A quark action for very coarse lattices

We investigate a tree-level O(a^3)-accurate action, D234c, on coarse lattices. For the improvement terms we use tadpole-improved coefficients, with the tadpole contribution measured by the mean link in Landau gauge. We measure the hadron spectrum for quark masses near that of the strange quark. We find that D234c shows much better rotational invariance than the Sheikholeslami-Wohlert action, and that mean-link tadpole improvement leads to smaller finite-lattice-spacing errors than plaquette tadpole improvement. We obtain accurate ratios of lattice spacings using a convenient ``Galilean quarkonium'' method. We explore the effects of possible O(alpha_s) changes to the improvement coefficients, and find that the two leading coefficients can be independently tuned: hadron masses are most sensitive to the clover coefficient, while hadron dispersion relations are most sensitive to the third derivative coefficient C_3. Preliminary non-perturbative tuning of these coefficients yields values that are consistent with the expected size of perturbative corrections.Comment: 22 pages, LaTe

Resummed one-loop gluonic contributions to the color superconducting color charge density vanish

It is shown that gluonic corrections to the tadpole diagrams vanish in the 2SC and CFL phases at the order where one might have expected NLO corrections. This implies that the gluonic part of the color charge density is negligible at the order of our computation. This statement remains true after inclusion of the gluon vertex correction and contributions from Nambu-Goldstone bosons.Comment: 9 pages, 3 figures, REVTeX4; title modified, comments about gauge independence added, accepted for publication in Phys. Rev.

Viscous damping of r-modes: Large amplitude saturation

We analyze the viscous damping of r-mode oscillations of compact stars, taking into account non-linear viscous effects in the large-amplitude regime. The qualitatively different cases of hadronic stars, strange quark stars, and hybrid stars are studied. We calculate the viscous damping times of r-modes, obtaining numerical results and also general approximate analytic expressions that explicitly exhibit the dependence on the parameters that are relevant for a future spindown evolution calculation. The strongly enhanced damping of large amplitude oscillations leads to damping times that are considerably lower than those obtained when the amplitude dependence of the viscosity is neglected. Consequently, large-amplitude viscous damping competes with the gravitational instability at all physical frequencies and could stop the r-mode growth in case this is not done before by non-linear hydrodynamic mechanisms.Comment: 18 pages, 17 figures, changed convention for the r-mode amplitude, version to be published in PR

Heating (Gapless) Color-Flavor Locked Quark Matter

We explore the phase diagram of neutral quark matter at high baryon density as a function of the temperature T and the strange quark mass Ms. At T=0, there is a sharp distinction between the insulating color-flavor locked (CFL) phase, which occurs where Ms^2/mu < 2 Delta, and the metallic gapless CFL phase, which occurs at larger Ms^2/mu. Here, mu is the chemical potential for quark number and Delta is the gap in the CFL phase. We find this distinction blurred at nonzero T, as the CFL phase undergoes an insulator-to-metal crossover when it is heated. We present an analytic treatment of this crossover. At higher temperatures, we map out the phase transition lines at which the gap parameters Delta_1, Delta_2 and Delta_3 describing ds-pairing, us-pairing and ud-pairing respectively, go to zero in an NJL model. For small values of Ms^2/mu, we find that Delta_2 vanishes first, then Delta_1, then Delta_3. We find agreement with a previous Ginzburg-Landau analysis of the form of these transitions and find quantitative agreement with results obtained in full QCD at asymptotic density for ratios of coefficients in the Ginzburg-Landau potential. At larger Ms^2/mu, we find that Delta_1 vanishes first, then Delta_2, then Delta_3. Hence, we find a "doubly critical'' point in the (Ms^2/mu,T)-plane at which two lines of second order phase transitions (Delta_1->0 and Delta_2->0) cross. Because we do not make any small-Ms approximation, if we choose a relatively strong coupling leading to large gap parameters, we are able to pursue the analysis of the phase diagram all the way up to such large values of Ms that there are no strange quarks present.Comment: 24 pages; 22 figures; typos in labelling of Figs. 7, 20 correcte

Ginzburg-Landau approach to the three flavor LOFF phase of QCD

We explore, using a Ginzburg-Landau expansion of the free energy, the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of QCD with three flavors, using the NJL four-fermion coupling to mimic gluon interactions. We find that, below the point where the QCD homogeneous superconductive phases should give way to the normal phase, Cooper condensation of the pairs u-s and d-u is possible, but in the form of the inhomogeneous LOFF pairing.Comment: 8 pages, 4 figures. Eq. (20) corrected. As a consequence figures have been modified to show only the solution with parallel total momenta of the us, ud pairs, as the other configurations are suppressed. Main conclusions of the paper are unchange

Color-flavor locked strangelets in a quark mass density-dependent model

The color-flavor locked (CFL) phase of strangelets is investigated in a quark mass density-dependent model. Parameters are determined by stability arguments. It is concluded that three solutions to the system equations can be found, corresponding, respectively, to positively charged, negatively charged, and nearly neutral CFL strangelets. The charge to baryon number of the positively charged strangelets is smaller than the previous result, while the charge of the negatively charged strangelets is nearly proportional in magnitude to the cubic-root of the baryon number. However, the positively charged strangelets are more stable compared to the other two solutions.Comment: 11 pages,7 figures, Accepted for publication in Int. J. Mod. Phys.

Evaluating the Gapless Color-Flavor Locked Phase

In neutral cold quark matter that is sufficiently dense that the strange quark mass M_s is unimportant, all nine quarks (three colors; three flavors) pair in a color-flavor locked (CFL) pattern, and all fermionic quasiparticles have a gap. We recently argued that the next phase down in density (as a function of decreasing quark chemical potential mu or increasing strange quark mass M_s) is the new ``gapless CFL'' (``gCFL'') phase in which only seven quasiparticles have a gap, while there are gapless quasiparticles described by two dispersion relations at three momenta. There is a continuous quantum phase transition from CFL to gCFL quark matter at M_s^2/mu approximately equal to 2*Delta, with Delta the gap parameter. Gapless CFL, like CFL, leaves unbroken a linear combination "Q-tilde" of electric and color charges, but it is a Q-tilde-conductor with gapless Q-tilde-charged quasiparticles and a nonzero electron density. In this paper, we evaluate the gapless CFL phase, in several senses. We present the details underlying our earlier work which showed how this phase arises. We display all nine quasiparticle dispersion relations in full detail. Using a general pairing ansatz that only neglects effects that are known to be small, we perform a comparison of the free energies of the gCFL, CFL, 2SC, gapless 2SC, and 2SCus phases. We conclude that as density drops, making the CFL phase less favored, the gCFL phase is the next spatially uniform quark matter phase to occur. A mixed phase made of colored components would have lower free energy if color were a global symmetry, but in QCD such a mixed phase is penalized severely.Comment: 18 pages, RevTeX; Version to appear in Phys Rev D. Minor rewording, references adde

Effective gluon interactions in the Colour Superconductive Phase of two flavor QCD

The gluon self-energies and dispersion laws in the color superconducting phase of QCD with two massless flavors are calculated using the effective theory near the Fermi surface. These quantities are calculated at zero temperature for all the eight gluons, those of the remaining SU(2) color group and those corresponding to the broken generators. The construction of the effective interaction is completed with the one loop calculation of the three- and four-point gluon interactions.Comment: LaTeX, p 17, 4 figures. Final version to be published in Phys. Lett. B. Several corrections have been done and some point clarifie