Constraints on the infrared behavior of the gluon propagator in Yang-Mills theories

We present rigorous upper and lower bounds for the zero-momentum gluon propagator D(0) of Yang-Mills theories in terms of the average value of the gluon field. This allows us to perform a controlled extrapolation of lattice data to infinite volume, showing that the infrared limit of the Landau-gauge gluon propagator in SU(2) gauge theory is finite and nonzero in three and in four space-time dimensions. In the two-dimensional case, we find D(0)=0, in agreement with Maas. We suggest an explanation for these results. We note that our discussion is general, although we apply our analysis only to pure gauge theory in the Landau gauge. Simulations have been performed on the IBM supercomputer at the University of Sao Paulo.

Linear covariant gauges on the lattice

Linear covariant gauges, such as Feynman gauge, are very useful in perturbative calculations. Their non-perturbative formulation is, however, highly non-trivial. In particular, it is a challenge to define linear covariant gauges on a lattice. We consider a class of gauges in lattice gauge theory that coincides with the perturbative definition of linear covariant gauges in the formal continuum limit. The corresponding gauge-fixing procedure is described and analyzed in detail, with an application to the pure SU(2) case. In addition, results for the gluon propagator in the two-dimensional case are given. (C) 2008 Elsevier B.V. All rights reserved.

A dynamical gluon mass solution in a coupled system of the Schwinger-Dyson equations

We study numerically the Schwinger-Dyson equations for the coupled system of gluon and ghost propagators in the Landau gauge and in the case of pure gauge QCD. We show that a dynamical mass for the gluon propagator arises as a solution while the ghost propagator develops an enhanced behavior in the infrared regime of QCD. Simple analytical expressions are proposed for the propagators, and the mass dependency on the ΛQCD scale and its perturbative scaling are studied. We discuss the implications of our results for the infrared behavior of the coupling constant, which, according to fits for the propagators infrared behavior, seems to indicate that α s(q2) → 0 as q2 → 0. © SISSA/ISAS 2004.

Modeling the gluon propagator in Landau gauge: Lattice estimates of pole masses and dimension-two condensates

We present an analytic description of numerical results for the Landau-gauge SU(2) gluon propagator D(p(2)), obtained from lattice simulations (in the scaling region) for the largest lattice sizes to date, in d = 2, 3 and 4 space-time dimensions. Fits to the gluon data in 3d and in 4d show very good agreement with the tree-level prediction of the refined Gribov-Zwanziger (RGZ) framework, supporting a massive behavior for D(p(2)) in the infrared limit. In particular, we investigate the propagator's pole structure and provide estimates of the dynamical mass scales that can be associated with dimension-two condensates in the theory. In the 2d case, fitting the data requires a noninteger power of the momentum p in the numerator of the expression for D(p(2)). In this case, an infinite-volume-limit extrapolation gives D(0) = 0. Our analysis suggests that this result is related to a particular symmetry in the complex-pole structure of the propagator and not to purely imaginary poles, as would be expected in the original Gribov-Zwanziger scenario.

SELF-CONSISTENT SOLUTION OF THE SCHWINGER-DYSON EQUATIONS FOR THE NUCLEON AND MESON PROPAGATORS

The Schwinger-Dyson equations for the nucleon and meson propagators are solved self-consistently in an approximation that goes beyond the Hartree-Fock approximation. The traditional approach consists in solving the nucleon Schwinger-Dyson equation with bare meson propagators and bare meson-nucleon vertices; the corrections to the meson propagators are calculated using the bare nucleon propagator and bare nucleon-meson vertices. It is known that such an approximation scheme produces the appearance of ghost poles in the propagators. In this paper the coupled system of Schwinger-Dyson equations for the nucleon and the meson propagators are solved self-consistently including vertex corrections. The interplay of self-consistency and vertex corrections on the ghosts problem is investigated. It is found that the self-consistency does not affect significantly the spectral properties of the propagators. In particular, it does not affect the appearance of the ghost poles in the propagators.

Ghost Cells In Pilomatrixoma, Craniopharyngioma, And Calcifying Cystic Odontogenic Tumor: Histological, Immunohistochemical, And Ultrastructural Study.

Pilomatrixoma, craniopharyngioma, and calcifying cystic odontogenic tumor are the main entities presenting ghost cells as an important histological feature, in spite their quite different clinical presentation; it seems that they share a common pathway in the formation of these cells. The aim of this study is to examine and compare the characteristics of ghost and other cells that form these lesions. Forty-three cases including 21 pilomatrixomas, 14 craniopharyngiomas, and eight calcifying cystic odontogenic tumors were evaluated by immunohistochemistry for cytokeratins, CD138, β-catenin, D2-40, Glut-1, FAS, CD10 and also by scanning electron microscopy. The CKs, CD138, β-catenin, Glut-1, FAS, and CD10 were more often expressed by transitional cells of craniopharyngioma and calcifying cystic odontogenic tumor, compared with pilomatrixoma. Basaloid cells of pilomatrixoma showed strong positivity for CD138 and CD10. Differences on expression pattern were identified in transitional and basal cells, as ghost cells were negative for most antibodies used, except by low expression for cytokeratins. By scanning electron microscopy, the morphology of ghost cells were similar in their fibrillar cytoplasm, but their pattern varied from sheets in pilomatrixoma to small clusters in craniopharyngioma and calcifying cystic odontogenic tumor. Mechanisms involved in formation of ghost cells are unknown, but probably they follow different pathways as protein expression in the basal/transitional cells was not uniform in the three tumors studied.

Three-point vertices in Landau-gauge Yang-Mills theory

Vertices are of central importance for constructing QCD bound states out of the individual constituents of the theory, i.e. quarks and gluons. In particular, the determination of three-point vertices is crucial in nonperturbative investigations of QCD. We use numerical simulations of lattice gauge theory to obtain results for the 3-point vertices in Landau-gauge SU(2) Yang-Mills theory in three and four space-time dimensions for various kinematic configurations. In all cases considered, the ghost-gluon vertex is found to be essentially tree-level-like, while the three-gluon vertex is suppressed at intermediate momenta. For the smallest physical momenta, reachable only in three dimensions, we find that some of the three-gluon-vertex tensor structures change sign.

Constraints on the infrared behavior of the ghost propagator in Yang-Mills theories

We present rigorous upper and lower bounds for the momentum-space ghost propagator G(p) of Yang-Mills theories in terms of the smallest nonzero eigenvalue (and of the corresponding eigenvector) of the Faddeev-Popov matrix. We apply our analysis to data from simulations of SU(2) lattice gauge theory in Landau gauge, using the largest lattice sizes to date. Our results suggest that, in three and in four space-time dimensions, the Landau gauge ghost propagator is not enhanced as compared to its tree-level behavior. This is also seen in plots and fits of the ghost dressing function. In the two-dimensional case, on the other hand, we find that G(p) diverges as p(-2-2 kappa) with kappa approximate to 0.15, in agreement with A. Maas, Phys. Rev. D 75, 116004 (2007). We note that our discussion is general, although we make an application only to pure gauge theory in Landau gauge. Our simulations have been performed on the IBM supercomputer at the University of Sao Paulo.

Mark-recapture may reveal more about ecology than about population trends: Demography of a threatened ghost bat (Macroderma gigas) population

Since European settlement in Australia, the geographical range of ghost bats (Macroderma gigas) has contracted northwards. Ghost bats are thought to occur in disjunct populations with little interpopulation migration, raising concerns over the current status and future viability of the southernmost colony, which has also been threatened by mining activity. To address these concerns, demographic parameters of the southernmost colony were estimated from a mark-recapture study conducted during 1975-1981. Female bats gave birth to a single young in late spring, but only 40% (22-70%, 95% CI) of females bred in their second year, increasing to 93% (87-97%, 95% CI) for females greater than or equal to 2 years old. Sixty-five percent of juveniles caught were female. Annual adult survival ranged between 0.57-0.77 for females and 0.43-0.66 for males, and was lowest over winter-spring and greatest in autumn-winter. Juvenile survival for the first year ranged between 0.35-0.46 for females and 0.29-0.42 for males. Adult survival varied among seasons, was negatively associated with rainfall, but was not associated with temperature beyond being lower in late winter. Poor survival may result from the inferior daytime roosts that bats must use if water seepage forces them to leave their normal roosts. Although these age-specific rates of fecundity and survival suggested a declining population, mark-recapture estimates of the population trend indicated stability over the study period. Counts at daytime roosts also suggested a population decline, but were considered unreliable because of an increasing tendency of bats to avoid detection. It is therefore likely that some assumptions in estimating survival were violated. These results provide a caution against the uncritical use of population projections derived from mark-recapture estimates of demographic parameters, and the use of untested indices as the basis for conservation decisions.

Population dynamics of the pea crab Austinixa aidae (Brachyura, Pinnotheridae): a symbiotic of the ghost shrimp Callichirus major (Thalassinidea, Callianassidae) from the southwestern Atlantic

The Pinnotheridae family is one of the most diverse and complex groups of brachyuran crabs, many of them symbionts of a wide variety of invertebrates. The present study describes the population dynamics of the pea crab Austinixa aidae (Righi, 1967), a symbiont associated with the burrows of the ghost shrimp Callichirus major (Say, 1818). Individuals (n = 588) were collected bimonthly from May, 2005 to September, 2006 along a sandy beach in the southwestern Atlantic, state of São Paulo, Brazil. Our data indicated that the population demography of A. aidae was characterized by a bimodal size-frequency distribution (between 2.0 and 4.0 mm and between 8.0 and 9.0 mm CW) that remained similar throughout the study period. Sex ratio does not differ significantly from 1:1 (p > 0.05), which confirms the pattern observed in other symbiontic pinnotherids. Density values (1.72 ± 1.34 ind. • ap.-1) are in agreement with those found for other species of the genus. The mean symbiosis incidence (75.6%) was one of the highest among species of the Pinnotheridae family, but it was the lowest among the three studied species of the genus. Recruitment pattern was annual, beginning in May and peaking in July, in both years, after the peak of ovigerous females in the population (from March to May). Our findings describe ecological and biological aspects of A. aidae similar to those of other species of this genus, even from different geographic localities.

Grey Ghost II

Combined media on photographic paper. 81½” x 54"