The Adler DD-function for N=1{\cal N}=1 SQCD regularized by higher covariant derivatives in the three-loop approximation

We calculate the Adler $D$-function for ${\cal N}=1$ SQCD in the three-loop approximation using the higher covariant derivative regularization and the NSVZ-like subtraction scheme. The recently formulated all-order relation between the Adler function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant is first considered and generalized to the case of an arbitrary representation for the chiral matter superfields. The correctness of this all-order relation is explicitly verified at the three-loop level. The special renormalization scheme in which this all-order relation remains valid for the $D$-function and the anomalous dimension defined in terms of the renormalized coupling constant is constructed in the case of using the higher derivative regularization. The analytic expression for the Adler function for ${\cal N}=1$ SQCD is found in this scheme to the order $O(\alpha_s^2)$. The problem of scheme-dependence of the $D$-function and the NSVZ-like equation is briefly discussed.Comment: 25 pages, 2 figures; the version accepted for publication in Nuclear Physics

Next-to-next-to-leading order fits to CCFR'97 xF3xF_3 data and infrared renormalons

We briefly summarize the outcomes of our recent improved fits to the experimental data of CCFR collaboration for $xF_3$ structure function of $\nu N$ deep-inelastic scattering at the next-to-next-to-leading order. Special attention is paid to the extraction of $\alpha_s(M_Z)$ and the parameter of the infrared renormalon model for $1/Q^2$-correction at different orders of perturbation theory. The results can be of interest for planning similar studies using possible future data of Neutrino Factories.Comment: 3 pages, presented at WG3 of 4th NuFact'02 Workshop, London 1-6 July, 200

Strong enhancement of spin fluctuations in the low-temperature-tetragonal phase of antiferromagnetically ordered La_{2-x-y}Eu_ySr_xCuO_4

Measurements of the static magnetization, susceptibility and ESR of Gd spin probes have been performed to study the properties of antiferromagnetically ordered La_{2-x-y}Eu_ySr_xCuO_4 (x less or equal 0.02) with the low temperature tetragonal structure. According to the static magnetic measurements the CuO_2 planes are magnetically decoupled in this structural phase. The ESR study reveals strong magnetic fluctuations at the ESR frequency which are not present in the orthorhombic phase. It is argued that this drastic enhancement of the spin fluctuations is due to a considerable weakening of the interlayer exchange and a pronounced influence of hole motion on the antiferromagnetic properties of lightly hole doped La_2CuO_4. No evidence for the stripe phase formation at small hole doping is obtained in the present study.Comment: 10 pages, LaTeX, 3 EPS figures; to be published in Journal of Physics: Condensed Matte

Reconsidered estimates of the 10th order QED contributions to the muon anomaly

The problem of estimating the 10th order QED corrections to the muon anomalous magnetic moment is reconsidered. The incorporation of the recently improved contributions to the $\alpha^4$ and $\alpha^5$- corrections to $a_{\mu}$ within the renormalization-group inspired scheme-invariant approach leads to the estimate $a_{\mu}^{(10)}\approx 643(\alpha/pi)^5$. It is in good agreement with the estimate $a_{\mu}^{(10)}= 663(20) (\alpha/\pi)^5$, obtained by Kinoshita and Nio from the numerical calculations of 2958 10-th order diagrams, which are considered to be more important than the still uncalculated 6122 10th-order $m_{\mu}/m_e$-dependent vertex graphs, and 12672 5-loop diagrams, responsible for the mass-independent constant contribution both to $a_{\mu}$ and $a_e$. This confirms Kinoshita and Nio guess about dominance of the 10-th order diagrams calculated by them. Comparisons with other estimates of the $\alpha^5$- contributions to $a_{\mu}$, which exist in the literature, are presented.Comment: 19 pages, LaTeX, some misprints in the text and literature corrected. Results unchaged, to appear in Phys.Rev.

The order O(αˉ αˉs)O(\bar{\alpha}~\bar{\alpha}_s) and O(αˉ2)O(\bar{\alpha}^2) corrections to the decay width of the neutral Higgs boson to the bˉb\bar{b}b pair

We present the analytical expressions for the contributions of the order $O(\bar{\alpha}~\bar{\alpha}_s)$ and $O(\bar{\alpha}^2)$ corrections to the decay width of the Standard Model Higgs boson into the $\bar{b}b$-pair. The numerical value of the mixed QED and QCD correction of order $O(\bar{\alpha}~\bar{\alpha}_s)$ is comparable with the previously calculated terms in the perturbative series for $\Gamma(H^0\to\bar{b}b)$.Comment: LaTeX 5 pages, accepted for publication in Pisma Zh. Eksp. Teor. Fiz. v 66, N5 (1997

Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale

In conventional treatments, predictions from fixed-order perturbative QCD calculations cannot be fixed with certainty due to ambiguities in the choice of the renormalization scale as well as the renormalization scheme. In this paper we present a general discussion of the constraints of the renormalization group (RG) invariance on the choice of the renormalization scale. We adopt the RG based equations, which incorporate the scheme parameters, for a general exposition of RG invariance, since they simultaneously express the invariance of physical observables under both the variation of the renormalization scale and the renormalization scheme parameters. We then discuss the self-consistency requirements of the RG, such as reflexivity, symmetry, and transitivity, which must be satisfied by the scale-setting method. The Principle of Minimal Sensitivity (PMS) requires the slope of the approximant of an observable to vanish at the renormalization point. This criterion provides a scheme-independent estimation, but it violates the symmetry and transitivity properties of the RG and does not reproduce the Gell-Mann-Low scale for QED observables. The Principle of Maximum Conformality (PMC) satisfies all of the deductions of the RG invariance - reflectivity, symmetry, and transitivity. Using the PMC, all non-conformal $\{\beta^{\cal R}_i\}$-terms (${\cal R}$ stands for an arbitrary renormalization scheme) in the perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC scales and the resulting finite-order PMC predictions are both to high accuracy independent of the choice of initial renormalization scale, consistent with RG invariance. [...More in the text...]Comment: 15 pages, 4 figures. References updated. To be published in Phys.Rev.

Finite size effects and magnetic order in the spin-1/2 honeycomb lattice compound InCu{2/3}V{1/3}O{3}

High field electron spin resonance, nuclear magnetic resonance and magnetization studies addressing the ground state of the quasi two-dimensional spin-1/2 honeycomb lattice compound InCu{2/3}V{1/3}O{3} are reported. Uncorrelated finite size structural domains occurring in the honeycomb planes are expected to inhibit long range magnetic order. Surprisingly, ESR data reveal the development of two collinear antiferromagnetic (AFM) sublattices below ~ 20 K whereas NMR results show the presence of the staggered internal field. Magnetization data evidence a spin reorientation transition at ~ 5.7 T. Quantum Monte-Carlo calculations show that switching on the coupling between the honeycomb spin planes in a finite size cluster yields a Neel-like AFM spin structure with a substantial staggered magnetization at finite temperatures. This may explain the occurrence of a robust AFM state in InCu{2/3}V{1/3}O{3} despite an unfavorable effect of structural disorder.Comment: revised version, accepted as a Rapid Communication in Phys. Rev. B (2010

Magnetism of the LTT phase of Eu doped La_{2-x}Sr_xCuO_4

The ESR signal of Gd spin probes (0.5 at %) as well as the static normal state susceptibility of Eu (J(Eu^{3+})=0) doped La_{2-x-y}Sr_xEu_yCuO_4 reveal pronounced changes of the Cu magnetism at the structural transition from the orthorhombic to the low temperature tetragonal phase for all non-superconducting compositions. Both a jumplike decrease of \chi as well as the ESR data show an increase of the in-plane magnetic correlation length in the LTT phase. From the Gd^{3+} ESR linewidth we find that for specific Eu and Sr concentrations in the LTT phase the correlation length increases up to more than 100 lattice constants and the fluctuation frequency of the CuO_2 spin system slows down to 10^{10}- 10^{11}sec^{-1}. However, there is no static order above T ~ 8K in contrast to the LTT phase of Nd doped La_{2-x}Sr_xCuO_4 with pinned stripe correlations.Comment: 7 pages, RevTex, 3 eps figures. To appear in the Proceedings of the International Conference "Stripes, Lattice Instabilities and High Tc Superconductivity", (Rome, Dec. 1996

QCD Tests of the Puzzling Scalar Mesons

Motivated by several recent data, we test the QCD spectral sum rules (QSSR) predictions based on different proposals (\bar qq, \bar q\bar q qq, and gluonium) for the nature of scalar mesons. In the I=1 and 1/2 channels, the unusual (wrong) splitting between the a_0(980) and \kappa(900) and the a_0(980) width can be understood from QSSR within a \bar qq assignement. However, none of the \bar qq and \bar q\bar q qq results can explain the large \kappa width, which may suggest that it can result from a strong interference with non-resonant backgrounds. In the I=0 channel, QSSR and some low-energy theorems (LET) require the existence of a low mass gluonium \sigma_B(1 GeV) coupled strongly to Goldstone boson pairs which plays in the U(1)_V channel, a similar role than the \eta' for the value of the U(1)_A topological charge. The observed \sigma(600) and f_0(980) mesons result from a maximal mixing between the gluonium \sigma_B and \bar qq(1 GeV) mesons, a mixing scheme which passes several experimental tests. OZI violating J/\psi--> \phi\pi^+\pi^-, D_s--> 3\pi decays and J/\psi--> \gamma S glueball filter processes may indicate that most of the I=0 mesons above 1 GeV have important gluonium in their wave functions. We expect that the f_0(1500), f_0(1710) and f_0(1790) have significant gluonium component in their wave functions, while the f_0(1370) is mostly \bar qq. Tests of these results can be provided by the measurements of the pure gluonium \eta'\eta and 4\pi specific U(1)_A decay channels.Comment: Version to appear in Phys. Rev. D (one previous figure corrupted