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The influence of uniaxial small-scale anisotropy on the stability of the scaling regimes and on the anomalous scaling of the structure functions of a passive scalar advected by a Gaussian solenoidal velocity field with finite correlation time is investigated by the field theoretic renormalization group and operator product expansion within one-loop approximation. Possible scaling regimes are found and classified in the plane of exponents $\epsilon-\eta$, where $\epsilon$ characterizes the energy spectrum of the velocity field in the inertial range $E\propto k^{1-2\epsilon}$, and $\eta$ is related to the correlation time of the velocity field at the wave number $k$ which is scaled as $k^{-2+\eta}$. It is shown that the presence of anisotropy does not disturb the stability of the infrared fixed points of the renormalization group equations which are directly related to the corresponding scaling regimes. The influence of anisotropy on the anomalous scaling of the structure functions of the passive scalar field is studied as a function of the fixed point value of the parameter $u$ which represents the ratio of turnover time of scalar field and velocity correlation time. It is shown that the corresponding one-loop anomalous dimensions, which are the same (universal) for all particular models with concrete value of $u$ in the isotropic case, are different (nonuniversal) in the case with the presence of small-scale anisotropy and they are continuous functions of the anisotropy parameters, as well as the parameter $u$. The dependence of the anomalous dimensions on the anisotropy parameters of two special limits of the general model, namely, the rapid-change model and the frozen velocity field model, are found when $u\to \infty$ and $u\to 0$, respectively., Comment: revtex, 25 pages, 37 figures

Influence of uniaxial small-scale anisotropy and compressibility on the stability of scaling regime and on the anomalous scaling of structure functions of a scalar field is investigated in the model of a passive scalar field advected by the compressible Gaussian strongly anisotropic velocity field with the covariance $\propto \delta(t-t^{\prime})|{\bf x}-{\bf x^{\prime}}|^{2\epsilon}$ by using the field theoretic renormalization group and the operator product expansion. The inertial-range stability of the corresponding scaling regime is established. The anomalous scaling of the single-time structure functions is studied and the corresponding anomalous exponents are calculated. Their dependence on the compressibility parameter and anisotropy parameters is analyzed. It is shown that the presence of compressibility leads to the decreasing of the critical dimensions of the important composite operators, i.e., the anomalous scaling is more pronounced in the compressible systems. This result is demonstrated for the structure function of the third order. All calculations are done to the first order in $\epsilon$., Comment: 6 pages, 4 figures, talk presented by R. Remecky at the Conference "The Small Triangle Meeting on Theoretical Physics 2006", September 17-20 2006, Herl'any, Slovakia; will be published in proceedings of the conference

Influence of weak uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of a passive transverse vector field advected by an incompressible turbulent flow is investigated by means of the field theoretic renormalization group. Weak anisotropy means that parameters which describe anisotropy are chosen to be close to zero, therefore in all expressions it is enough to leave only linear terms in anisotropy parameters. Turbulent fluctuations of the velocity field are taken to have the Gaussian statistics with zero mean and defined noise with finite correlations in time. It is shown that stability of the inertial-range scaling regimes in the three-dimensional case is not destroyed by anisotropy but the corresponding stability of the two-dimensional system can be destroyed even by the presence of weak anisotropy. A borderline dimension $d_c$ below which the stability of the scaling regime is not present is calculated as a function of anisotropy parameters., Comment: 6 pages, 4 figures, talk presented by M. Scholtz at the Conference "The Small Triangle Meeting on Theoretical Physics 2006", September 17-20 2006, Herl'any, Slovakia; will be published in proceedings of the conference

Influence of strong uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of a passive transverse vector field advected by an incompressible turbulent flow is investigated by means of the field theoretic renormalization group. Turbulent fluctuations of the velocity field are taken in the form of a Gaussian statistics with zero mean and defined noise with finite correlations in time. It is shown that stability of the inertial-range scaling regimes in the three-dimensional case is not destroyed by anisotropy but the corresponding stability of the two-dimensional system can be corrupted by the presence of anisotropy. A borderline dimension $d_c$ below which the stability of the scaling regime is not present is calculated as a function of anisotropy parameters., Comment: 6 pages, 3 figures, talk given by M. Jurcisin at the conference "Mathematical Modeling and Computational Physics 2006", High Tatra Mountains, Slovakia, August 28 - September 1, 2006

The influence of compressibility and helicity on the stability of the scaling regimes of a passive scalar advected by a Gaussian velocity field with finite correlation time is investigated by the field theoretic renormalization group within two-loop approximation. The influence of helicity and compressibility on the scaling regimes is discussed as a function of the exponents $\epsilon$ and $\eta$, where $\epsilon$ characterizes the energy spectrum of the velocity field in the inertial range $E\propto k^{1-2\epsilon}$, and $\eta$ is related to the correlation time at the wave number $k$ which is scaled as $k^{-2+\eta}$. The restrictions given by nonzero compressibility and helicity on the regions with stable infrared fixed points which correspond to the stable infrared scaling regimes are discussed. A special attention is paid to the case of so-called frozen velocity field when the velocity correlator is time independent. In this case, explicit inequalities which must be fulfilled in the plane $\epsilon-\eta$ are determined within two-loop approximation., Comment: 6 pages, missing letter in title is supplemented, Talk presented by M. Jurcisin at the Conference "The Small Triangle Meeting on Theoretical Physics 2005", September 2-4 2005, Snina, Slovakia; will be published in proceedings of the conference

Model of a passive scalar field advected by the compressible Gaussian strongly anisotropic velocity field with the covariance $\propto \delta(t-t^{\prime})|{\bf x}-{\bf x^{\prime}}|^{2\epsilon}$ is studied by using the field theoretic renormalization group and the operator product expansion. The inertial-range stability of the corresponding scaling regime is established. The anomalous scaling of the single-time structure functions is studied and the corresponding anomalous exponents are calculated. Their dependence on the compressibility parameter and anisotropy parameters is analyzed. It is shown that, as in the isotropic case, the presence of compressibility leads to the decreasing of the critical dimensions of the important composite operators, i.e., the anomalous scaling is more pronounced in the compressible systems. All calculations are done to the first order in $\epsilon$., Comment: 35 pages, 28 figures, references are changed, mirror changes in the text

Developed magnetohydrodynamic turbulence near two dimensions $d$ up to three dimensions has been investigated by means of renormalization group approach and double expansion regularization. A modification of standard minimal subtraction scheme has been used to analyze the stability of the Kolmogorov scaling regime which is governed by the renormalization group fixed point. The exact analytical expressions have been obtained for the fixed points. The continuation of the universal value of the inverse Prandtl number $u=1.562$ determined at $d=2$ up to $d=3$ restores the value of $u=1.393$ which is known in the kinetic fixed point from usual $\epsilon$-expansion. The magnetic stable fixed point has been calculated and its stability region has been also examined. This point losses stability: (1) below critical value of dimension $d_c=2.36$ (independently on the $a$-parameter of a magnetic forcing) and, (2) below the value of $a_c=0.146$ (independently on the dimension)., Comment: 16 pages, Talk presented by M. Stehlik at the Conference "Renormalization Group 2005", Helsinki, Finland 30 August - 3 September 2005. To apear in J. Phys. A: Math. Gen

We have investigated the advection of a passive scalar quantity by incompressible helical turbulent flow in the frame of extended Kraichnan model. Turbulent fluctuations of velocity field are assumed to have the Gaussian statistics with zero mean and defined noise with finite time-correlation. Actual calculations have been done up to two-loop approximation in the frame of field-theoretic renormalization group approach. It turned out that space parity violation (helicity) of turbulent environment does not affect anomalous scaling which is peculiar attribute of corresponding model without helicity. However, stability of asymptotic regimes, where anomalous scaling takes place, strongly depends on the amount of helicity. Moreover, helicity gives rise to the turbulent diffusivity, which has been calculated in one-loop approximation., Comment: 16 pages, talk given by M. Hnatich at "Renormalization Group 2005", Helsinki, Finland 30 August - 3 September 2005. To apear in J. Phys. A: Math. Gen

The influence of compressibility on the stability of the scaling regimes of the passive scalar advected by a Gaussian velocity field with finite correlation time is investigated by the field theoretic renormalization group within two-loop approximation. The influence of compressibility on the scaling regimes is discussed as a function of the exponents $\epsilon$ and $\eta$, where $\epsilon$ characterizes the energy spectrum of the velocity field in the inertial range $E\propto k^{1-2\epsilon}$, and $\eta$ is related to the correlation time at the wave number $k$ which is scaled as $k^{-2+\eta}$. The restrictions given by nonzero compressibility on the regions with stable infrared fixed points which correspond to the stable infrared scaling regimes are discussed in detail. A special attention is paid to the case of so-called frozen velocity field, when the velocity correlator is time independent. In this case, explicit inequalities which must be fulfilled in the plane $\epsilon-\eta$ are determined within two-loop approximation. The existence of a "critical" value $\alpha_c$ of the parameter of compressibility $\alpha$ at which one of the two-loop conditions is canceled as a result of the competition between compressible and incompressible terms is discussed. Brief general analysis of the stability of the scaling regime of the model with finite correlations in time of the velocity field within two-loop approximation is also given., Comment: 16 pages, Talk presented by M. Jurcissin at the Conference "Renormalization Group 2005", Helsinki, Finland 30 August - 3 September 2005. To apear in J. Phys. A: Math. Gen

The influence of helicity on the stability of scaling regimes, on the effective diffusivity, and on the anomalous scaling of structure functions of a passive scalar advected by a Gaussian solenoidal velocity field with finite correlation time is investigated by the field theoretic renormalization group and operator product expansion within two-loop approximation. The influence of helicity on the scaling regimes is discussed and shown in the plane of exponents $\epsilon-\eta$, where $\epsilon$ characterizes the energy spectrum of the velocity field in the inertial range $E\propto k^{1-2\epsilon}$, and $\eta$ is related to the correlation time at the wave number $k$ which is scaled as $k^{-2+\eta}$. The restrictions given by nonzero helicity on the regions with stable fixed points which correspond to the scaling regimes are analyzed in detail. The dependence of the effective diffusivity on the helicity parameter is discussed. The anomalous exponents of the structure functions of the passive scalar field which define their anomalous scaling are calculated and it is shown that although the separate composite operators which define them strongly depend on the helicity parameter the resulting two-loop contributions to the critical dimensions of the structure functions are independent of helicity. Details of calculations are shown., Comment: revtex4, 28 pages, 13 figures, final version published in Phys. Rev. E

A quantum field model of helical MHD stochastically forced by gaussian hydrodynamic, magnetic and mixed noices is investigated. These helical noises lead to an exponential increase of magnetic fluctuations in the large scale range. Instabilities, which are produced in this process, are eliminated by spontaneous symmetry breaking mechanism accompanied by creation of the homogeneous stationary magnetic field., Comment: Latex, 10 pages

We investigate focus points of the renormalization group equations of the Minimal Supersymmetric Standard Model. We show that within this model the up- and down-type Higgs mass soft supersymmetry breaking parameters have focus point behavior at the electroweak scale simultaneously when appropriate conditions are fulfilled. The focus point scenario is holding for large $\tan \beta$. This two focus point scenario allows to fix the pole top-quark mass which is within the experimentally allowed interval. The main goal of the present paper is the investigation of the influence of the existence of focus points on the determination of the mass of the lightest Higgs boson., Comment: latex, 7 pages, 4 figures, references are added, one e-mail is corrected

Inertial-range scaling behavior of high-order (up to order N=51) structure functions of a passively advected vector field has been analyzed in the framework of the rapid-change model with strong small-scale anisotropy with the aid of the renormalization group and the operator-product expansion. It has been shown that in inertial range the leading terms of the structure functions are coordinate independent, but powerlike corrections appear with the same anomalous scaling exponents as for the passively advected scalar field. These exponents depend on anisotropy parameters in such a way that a specific hierarchy related to the degree of anisotropy is observed. Deviations from power-law behavior like oscillations or logarithmic behavior in the corrections to structure functions have not been found., Comment: 15 pages, 18 figures

Interplay of kinematic and magnetic forcing in a model of a conducting fluid with randomly driven magnetohydrodynamic equations has been studied in space dimensions $d\ge 2$ by means of the renormalization group. A perturbative expansion scheme, parameters of which are the deviation of the spatial dimension from two and the deviation of the exponent of the powerlike correlation function of random forcing from its critical value, has been used in one-loop approximation. Additional divergences have been taken into account which arise at two dimensions and have been inconsistently treated in earlier investigations of the model. It is shown that in spite of the additional divergences the kinetic fixed point associated with the Kolmogorov scaling regime remains stable for all space dimensions $d\ge 2$ for rapidly enough falling off correlations of the magnetic forcing. A scaling regime driven by thermal fluctuations of the velocity field has been identified and analyzed. The absence of a scaling regime near two dimensions driven by the fluctuations of the magnetic field has been confirmed. A new renormalization scheme has been put forward and numerically investigated to interpolate between the $\epsilon$ expansion and the double expansion., Comment: 12 pages, 4 figures

The fully developed turbulence with weak anisotropy is investigated by means of renormalization group approach (RG) and double expansion regularization for dimensions $d\ge 2$. Some modification of the standard minimal substraction scheme has been used to analyze stability of the Kolmogorov scaling regime which is governed by the renormalization group fixed point. This fixed point is unstable at $d=2$; thus, the infinitesimally weak anisotropy destroyes above scaling regime in two-dimensional space. The restoration of the stability of this fixed point, under transition from $d=2$ to $d=3,$ has been demonstrated at borderline dimension $ 2

In the framework of the MSSM the non-universal boundary conditions of soft SUSY breaking parameters are considered. Taking as input the top, bottom and Z-boson masses, the values of the gauge couplings at the EW scale and the infrared quasi-fixed points for Yukawa couplings and the soft parameters the mass of the lightest CP-even Higgs boson is found to be m_h=92.7^{+10}_{-4.9} +- 5 +- 0.4 GeV/c^2 for the low \tan\beta case and m_h=125.7^{+6.4}_{-9.0} +- 5 +- 0.4 GeV/c^2 (\mu > 0) or m_h =125.4^{+6.6}_{-9.0} +-5 +- 0.4 GeV/c^2 (\mu < 0) in the case of large $\tan\beta$., Comment: 12 pages, LaTeX, 12 .eps figures, final version

We consider the infrared quasi fixed point solutions of the renormalization group equations for the Yukawa couplings and soft supersymmetry breaking parameters in the MSSM in the \underline{large $\tan\beta$} regime. The existence of IR quasi fixed points together with the values of gauge couplings, third generation quarks, lepton and Z-boson masses allows one to predict masses of the Higgs bosons and SUSY particles as functions of the only free parameter, $m_{1/2}$, or the gluino mass. The lightest Higgs boson mass for $M_{SUSY} \approx 1$ TeV is found to be $m_h=128.2-0.4-7.1 \pm 5$ GeV for $\mu>0$ and $m_h=120.6-0.1-3.8 \pm 5$ GeV for $\mu<0$., Comment: 15 pages, LateX file with 4 eps figures, corrected numbers, new column in table, last version

We consider the infrared quasi-fixed point solutions of the renormalization group equations for the top-quark Yukawa coupling and soft supersymmetry breaking parameters in the MSSM. The IR quasi-fixed points together with the values of the gauge couplings, the top-quark and Z-boson masses allow one to predict masses of the Higgs bosons, the stop squarks and the lightest chargino as functions of the only free parameter $m_{1/2}$ or the gluino mass. The mass of the lightest Higgs boson for $\mu>0$ and $M_{SUSY} \approx 1$ TeV is found to be $m_h=(94.3+1.6+0.6\pm5\pm0.4)$ GeV. The case with $\mu<0$ is excluded by experimental data., Comment: 17 pages, LateX file with 13 eps figures, Corrected version, references are added. Final version to be published in Modern Physics Letters A