of the thermal diagrams of QCD in its perturbative region. The zero mode of the quadratic term coefficient yields the same transition temperature, including the pre-exponential factor, as the one obtained previously from the Fredholm determinant of the two quark scattering amplitude. All coefficients of the free energy can be made identical to those of a BCS model by setting the Fermi velocity of the latter equal to the speed of light. We also calculate the induced symmetric color condensate near $T_c$ and find that it scales as the cubic power of the dominant antisymmetric color component. We show that in the presence of an inhomogeneity and a nonzero gauge potential, while the color-flavor locked condensate dominates in the bulk, the unlocked condensate, the octet, emerges as a result of a simultaneous color-flavor rotation in the core region of a vortex filament or at the junction of super and normal phases.Comment: 32 pages, Plain Tex, 3 figure

On Color Superconductivity in External Magnetic Field

We study color superconductivity in external magnetic field. We discuss the reason why the mixing angles in color-flavor locked (CFL) and two-flavor superconductivity (2SC) phases are different despite the fact that the CFL gap goes to the 2SC gap for $m_s \to \infty$. Although flavor symmetry is explicitly broken in external magnetic field, we show that all values of gaps in their coset spaces of possible solutions in the CFL phase are equivalent in external magnetic field.Comment: 12 pages, LaTe

Anisotropic admixture in color-superconducting quark matter

The analysis of color-superconducting two-flavor deconfined quark matter at moderate densities is extended to include a particular spin-1 Cooper pairing of those quarks which do not participate in the standard spin-0 diquark condensate. (i) The relativistic spin-1 gap Delta' implies spontaneous breakdown of rotation invariance manifested in the form of the quasi-fermion dispersion law. (ii) The critical temperature of the anisotropic component is approximately given by the relation T_c'~ Delta'(T=0)/3. (iii) For massless fermions the gas of anisotropic Bogolyubov-Valatin quasiquarks becomes effectively gapless and two-dimensional. Consequently, its specific heat depends quadratically on temperature. (iv) All collective Nambu-Goldstone excitations of the anisotropic phase have a linear dispersion law and the whole system remains a superfluid. (v) The system exhibits an electromagnetic Meissner effect.Comment: v2: references added, angular dependence of the gap clarified, v3: extended discussion, typo in eq. (5) corrected, version accepted for publication in PR

Properties of neutral mesons in a hot and magnetized quark matter

The properties of non-interacting $\sigma$ and $\pi^{0}$ mesons are studied at finite temperature, chemical potential and in the presence of a constant magnetic field. To do this, the energy dispersion relations of these particles, including nontrivial form factors, are derived using a derivative expansion of the effective action of a two-flavor, hot and magnetized Nambu--Jona-Lasinio (NJL) model up to second order. The temperature dependence of the pole and screening masses as well as the directional refraction indices of magnetized neutral mesons are explored for fixed magnetic fields and chemical potentials. It is shown that, because of the explicit breaking of the Lorentz invariance by the magnetic field, the refraction index and the screening mass of neutral mesons exhibit a certain anisotropy in the transverse and longitudinal directions with respect to the direction of the external magnetic field. In contrast to their longitudinal refraction indices, the transverse indices of the neutral mesons are larger than unity.Comment: V1: 26 pages, 15 figures; V2: Discussions improved, references added. Version accepted for publication in PR

Infrared divergence in QED3_3 at finite temperature

We consider various ways of treating the infrared divergence which appears in the dynamically generated fermion mass, when the transverse part of the photon propagator in N flavour $QED_{3}$ at finite temperature is included in the Matsubara formalism. This divergence is likely to be an artefact of taking into account only the leading order term in the $1 \over N$ expansion when we calculate the photon propagator and is handled here phenomenologically by means of an infrared cutoff. Inserting both the longitudinal and the transverse part of the photon propagator in the Schwinger-Dyson equation we find the dependence of the dynamically generated fermion mass on the temperature and the cutoff parameters. It turns out that consistency with certain statistical physics arguments imposes conditions on the cutoff parameters. For parameters in the allowed range of values we find that the ratio $r=2*Mass(T=0)/critical temperature$ is approximately 6, consistently with previous calculations which neglected the transverse photon contribution.Comment: 37 pages, 12 figures, typos corrected, references added, Introduction rewritte

The omega meson at high temperatures

The decays of the omega meson in a heat bath of thermally excited pions is studied within the framework of real-time thermal field theory using an appropriate effective Lagrangian. We show that the omega meson spectrum broadens considerably at temperatures T > 100 MeV, primarily because of omega pi -> pi pi reactions in the thermal environment.Comment: 7 pages, 2 figures; reference and paragraph added; version to appear in Phys. Lett.

Topological String Defect Formation During the Chiral Phase Transition

We extend and generalize the seminal work of Brandenberger, Huang and Zhang on the formation of strings during chiral phase transitions(berger) and discuss the formation of abelian and non-abelian topological strings during such transitions in the early Universe and in the high energy heavy-ion collisions. Chiral symmetry as well as deconfinement are restored in the core of these defects. Formation of a dense network of string defects is likely to play an important role in the dynamics following the chiral phase transition. We speculate that such a network can give rise to non-azimuthal distribution of transverse energy in heavy-ion collisions.Comment: 10 pages, 4 figures, minor correction