Fixing the renormalisation scheme in NNLO perturbative QCD using conformal limit arguments

We discuss how the renormalisation scheme ambiguities in QCD can be fixed, when two observables are related, by requiring the coefficients in the perturbative expansion relating the two observables to have their conformal limit values, i.e. to be independent of the $\beta$-function of the renormalised coupling. We show how the next-to-leading order BLM automatic scale fixing method can be extended to next-to-next-to-leading order to fix both the renormalisation scale and $\beta_2$ in a unique way. As an example we apply the method to the relation between Bjorken's sum rule and $R_{e+e-}$ and compare with experimental data as well as other scheme fixing methods.Comment: 14 pages LaTeX, uses revtex.sty, 1 encapsulated PostScript figur

Increased BOLD signal in the fusiform gyrus during implicit emotion processing in anorexia nervosa

Background The behavioural literature in anorexia nervosa (AN) has suggested impairments in psychosocial functioning and studies using facial expression processing tasks (FEPT) have reported poorer recognition and slower identification of emotions. Methods Functional magnetic resonance imaging (fMRI) was used alongside a FEPT, depicting neutral, mildly happy and happy faces, to examine the neural correlates of implicit emotion processing in AN. Participants were instructed to specify the gender of the faces. Levels of depression, anxiety, obsessive–compulsive symptoms and eating disorder behaviour were obtained and principal component analysis (PCA) was performed to acquire uncorrelated variables. Results fMRI analysis revealed a greater blood-oxygenation level dependent (BOLD) response in AN in the right fusiform gyrus to all facial expressions. This response showed a linear increase with the happiness of the facial expression and was found to be stronger in those not taking medication. PCA analysis revealed a single component indicating a greater level of general clinical symptoms. Conclusion Neuroimaging findings would suggest that alterations in implicit emotion processing in AN occur during early perceptual processing of social signals and illustrate greater engagement on the FEPT. The lack of separate components using PCA suggests that the questionnaires used might not be suited as predictive measures

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

Commensurate Scale Relations in Quantum Chromodynamics

We use the BLM method to show that perturbatively-calculable observables in QCD can be related to each other without renormalization scale or scheme ambiguity. We define and study the commensurate scale relations. We show that the commensurate scales satisfy the renormalization group transitivity rule which ensures that predictions in PQCD are independent of the choice of an intermediate renormalization scheme. We generalize the BLM procedure to higher order. The application of this procedure to relate known physical observables in QCD gives surprisingly simple results. In particular, the annihilation ratio $R_{e^+e^-}$ and the Bjorken sum rule for polarized electroproduction are related through simple coefficients, which reinforces the idea of a hidden symmetry between these two observables.Comment: 35 pages (RevTeX), one PostScript figure included at the end. SLAC-PUB-6481, UMD Preprint #94-13

Non-perturbative renormalization of lattice operators in coordinate space

We present the first numerical implementation of a non-perturbative renormalization method for lattice operators, based on the study of correlation functions in coordinate space at short Euclidean distance. The method is applied to compute the renormalization constants of bilinear quark operators for the non-perturbative O(a)-improved Wilson action in the quenched approximation. The matching with perturbative schemes, such as MS-bar, is computed at the next-to-leading order in continuum perturbation theory. A feasibility study of this technique with Neuberger fermions is also presented.Comment: 11 pages and 9 figures, LaTeX2

Effects of technicolor on standard model running couplings

We discuss the running couplings in the standard model, SU(3$)_C \times$SU(2$)_L \times$U(1$)_Y$, when the Higgs sector is replaced by SU($N_{TC})$ technicolor. Particular attention is given to the running of the couplings at momentum scales where technicolor is nonperturbative, and in this region we apply a relativistic constituent technifermion model. This model has been tested against the known running of the QED coupling due to nonperturbative QCD. An understanding of this low momentum running allows the calculation of the couplings at a higher scale, $\Lambda_{pert}$, where technicolor becomes perturbative. We provide numerical values for the changes in the three standard model couplings between $m_Z$ and $\Lambda_{pert}$ due to technicolor, assuming separately ``one doublet'' and ``one family'' technicolor models. The distinction between a running and walking technicolor coupling is also considered.Comment: 14 pages of LaTeX, UTPT-94-

Tau Polarimetry with Inclusive Decays

The spin asymmetry parameter $A_\tau$ characterizing the angular distribution of the total hadron momentum in the decay of a polarized tau can be calculated rigorously using perturbative QCD and the operator product expansion. Perturbative QCD corrections to the free quark result $A_\tau = 1/3$ can be expressed as a power series in $\alpha_s(M_\tau)$ and nonperturbative QCD corrections can be expanded systematically in powers of $1/M_\tau^2$. The QCD prediction is $A_\tau = 0.41 \pm 0.02$. In the decay of a high energy tau into hadrons, the value of the hadronic energy distribution $dR_\tau/dz$ evaluated at the maximum hadronic energy fraction $z = 1$ can also be calculated rigorously from QCD.Comment: LateX, 11 pages, no figures, NUHEP-TH-93-

Renormalization-Scale-Invariant PQCD Predictions for R_e+e- and the Bjorken Sum Rule at Next-to-Leading Order

We discuss application of the physical QCD effective charge $\alpha_V$, defined via the heavy-quark potential, in perturbative calculations at next-to-leading order. When coupled with the Brodsky-Lepage-Mackenzie prescription for fixing the renormalization scales, the resulting series are automatically and naturally scale and scheme independent, and represent unambiguous predictions of perturbative QCD. We consider in detail such commensurate scale relations for the $e^+e^-$ annihilation ratio $R_{e^+e^-}$ and the Bjorken sum rule. In both cases the improved predictions are in excellent agreement with experiment.Comment: 13 Latex pages with 5 figures; to be published in Physical Review

Lattice study of vacuum polarization function and determination of strong coupling constant

We calculate the vacuum polarization functions on the lattice using the overlap fermion formulation.By matching the lattice data at large momentum scales with the perturbative expansion supplemented by Operator Product Expansion (OPE), we extract the strong coupling constant $\alpha_s(\mu)$ in two-flavor QCD as $\Lambda^{(2)}_{\overline{MS}}$ = $0.234(9)(^{+16}_{- 0})$ GeV, where the errors are statistical and systematic, respectively. In addition, from the analysis of the difference between the vector and axial-vector channels, we obtain some of the four-quark condensates.Comment: 24 pages, 9 figures, enlarged version published in Phys. Rev.

Higgs Decay to Top Quarks at O(\alpha_s^2)

Three-loop corrections to the scalar and pseudo-scalar current correlator are calculated. By applying the large momentum expansion mass terms up to order (m^2/q^2)^4 are evaluated analytically. As an application O(\alpha_s^2) corrections to the decay of a scalar and pseudo-scalar Higgs boson into top quarks are considered. It is shown that for a Higgs mass not far above the $t\bar{t}$ threshold these higher order mass corrections are necessary to get reliable results.Comment: Latex, 20 pages, 14 ps-figures. The complete paper, including figures, is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints