On finite-density QCD at large Nc

Deryagin, Grigoriev, and Rubakov (DGR) have shown that in finite-density QCD at infinite Nc the Fermi surface is unstable with respect to the formation of chiral waves with wavenumber twice the Fermi momentum, while the BCS instability is suppressed. We show here that at large, but finite Nc, the DGR instability only occurs in a finite window of chemical potentials from above Lambda_QCD to mu_critical = exp(gamma ln^2 Nc + O(ln Nc ln ln Nc))Lambda_QCD, where gamma = 0.02173. Our analysis shows that, at least in the perturbative regime, the instability occurs only at extremely large Nc, Nc > 1000 Nf, where Nf is the number of flavors. We conclude that the DGR instability is not likely to occur in QCD with three colors, where the ground state is expected to be a color superconductor. We speculate on possible structure of the ground state of finite-density QCD with very large Nc.Comment: 13 pages, 5 figures, 3 figures drawn using PicTe

Patterns of Symmetry Breaking in QCD at High Baryon Density

We study the structure of QCD at very large baryon density for an arbitrary number of flavors $N_f$. We provide evidence that for any number of flavors larger than $N_f=2$ chiral symmetry remains broken at asymptotically large chemical potential. For $N_c=N_f=3$, chiral symmetry breaking follows the standard pattern $SU(3)_L\times SU(3)_R\to SU(3)$, but for $N_f>3$ unusual patterns emerge. We study the case $N_f=3$ in more detail and calculate the magnitude of the chiral order parameters $$and$$ in perturbative QCD. We show that, asymptotically, $^{1/3}$ is much smaller than $^{1/6}$. The result can be understood in terms of an approximate discrete symmetry.Comment: 23 pages, revtex, erratum adde

Confinement- Deconfinement Phase Transition in Hot and Dense QCD at Large N

We conjecture that the confinement- deconfinement phase transition in QCD at large number of colors N and N_f\ll N at T\neq 0 and \mu\neq 0 is triggered by the drastic change in \theta behavior. The conjecture is motivated by the holographic model of QCD where confinement -deconfinement phase transition indeed happens precisely at the value of temperature T=T_c where \theta dependence experiences a sudden change in behavior[1]. The conjecture is also supported by quantum field theory arguments when the instanton calculations (which trigger the \theta dependence) are under complete theoretical control for T>T_c, suddenly break down immediately below T<T_c with sharp changes in the \theta dependence. Finally, the conjecture is supported by a number of numerical lattice results. We employ this conjecture to study confinement -deconfinement phase transition of dense QCD at large \mu in large N limit by analyzing the \theta dependence. We find that the confinement- deconfinement phase transition at N_f\ll N happens at very large quark chemical potential \mu_c\sim \sqrt{N}\Lambda_{QCD}. This result agrees with recent findings by McLerran and Pisarski[2]. We also speculate on case when N_f\sim N.Comment: 10 pages, final version to appear in Nucl. Phys.

Superdense Matter

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss the use of weak coupling methods. We study the phase structure as a function of the number of flavors and their masses. We also introduce effective theories that describe low energy excitations at high baryon density. Finally, we study the possibility of kaon condensation at very large baryon density.Comment: 13 pages, talk at ICPAQGP, Jaipur, India, Nov. 26-30, 2001; to appear in the proceeding

Phases of QCD at High Baryon Density

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss how the quark masses and chemical potentials determine the structure of the superfluid quark phase. We comment on the possibility of kaon condensation at very high baryon density and study the competition between superfluid, density wave, and chiral crystal phases at intermediate density.Comment: 15 pages. To appear in the proceedings of the ECT Workshop on Neutron Star Interiors, Trento, Italy, June 200

Preinfection in vitro chemotaxis, phagocytosis, oxidative burst, and expression of CD11/CD18 receptors and their predictive capacity on the outcome of mastitis induced in dairy cows with Escherichia coli.

Four to 6 wk after parturition, 12 cows in second, fourth, or fifth lactation were experimentally infected in one gland with Escherichia coli. The capacity of chemotaxis, phagocytosis, oxidative burst, and expression of CD11/CD18 receptors to predict the severity of IMI was measured. Bacterial counts in the infected quarter, expressed as area under the curve, and residual milk production in the uninfected quarters were compared to determine severity of the infection. Although these two outcome parameters were highly negatively correlated, regression models with preinfection tests for leukocyte function fitted best with bacterial counts as an outcome parameter. Of the preinfection tests for leukocyte function, chemotaxis best predicted the outcome of the IMI that had been experimentally induced by E. coli. The number of circulating peripheral leukocytes just prior to inoculation was used to predict 52 and 45% of the severity of IMI for bacterial counts and residual milk production, respectively. As a categorical variable, parity predicted 75 and 56% of the severity of IMI expressed as bacterial counts and residual milk production, respectively. Because of the strong effect of parity on the outcome of the experimentally induced mastitis, analysis was performed to discriminate between second parity cows and older cows. Significant differences were found for the number of circulating peripheral leukocytes and for the expression of CD11b/CDl8 and CD11c/CD18 receptors between younger and older cows

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

Plate tectonic cycling modulates Earth's 3 He/ 22 Ne ratio

The ratio of 3He and 22Ne varies throughout the mantle. This observation is surprising because 3He and 22Ne are not produced in the mantle, are highly incompatible during mantle melting, and are not recycled back into the mantle by subduction of oceanic sediment or basaltic crust. Our new compilation yields average 3He/22Ne ratios of 7.5 ± 1.2 and 3.5 ± 2.4 for mid-ocean ridge basalt (MORB) mantle and ocean island basalt (OIB) mantle sources respectively. The low 3He/22Ne of OIB mantle approaches planetary precursor 3He/22Ne values; ∼1 for chondrites and ∼1.5 for the solar nebula. The high 3He/22Ne of the MORB mantle is not similar to any planetary precursor, requiring a mechanism for fractionating He from Ne in the mantle and suggesting isolation of distinct mantle reservoirs throughout geologic time. New experimental results reported here demonstrate that He and Ne diffuse at rates differing by one or more orders of magnitude at relevant temperatures in mantle materials. We model the formation of a MORB mantle with an elevated 3He/22Ne ratio through kinetically modulated chemical exchange between dunite channel-hosted basaltic liquids and harzburgite wallrock beneath mid-ocean ridges. Over timescales relevant to mantle upwelling beneath spreading centers, He may diffuse tens to hundreds of meters into wallrock while Ne is effectively immobile, producing a mantle lithosphere regassed with respect to He and depleted with respect to Ne, with a net elevated 3He/22Ne. Subduction of high 3He/22Ne mantle lithosphere throughout geologic time would generate a MORB source with high 3He/22Ne. Mixing models suggest that to preserve a high 3He/22Ne reservoir, MORB mantle mixing timescales must be on the order of hundreds of millions of years or longer, that mantle convection has not been layered about the transition zone for most of geologic time, and that Earth's convecting mantle has lost at least 96% of its primordial volatile elements. The most depleted, highest 3He/22Ne mantle may be best preserved in the lower mantle where relatively high viscosities impede mechanical mixing

A Diagrammatic Approach to Crystalline Color Superconductivity

We present a derivation of the gap equation for the crystalline color superconducting phase of QCD which begins from a one-loop Schwinger-Dyson equation written using a Nambu-Gorkov propagator modified to describe the spatially varying condensate. Some aspects of previous variational calculations become more straightforward when rephrased beginning from a diagrammatic starting point. This derivation also provides a natural base from which to generalize the analysis to include quark masses, nontrivial crystal structures, gluon propagation at asymptotic densities, and nonzero temperature. In this paper, we analyze the effects of nonzero temperature on the crystalline color superconducting phase.Comment: 15 pages. 2 eps figure