RS-invariant all-orders renormalon resummations for some QCD observables

We propose a renormalon-inspired resummation of QCD perturbation theory based on approximating the renormalization scheme (RS) invariant effective charge beta-function coefficients by the portion containing the highest power of $b$=$\frac{1}{6}(11N$--$2N_{f})$, for SU($N$) QCD with $N_{f}$ quark flavours. This can be accomplished using exact large-$N_{f}$ all-orders results. The resulting resummation is RS-invariant and the exact next-to-leading order (NLO) and next-to-NLO (NNLO) coefficients in any RS are included. This improves on a previously employed naive resummation of the leading-$b$ piece of the perturbative coefficients which is RS-dependent, making its comparison with fixed-order perturbative results ambiguous. The RS-invariant resummation is used to assess the reliability of fixed-order perturbation theory for the $e^{+}e^{-}$ $R$-ratio, the analogous $\tau$-lepton decay ratio $R_{\tau}$, and Deep Inelastic Scattering (DIS) sum rules, by comparing it with the exact NNLO results in the effective charge RS. For the $R$-ratio and $R_{\tau}$, where large-order perturbative behaviour is dominated by a leading ultra-violet renormalon singularity, the comparison indicates fixed-order perturbation theory to be very reliable. For DIS sum rules, which have a leading infra-red renormalon singularity, the performance is rather poor. In this way we estimate that at LEP/SLD energies ideal data on the $R$-ratio could determine $\alpha_{s}(M_{Z})$ to three-significant figures, and for the $R_{\tau}$ we estimate a theoretical uncertainty $\delta\alpha_{s}(m_{\tau})\simeq0.008$ corresponding to $\delta\alpha_{s}(M_{Z})\simeq0.001$. This encouragingly small uncertainty is much less than has recently been deduced from comparison with the ambiguous naive resummation.Comment: 25 pages, uses LaTeX, 12 Postscript figures, epsfig.sty 'elsart.sty' and 'elsart12.sty' are available via anonymous-ftp at ftp://ftp.tex.ac.uk/tex-archive/macros/latex/contrib/supported/elsevie

On the Behavior of the Effective QCD Coupling alpha_tau(s) at Low Scales

The hadronic decays of the tau lepton can be used to determine the effective charge alpha_tau(m^2_tau') for a hypothetical tau-lepton with mass in the range 0 < m_tau' < m_tau. This definition provides a fundamental definition of the QCD coupling at low mass scales. We study the behavior of alpha_tau at low mass scales directly from first principles and without any renormalization-scheme dependence by looking at the experimental data from the OPAL Collaboration. The results are consistent with the freezing of the physical coupling at mass scales s = m^2_tau' of order 1 GeV^2 with a magnitude alpha_tau ~ 0.9 +/- 0.1.Comment: 15 pages, 4 figures, submitted to Physical Review D, added references, some text added, no results nor figures change

A Constraint on Planck-scale Modifications to Electrodynamics with CMB polarization data

We show that the Cosmic Microwave Background (CMB) polarization data gathered by the BOOMERanG 2003 flight and WMAP provide an opportunity to investigate {\it in-vacuo} birefringence, of a type expected in some quantum pictures of space-time, with a sensitivity that extends even beyond the desired Planck-scale energy. In order to render this constraint more transparent we rely on a well studied phenomenological model of quantum-gravity-induced birefringence, in which one easily establishes that effects introduced at the Planck scale would amount to values of a dimensionless parameter, denoted by $\xi$, with respect to the Planck energy which are roughly of order 1. By combining BOOMERanG and WMAP data we estimate $\xi \simeq -0.110 \pm 0.076$ at the 68% c.l. Moreover, we forecast on the sensitivity to $\xi$ achievable by future CMB polarization experiments (PLANCK, Spider, EPIC), which, in the absence of systematics, will be at the 1-$\sigma$ confidence of $8.5 \times 10^{-4}$ (PLANCK), $6.1 \times 10^{-3}$ (Spider), and $1.0 \times 10^{-5}$ (EPIC) respectively. The cosmic variance-limited sensitivity from CMB is $6.1\times 10^{-6}$.Comment: 16 page

Studies on mosquitoes (Diptera: Culicidae) and anthropic environment: 6 - Breeding in empty conditions of rice fields in South-Eastern Brazil Estudos sobre mosquitos (Diptera: Culicidae) e ambiente antrópico: 6 - Observações em campos de arroz não cultivados, na região sudeste do Brasil

Studies on culicid breeding in empty rice fields were carried out during the cultivation cycle from May to November 1993. This period corresponded to stages 1 and 2, when empty conditions prevailed. Breeding occurred in stage 1 and the first part of stage 2, corresponding respectively to fallow uncultivated and ploughing situations. No breeding was found to take place during the second part of stage 2 when transient floods and harrowing occurred. The predominant species were Aedes scapularis, Culex nigripalpus and Cx. mollis. The Pilosus Group of Culex (Melanoconion) was found at lower densities. Some epidemiological considerations are presented.<br>Apresentam-se os resultados obtidos com a pesquisa sistemática de criadouros nas fases não cultivadas dos campos de arroz, correspondendo ao período de maio a novembro de 1993. Esse lapso de tempo foi o referente aos estádios de repouso, de aradura do terreno e de gradeamento. Este foi realizado mediante inundações transitórias e a homogeneização mecânica da terra. O primeiro correspondeu ao estádio 1, enquanto os outros dois, ao estádio 2. Foram encontrados criadouros nas etapas concernentes aos estados de repouso e de aradura. Foram negativas as pesquisas referentes às fases de gradeamento. As espécies predominantes foram Aedes scapularis, Culex nigripalpus e Cx. mollis. Observou-se a existência de associações com o ritmo local das precipitações atmosféricas. São apresentadas considerações sobre o potencial epidemiológico desses encontros

All-orders infrared freezing of Re+e− in perturbative QCD.

We consider the behaviour of the perturbative QCD corrections to the Re+e− ratio, in the limit that the c.m. energy vanishes. Writing , with Qf denoting the electric charge of quark flavour f, we find that for Nf<9 flavours of massless quarks, the perturbative correction to the parton model result smoothly approaches from below the infrared limit , as s→0. Here b=(33−2Nf)/6 is the first QCD beta-function coefficient. This freezing holds to all-orders in perturbation theory. The s-dependence can be written analytically in closed form in terms of the Lambert W function