Infrared renormalons and analyticity structure in pQCD

Relation between the infrared renormalons, the Borel resummation prescriptions, and the analyticity structure of Green functions in perturbative QCD (pQCD) is investigated. A specific recently suggested Borel resummation prescription resulted in the Principal Value and an additional power-suppressed correction that is consistent with the Operator Product Expansion. Arguments requiring the finiteness of the result for any power coefficient of the leading infrared renormalon, and the consistency in the case of the absence of that renormalon, require that this prescription be modified. The apparently most natural modification leads to the result represented by the Principal Value. The analytic structure of the amplitude in the complex coupling plane, obtained in this way, is consistent with that obtained in the literature by other methods.Comment: 6 pages, revtex4, 1 eps-figure; improved version - the paragraph containing Eqs.(18) and (19) is new, as well as the next paragraph; the Title modified; some references added; version to appear in Phys. Rev.

Pade-related resummations of the pressure of quark-gluon plasma by approximate inclusion of g**6-terms

We perform various resummations of the hot QCD pressure based on the actual knowledge of the perturbation series which includes the g**6 ln(1/g) and part of the g**6 terms. Resummations are performed separately for the short- and long-distance parts. The g**6 term of the short-distance pressure is estimated on the basis on the known UV cutoff dependence of the long-distance part. The resummations are of the Pade and Borel-Pade type, using in addition the (Pade-)resummed expression for the squared screening mass mE**2 and for the EQCD coupling parameter gE**2. The resummed results depend weakly on the yet unknown g**6 terms and on the the short-range renormalization scale, at all temperatures. The dependence on the long-range renormalization scale is appreciable at low temperatures T < 1 GeV. The resulting dependence of pressure on temperature T is compatible with the results of the lattice calculations at low T.Comment: 25 pages, 15 double figures, 4 single figures, revtex4; thoroughly extended analysis; more figures; conclusions more clearly formulated; new references added; title slightly changed; accepted for publication in Phys.Rev.

Scale-independent mixing angles

A radiatively-corrected mixing angle has to be independent of the choice of renormalization scale to be a physical observable. At one-loop in MS-bar, this only occurs for a particular value, p*, of the external momentum in the two-point functions used to define the mixing angle: p*^2=(M1^2+M2^2)/2, where M1, M2 are the physical masses of the two mixed particles. We examine two important applications of this to the Minimal Supersymmetric Standard Model: the mixing angle for a) neutral Higgs bosons and b) stops. We find that this choice of external momentum improves the scale independence (and therefore provides a more reliable determination) of these mixing angles.Comment: 14 pages, 11 ps figures Version to appear in PR

One-Loop QCD Mass Effects in the Production of Polarized Bottom and Top Quarks

The analytic expressions for the production cross sections of polarized bottom and top quarks in $e^+e^-$ annihilation are explicitly derived at the one-loop order of strong interactions. Chirality-violating mass effects will reduce the longitudinal spin polarization for the light quark pairs by an amount of $3\%$, when one properly considers the massless limit for the final quarks. Numerical estimates of longitudinal spin polarization effects in the processes $e^+e^-\to b\bar{b}(g)$ and $e^+e^- \to t\bar{t}(g)$ are presented.Comment: 17 p. (5 figs available upon request), LaTeX, MZ-TH/93-30, RAL/93-81, FTUV/93-4

Presence of asthma risk factors and environmental exposures related to upper respiratory infection-triggered wheezing in middle school-age children.

Viral respiratory infections and exposure to environmental constituents such as tobacco smoke are known or suspected to trigger wheezing/asthma exacerbations in children. However, few population-based data exist that examine the relationship between wheezing triggered by viral respiratory infections and environmental exposures. In this investigation we used population-based data to evaluate differences in exposures between symptomatic middle school-age children who did and did not report wheezing triggered by viral respiratory infections. As part of the North Carolina School Asthma Survey (NCSAS), a 66-question data instrument was used to collect information from children enrolled in North Carolina public middle schools during the 1999-2000 school year. Associations between exposures and upper respiratory infection-triggered wheezing (URI-TW) among symptomatic children were examined using adjusted prevalence odds ratios (PORs). Video methods developed for the International Study of Asthma and Allergies in Childhood were used to assess wheezing. Among the 33,534 NCSAS symptomatic participants, positive associations were observed between most exposures and URI-TW. Reported presence of all allergy variables (PORs ranging from 2.11 to 2.45) was more strongly associated with URI-TW than either smoking or other exposures. Presence of URI-TW was higher at increasing levels of tobacco smoke exposure, but no apparent dose-response effect was observed for other indoor air pollutants. URI-TW in middle school children is most associated with reported allergen sensitivity, relative to other asthma risk factors and environmental exposures. Data from this investigation may be useful in developing assessment, screening, and targeting strategies to improve asthma and wheezing management in children

Relating Physical Observables in QCD without Scale-Scheme Ambiguity

We discuss the St\"uckelberg-Peterman extended renormalization group equations in perturbative QCD, which express the invariance of physical observables under renormalization-scale and scheme-parameter transformations. We introduce a universal coupling function that covers all possible choices of scale and scheme. Any perturbative series in QCD is shown to be equivalent to a particular point in this function. This function can be computed from a set of first-order differential equations involving the extended beta functions. We propose the use of these evolution equations instead of perturbative series for numerical evaluation of physical observables. This formalism is free of scale-scheme ambiguity and allows a reliable error analysis of higher-order corrections. It also provides a precise definition for $\Lambda_{\overline{\rm MS}}$ as the pole in the associated 't Hooft scheme. A concrete application to $R(e^+e^- \to {\rm hadrons})$ is presented.Comment: Plain TEX, 4 figures (available upon request), 22 pages, DOE/ER/40322-17

Non-Abelian Dipole Radiation and the Heavy Quark Expansion

Dipole radiation in QCD is derived to the second order in $\alpha_s$. A power-like evolution of the spin-singlet heavy quark operators is obtained to the same accuracy. In particular, ${\cal O}(\alpha_s^2)$ relation between a short-distance low-scale running heavy quark mass and the \barMS mass is given. We discuss the properties of the effective QCD coupling \aw(E) which governs the dipole radiation. This coupling is advantageous for heavy quark physics.Comment: 12 pages, Late

Dynamical mass generation by source inversion: Calculating the mass gap of the Gross-Neveu model

We probe the U(N) Gross-Neveu model with a source-term $J\bar{\Psi}\Psi$. We find an expression for the renormalization scheme and scale invariant source $\hat{J}$, as a function of the generated mass gap. The expansion of this function is organized in such a way that all scheme and scale dependence is reduced to one single parameter d. We get a non-perturbative mass gap as the solution of $\hat{J}=0$. In one loop we find that any physical choice for d gives good results for high values of N. In two loops we can determine d self-consistently by the principle of minimal sensitivity and find remarkably accurate results for N>2.Comment: 13 pages, 3 figures, added referenc

High Salinity Effects on the Components of Relative Growth Rate in Rhodes Grass

Rhodes grass (Chloris gayana Kunth), is widely cultivated in the semiarid tropics and favored for its salt tolerance. Nevertheless, productivity decreases significantly under saline conditions, especially in tetraploid cultivars. The purpose of this work was to explore, in tetraploid cultivar Boma, the physiological causes for the observed salt-associated growth reduction. The effects of high salinity (200 mM NaCl) on the components of relative growth rate were analyzed in greenhouse experiments. An early reduction in leaf area expansion was observed, which later resulted in decreased dry matter accumulation. Plant leafiness was reduced by effects both on dry matter allocation to photosynthetic organs and, more significantly, on leaf surface expansion. This caused reductions in the number of tillers, and afterwards, stolons. Photosynthetic production was altered later than leaf area expansion, indicating, as has been seen in other species, that the main effect of salinity was a limitation of leaf growth

Analytic Approach to Perturbative QCD

The two-loop invariant (running) coupling of QCD is written in terms of the Lambert W function. The analyticity structure of the coupling in the complex Q^2-plane is established. The corresponding analytic coupling is reconstructed via a dispersion relation. We also consider some other approximations to the QCD beta-function, when the corresponding couplings are solved in terms of the Lambert function. The Landau gauge gluon propagator has been considered in the renormalization group invariant analytic approach (IAA). It is shown that there is a nonperturbative ambiguity in determination of the anomalous dimension function of the gluon field. Several analytic solutions for the propagator at the one-loop order are constructed. Properties of the obtained analytical solutions are discussed.Comment: Latex-file, 19 pages, 2 tables, 51 references, to be published in Int. J. Mod. Phys.