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

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

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

CFL Phase of High Density QCD at Non Zero Strange Quark Mass

We compute free energy of quark matter at asymptotically high baryon number density in the presence of non zero strange quark mass including dynamics of pseudo Nambu-Goldstone bosons due to chiral symmetry breaking, extending previously existing analysis based on perturbative expansion in $m_s^2/4\mu\Delta.$ We demonstrate that the CFL$K^0$ state has lower free energy than the symmetric CFL state for $0<m_s^2/4\mu\Delta<2/3$. We also calculate the spectrum of the fermionic quasiparticle excitations about the kaon condensed ground state in the regime $m_s^2/4\mu\Delta \sim 1$ and find that $(m_s^2/4\mu\Delta)_{crit}=2/3$ for the CFL-gCFL phase transition, the leading order result reported in [1], is not modified.Comment: 16 pages, 3 figure

Geometry Technology Module (GTM). Volume 1: Engineering description and utilization manual

The geometry technology module (GTM) is described as a system of computerized elements residing in the engineering design integration system library developed for the generation, manipulation, display, computation of mass properties, and data base management of panelled geometry. The GTM is composed of computer programs and associated data for performing configuration analysis on geometric shapes. The program can be operated in batch or demand mode and is designed for interactive use

The Stability of Strange Star Crusts and Strangelets

We construct strangelets, taking into account electrostatic effects, including Debye screening, and arbitrary surface tension sigma of the interface between vacuum and quark matter. We find that there is a critical surface tension sigma_crit below which large strangelets are unstable to fragmentation and below which quark star surfaces will fragment into a crystalline crust made of charged strangelets immersed in an electron gas. We derive a model-independent relationship between sigma_crit and two parameters that characterize any quark matter equation of state. For reasonable model equations of state, we find sigma_crit typically of order a few MeV/fm^2. If sigma <= sigma_crit, the size-distribution of strangelets in cosmic rays could feature a peak corresponding to the stable strangelets that we construct.Comment: 11 pages, LaTe