Gauge invariance of the color-superconducting gap on the mass shell

The gap parameter for color superconductivity is expected to be a gauge invariant quantity, at least on the appropriate mass shell. Computing the gap to subleading order in the QCD coupling constant, g, we show that the prefactor of the exponential in 1/g is gauge dependent off the mass shell, and independent of gauge on the mass shell.Comment: 8 pages, Proceedings of the Conference on Statistical QCD, Bielefeld, August 26 - 30, 200

Color superconductivity in cold, dense quark matter

We review what is different and what is similar in a color superconductor as compared to an ordinary BCS superconductor. The parametric dependence of the zero-temperature gap on the coupling constant differs in QCD from that in BCS theory. On the other hand, the transition temperature to the superconducting phase is related to the zero-temperature gap in the same way in QCD as in BCS theory.Comment: 11 pages, 1 figure, proceedings of the "Fifth Workshop on QCD", Villefranche, Jan. 3-7, 200

Longitudinal gluons and Nambu-Goldstone bosons in a two-flavor color superconductor

In a two-flavor color superconductor, the SU(3)_c gauge symmetry is spontaneously broken by diquark condensation. The Nambu-Goldstone excitations of the diquark condensate mix with the gluons associated with the broken generators of the original gauge group. It is shown how one can decouple these modes with a particular choice of 't Hooft gauge. We then explicitly compute the spectral density for transverse and longitudinal gluons of adjoint color 8. The Nambu-Goldstone excitations give rise to a singularity in the real part of the longitudinal gluon self-energy. This leads to a vanishing gluon spectral density for energies and momenta located on the dispersion branch of the Nambu-Goldstone excitations.Comment: 16 pages, 4 figures, minor revisions to text, one ref. adde

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

Superfluidity in a Model of Massless Fermions Coupled to Scalar Bosons

We study superfluidity in a model of massless fermions coupled to a massive scalar field through a Yukawa interaction. Gap equations for a condensate with total spin J=0 are solved in the mean-field approximation. For the Yukawa interaction, the gaps for right- and left-handed fermions are equal in magnitude and opposite in sign, so that condensation occurs in the J^P = 0^+ channel. At finite scalar mass, there are two different gaps for fermions of a given chirality, corresponding to condensation of particle pairs or of antiparticle pairs. These gaps become degenerate in the limit of infinite scalar mass.Comment: 26 pages, 9 figures, RevTeX, epsf and psfig style files required. Revised version, discussion of the excitation spectrum extended, Fig. 2 adde

Debye screening and Meissner effect in a two-flavor color superconductor

I compute the gluon self-energy in a color superconductor with two flavors of massless quarks, where condensation of Cooper pairs breaks SU(3)_c to SU(2)_c. At zero temperature, there is neither Debye screening nor a Meissner effect for the three gluons of the unbroken SU(2)_c subgroup. The remaining five gluons attain an electric as well as a magnetic mass. For temperatures approaching the critical temperature for the onset of color superconductivity, or for gluon momenta much larger than the color-superconducting gap, the self-energy assumes the form given by the standard hard-dense loop approximation. The gluon self-energy determines the coefficient of the kinetic term in the effective low-energy theory for the condensate fields.Comment: 29 pages, RevTe

Asymptotic deconfinement in high-density QCD

We discuss QCD with two light flavors at large baryon chemical potential mu. Color superconductivity leads to partial breaking of the color SU(3) group. We show that the infrared physics is governed by the gluodynamics of the remaining SU(2) group with an exponentially soft confinement scale Lambda_QCD' Delta*exp[-a*mu/(g*Delta)], where Delta<<mu is the superconducting gap, g is the strong coupling, and a=0.81... We estimate that at moderate baryon densities Lambda_QCD' is O(10 MeV) or smaller. The confinement radius increases exponentially with density, leading to "asymptotic deconfinement." The velocity of the SU(2) gluons is small due to the large dielectric constant of the medium.Comment: 4 pages; restructured, published versio

Color superconductivity in weak coupling

We derive perturbatively the gap equations for a color-superconducting condensate with total spin J=0 in dense QCD. At zero temperature, we confirm the results of Son for the dependence of the condensate on the coupling constant, and compute the prefactor to leading logarithmic accuracy. At nonzero temperature, we find that to leading order in weak coupling, the temperature dependence of the condensate is identical to that in BCS-like theories. The condensates for total spin J=1 are classified; to leading logarithmic accuracy these condensates are of the same order as those of spin J=0.Comment: 30 pages, 3 figures, RevTeX, epsf and psfig style files require

On the Applicability of Weak-Coupling Results in High Density QCD

Quark matter at asymptotically high baryon chemical potential is in a color superconducting state characterized by a gap Delta. We demonstrate that although present weak-coupling calculations of Delta are formally correct for mu -> Infinity, the contributions which have to this point been neglected are large enough that present results can only be trusted for mu >> mu_c ~ 10^8 MeV. We make this argument by using the gauge dependence of the present calculation as a diagnostic tool. It is known that the present calculation yields a gauge invariant result for mu -> Infinity; we show, however, that the gauge dependence of this result only begins to decrease for mu > mu_c, and conclude that the result can certainly not be trusted for mu < mu_c. In an appendix, we set up the calculation of the influence of the Meissner effect on the magnitude of the gap. This contribution to Delta is, however, much smaller than the neglected contributions whose absence we detect via the resulting gauge dependence.Comment: 21 pages, 3 figures, uses LaTeX2e and ReVTeX, updated figures, made minor text change