Advection of a passive scalar field by turbulent compressible fluid: renormalization group analysis near d=4d = 4

The field theoretic renormalization group (RG) and the operator product expansion (OPE) are applied to the model of a density field advected by a random turbulent velocity field. The latter is governed by the stochastic Navier-Stokes equation for a compressible fluid. The model is considered near the special space dimension $d = 4$. It is shown that various correlation functions of the scalar field exhibit anomalous scaling behaviour in the inertial-convective range. The scaling properties in the RG+OPE approach are related to fixed points of the renormalization group equations. In comparison with physically interesting case $d = 3$, at $d = 4$ additional Green function has divergences which affect the existence and stability of fixed points. From calculations it follows that a new regime arises there and then by continuity moves into $d = 3$. The corresponding anomalous exponents are identified with scaling dimensions of certain composite fields and can be systematically calculated as series in $y$ (the exponent, connected with random force) and $\epsilon=4-d$. All calculations are performed in the leading one-loop approximation.Comment: 11pages, 6 figures, LATEX2e. arXiv admin note: substantial text overlap with arXiv:1611.00327; text overlap with arXiv:1611.0130

Scaling Functions and Superscaling in Medium and Heavy Nuclei

The scaling function $f(\psi')$ for medium and heavy nuclei with $Z\neq N$ for which the proton and neutron densities are not similar is constructed within the coherent density fluctuation model (CDFM) as a sum of the proton and neutron scaling functions. The latter are calculated in the cases of $^{62}$Ni, $^{82}$Kr, $^{118}$Sn, and $^{197}$Au nuclei on the basis of the corresponding proton and neutron density distributions which are obtained in deformed self-consistent mean-field Skyrme HF+BCS method. The results are in a reasonable agreement with the empirical data from the inclusive electron scattering from nuclei showing superscaling for negative values of $\psi'$, including those smaller than -1. This is an improvement over the relativistic Fermi gas (RFG) model predictions where $f(\psi')$ becomes abruptly zero for $\psi'\leq -1$. It is also an improvement over the CDFM calculations made in the past for nuclei with $Z\neq N$ assuming that the neutron density is equal to the proton one and using only the phenomenological charge density.Comment: 4 pages, 1 figure, ReVTeX, accepted for publication in Phys. Rev.

3D Georgi-Glashow model and confining strings at zero and finite temperatures

In this review, we discuss the confining and finite-temperature properties of the 3D SU(N) Georgi-Glashow model, and of 4D compact QED. At zero temperature, we derive string representations of both theories, thus constructing the SU(N)-version of Polyakov's theory of confining strings. We discuss the geometric properties of confining strings, as well as the appearance of the string theta-term from the field-theoretical one in 4D, and k-string tensions at N larger than 2. In particular, we point out the relevance of negative stiffness for stabilizing confining strings, an effect recently re-discovered in material science. At finite temperature, we present a derivation of the confining-string free energy and show that, at the one-loop level and for a certain class of string models in the large-D limit, it matches that of QCD at large N. This crucial matching is again a consequence of the negative stiffness. In the discussion of the finite-temperature properties of the 3D Georgi-Glashow model, in order to be closer to QCD, we mostly concentrate at the effects produced by some extensions of the model by external matter fields, such as dynamical fundamental quarks or photinos, in the supersymmetric generalization of the model.Comment: 79 pages, LaTeX2e, uses ws-procs975x65.cls, no figures, minor editorial corrections are included. To be published in the Ian Kogan Memorial Collection "From Fields to Strings: Circumnavigating Theoretical Physics", World Scientific, 200

Superscaling in Nuclei: A Search for Scaling Function Beyond the Relativistic Fermi Gas Model

We construct a scaling function $f(\psi^{\prime})$ for inclusive electron scattering from nuclei within the Coherent Density Fluctuation Model (CDFM). The latter is a natural extension to finite nuclei of the Relativistic Fermi Gas (RFG) model within which the scaling variable $\psi^{\prime}$ was introduced by Donnelly and collaborators. The calculations show that the high-momentum components of the nucleon momentum distribution in the CDFM and their similarity for different nuclei lead to quantitative description of the superscaling in nuclei. The results are in good agreement with the experimental data for different transfer momenta showing superscaling for negative values of $\psi^{\prime}$, including those smaller than -1.Comment: 16 pages, 5 figures, submitted for publication to Phys. Rev.

Superscaling and Neutral Current Quasielastic Neutrino-Nucleus Scattering beyond the Relativistic Fermi Gas Model

The superscaling analysis is extended to include quasielastic (QE) scattering via the weak neutral current of neutrinos and antineutrinos from nuclei. The scaling function obtained within the coherent density fluctuation model (used previously in calculations of QE inclusive electron and charge-changing (CC) neutrino scattering) is applied to neutral current neutrino and antineutrino scattering with energies of 1 GeV from $^{12}$C with a proton and neutron knockout (u-channel inclusive processes). The results are compared with those obtained using the scaling function from the relativistic Fermi gas model and the scaling function as determined from the superscaling analysis (SuSA) of QE electron scattering.Comment: 10 pages, 6 figures, published in Phys. Rev.