QCD effective action with dressing functions - consistency checks in the perturbative regime

In a previous paper, we presented solution to the Slavnov--Taylor identity for the QCD effective action, and argued that the action terms containing (anti)ghost fields are unique. These terms have the same form as those in the classical action, but the gluon and (anti)ghost effective fields are convoluted with gluon and ghost dressing functions G_A and G_c, the latter containing perturbative and nonperturbative effects (but not including the soliton-like vacuum effects). In the present work we show how the perturbative QCD (pQCD) can be incorporated into the framework of this action, and we present explicit one-loop pQCD expressions for G_A and G_c. We then go on to check the consistency of the obtained results by considering an antighost Dyson--Schwinger equation (DSE). By solving the relations that result from the Legendre transformation leading to the effective action, we obtain the effective fields as power expansions of sources. We check explicitly that the aforementioned one-loop functions G_A and G_c fulfil the antighost DSE at the linear source level. We further explicitly check that these one-loop G_A and G_c have the regularization-scale and momentum dependence consistent with the antighost DSE at the quadratic source level. These checks suggest that the the effective action with dressing functions represents a consistent framework for treating QCD, at least at the one-loop level.Comment: 17 pages, revtex4; dimensional regularization used instead of Pauli-Villars, the check of identity in the linear-in-sources Dyson-Schwinger equation now includes the finite part; conclusions unchanged; to appear in Phys.Rev.

The radiative decay of a high energy neutrino in the Coulomb field of a nucleus

In the framework of the Standard Model with lepton mixing the radiative decay $\nu_i \rightarrow \nu_j \gamma$ of a neutrino of high ($E_\nu \sim 100 \, GeV$) and super-high ($E_\nu \ge 1 \, TeV$) energy is investigated in the Coulomb field of a nucleus. Estimates of the decay probability and ``decay cross-section'' for neutrinos of these energies in the electric field of a nucleus permit one to discuss the general possibility of carrying out a neutrino experiment, subject to the condition of availability in the future of a beam of neutrinos of these high energies. Such an experiment could give unique information on mixing angles in the lepton sector of the Standard Model which would be independent of the specific neutrino masses if only the threshold factor ($1 - m_j^4 / m_i^4$) was not close to zero. (Published in Phys.Lett.B 323 (1994) 179).Comment: 5 pages, LaTeX, Yaroslavl, Yaroslavl State University preprint YARU-HE-93/0

Hierarchy of massive gauge fields

An explicitely gauge invariant polynomial action for massive gauge fields is proposed. For different values of parameters it describes massive Yang-Mills field, the Higgs-Kibble model, the model with spontaneously broken symmetry and two scalar mesons.Comment: 8 pages, no figure

An approach to solve Slavnov-Taylor identities in nonsupersymmetric non-Abelian gauge theories

We present a way to solve Slavnov--Taylor identities in a general nonsupersymmetric theory. The solution can be parametrized by a limited number of functions of spacetime coordinates, so that all the effective fields are dressed by these functions via integral convolution. The solution restricts the ghost part of the effective action and gives predictions for the physical part of the effective action.Comment: revised version, section 3 is enlarged, 24 pages, Latex2e, no figures, version accepted by Phys. Rev.

On Pair-Particle Distribution in Imperfect Bose Gas

A simple model of estimating the radial distribution function of an imperfect Bose gas in the ground state is presented. The model is based on integro-differential equations derived by considering the space boson distribution in an external field. With the approach proposed, the particular case of dilute Bose gas is investigated within the hard sphere approximation and beyond.Comment: 8 pages, LaTEX, no Figures. Submitted to Phys. Lett.

A post-tsunami assessment of coastal living resources of Langkawi Archipelago, Peninsular Malaysia

Rapid and detailed post-tsunami surveys carried out in the Langkawi archipelago in January 2005 showed that the coral reefs dOld_ID not suffer any significant structural damage. Nevertheless, there were signs of recent sediment resuspension at the sites studied. The diversity and abundance of coral reef fishes and invertebrates were low. However, this was not attributed to the tsunami effect but rather to the present environmental conditions. The extent of damage at the villages of Kubang Badak and Kuala Teriang may indicate that intact coastal ecosystems such as mangroves have the potential to protect lives and property during natural disasters

Quasiparticle density of states in dirty high-T_c superconductors

We study the density of quasiparticle states of dirty d-wave superconductors. We show the existence of singular corrections to the density of states due to quantum interference effects. We then argue that the density of states actually vanishes in the localized phase as $|E|$ or $E^2$ depending on whether time reversal is a good symmetry or not. We verify this result for systems without time reversal symmetry in one dimension using supersymmetry techniques. This simple, instructive calculation also provides the exact universal scaling function for the density of states for the crossover from ballistic to localized behaviour in one dimension. Above two dimensions, we argue that in contrast to the conventional Anderson localization transition, the density of states has critical singularities which we calculate in a $2+\epsilon$ expansion. We discuss consequences of our results for various experiments on dirty high-$T_c$ materials

Anyonic Bogomol'nyi Solitons in a Gauged O(3) Sigma Model

We introduce the self-dual abelian gauged $O(3)$ sigma models where the Maxwell and Chern-Simons terms constitute the kinetic terms for the gauge field. These models have quite rich structures and various limits. Our models are found to exhibit both symmetric and broken phases of the gauge group. We discuss the pure Chern-Simons limit in some detail and study rotationally symmetric solitons.Comment: 14 pages, 6 Postscript figures uuencoded, written in REVTe

Pareto's Law of Income Distribution: Evidence for Germany, the United Kingdom, and the United States

We analyze three sets of income data: the US Panel Study of Income Dynamics PSID), the British Household Panel Survey (BHPS), and the German Socio-Economic Panel (GSOEP). It is shown that the empirical income distribution is consistent with a two-parameter lognormal function for the low-middle income group (97%-99% of the population), and with a Pareto or power law function for the high income group (1%-3% of the population). This mixture of two qualitatively different analytical distributions seems stable over the years covered by our data sets, although their parameters significantly change in time. It is also found that the probability density of income growth rates almost has the form of an exponential function.Comment: Latex2e v1.6; 16 pages with 5 figure