On the Perturbative Nature of Color Superconductivity

Color superconductivity is a possible phase of high density QCD. We present a systematic derivation of the transition temperature, T_C, from the QCD Lagrangian through study of the di-quark proper vertex. With this approach, we confirm the dependence of T_C on the coupling g, namely $T_C \sim \mu g^{-5} e^{-\kappa/g}$, previously obtained from the one-gluon exchange approximation in the superconducting phase. The diagrammatic approach we employ allows us to examine the perturbative expansion of the vertex and the propagators. We find an additional O(1) contribution to the prefactor of the exponential from the one-loop quark self energy and that the other one-loop radiative contributions and the two gluon exchange vertex contribution are subleading.Comment: 13 pages, 3 figures, revtex, details and discussion expande

Damping Rate of a Yukawa Fermion at Finite Temperature

The damping of a massless fermion coupled to a massless scalar particle at finite temperature is considered using the Braaten-Pisarski resummation technique. First the hard thermal loop diagrams of this theory are extracted and effective Green's functions are constructed. Using these effective Green's functions the damping rate of a soft Yukawa fermion is calculated. This rate provides the most simple example for the damping of a soft particle. To leading order it is proportional to $g^2T$, whereas the one of a hard fermion is of higher order.Comment: 5 pages, REVTEX, postscript figures appended, UGI-94-0

Soft Photon Production Rate in Resummed Perturbation Theory of High Temperature QCD

We calculate the production rate of soft real photons from a hot quark -- gluon plasma using Braaten -- Pisarski's perturbative resummation method. To leading order in the QCD coupling constant $g$ we find a logarithmically divergent result for photon energies of order $gT$, where $T$ is the plasma temperature. This divergent behaviour is due to unscreened mass singularities in the effective hard thermal loop vertices in the case of a massless external photon.Comment: 13 pages (2 figures not included), PLAINTEX, LPTHE-Orsay 93/46, BI-TP 93/5

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

How the quark self-energy affects the color-superconducting gap

We consider color superconductivity with two flavors of massless quarks which form Cooper pairs with total spin zero. We solve the gap equation for the color-superconducting gap parameter to subleading order in the QCD coupling constant $g$ at zero temperature. At this order in $g$, there is also a previously neglected contribution from the real part of the quark self-energy to the gap equation. Including this contribution leads to a reduction of the color-superconducting gap parameter \f_0 by a factor b_0'=\exp \big[ -(\p ^2+4)/8 \big]\simeq 0.177. On the other hand, the BCS relation T_c\simeq 0.57\f_0 between \f_0 and the transition temperature $T_c$ is shown to remain valid after taking into account corrections from the quark self-energy. The resulting value for $T_c$ confirms a result obtained previously with a different method.Comment: Revtex, 8 pages, no figur

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

Gluon self-energy in a two-flavor color superconductor

The energy and momentum dependence of the gluon self-energy is investigated in a color superconductor with two flavors of massless quarks. The presence of a color-superconducting quark-quark condensate modifies the gluon self-energy for energies which are of the order of the gap parameter. For gluon energies much larger than the gap, the self-energy assumes the form given by the standard hard-dense loop approximation. It is shown that this modification of the gluon self-energy does not affect the magnitude of the gap to leading and subleading order in the weak-coupling limit.Comment: 21 pages, 6 figures, RevTeX, aps and epsfig style files require

The deconfined phase near Tc and its decay into hadrons

We sketch an effective theory for the deconfined state of QCD near Tc. This relates the behavior of the expectation value of the Polyakov loop, and its two-point functions, to the pressure. Defining the ``mass'' of three and two gluon states from the imaginary and real parts of the Polyakov loop, while this ratio is 3:2 in perturbation theory, at Tc it is 3:1. We also discuss the decay of the deconfined state into hadrons.Comment: 4 pages, no figures, Contribution to the Proceedings of "Quark Matter 2002", Nantes, France, 18-24 Jul 200

Another weak first order deconfinement transition: three-dimensional SU(5) gauge theory

We examine the finite-temperature deconfinement phase transition of (2+1)-dimensional SU(5) Yang-Mills theory via non-perturbative lattice simulations. Unsurprisingly, we find that the transition is of first order, however it appears to be weak. This fits naturally into the general picture of "large" gauge groups having a first order deconfinement transition, even when the center symmetry associated with the transition might suggest otherwise.Comment: 17 pages, 8 figure

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