QCD coupling up to third order in standard and analytic perturbation theories

We analyze two sets of specific functions, that/which form the basis of the nonpower asymptotic expansions both in the timelike and spacelike regions for single scale dependent QCD observables in the Shirkov--Solovtsov's Analytic Perturbation Theory (APT) free of unphysical singularities. These functions are explicitly derived up to the third order in the closed form in terms of the Lambert-W function. As an input we used the exact two loop and the three loop (corresponding to Pad\'e transformed beta-function) RG solutions for common invariant coupling \alpha_s. The elegant recurrence formulas, helpful for numerical analysis, are obtained for the both sets of the APT functions. Then we construct the global versions of APT functions using the continuity conditions (at the quark thresholds) on the \alpha_s in the \bar{MS} scheme and give numerical results. For first three of these functions \mathfrak{A}_n(s) and {\cal A}_n(Q^2); n=1,2,3 in the large interval of the momentum transfer and energy (1 GeV <Q,{\sqrt s}< 170 GeV), numerical tables are presented. From these we observe that, for the timelike arguments, the differences between functions \mathfrak{A}_n(s) and the corresponding powers of the standard iteratively approximated coupling \alpha_s^n(s) are not negligible even for moderate energies in the five--flavor region.Comment: 21 pages, Latex, 12 tables. Abstract is changed. The recurrence formulas (18)-(20) are added. Formula (35) corrected and Table 2 is revised. Misprint in formula (37) is corrected. Formula (38) adde

Generalization of the BLM procedure and its scales in any order of pQCD

The Brodsky--Lepage--Mackenzie procedure is sequentially and unambiguously extended to any fixed order of perturbative QCD beyond the so called ``large--\beta_0 approximation''. As a result of this procedure, the obtained perturbation series looks like a continued-fraction representation. A subsequent generalization of this procedure is developed, in order to optimize the convergence of the final series, along the lines of the Fastest Convergence Prescription. This generalized BLM procedure is applied to the Adler D function and also to R_{e^+e^-} in QCD at N$^3$LO. A further extension of the sequential BLM is presented which makes use of additional parameters to optimize the convergence of the power-series at any fixed order of expansion.Comment: 24 pages, JHEP3, 4 figures are enclosed as eps-file, final version to be published in JHE

Monitoring and Optimization of ATLAS Tier 2 Center GoeGrid

The demand on computational and storage resources is growing along with the amount of infor- mation that needs to be processed and preserved. In order to ease the provisioning of the digital services to the growing number of consumers, more and more distributed computing systems and platforms are actively developed and employed. The building block of the distributed computing infrastructure are single computing centers, similar to the Worldwide LHC Computing Grid, Tier 2 centre GoeGrid. The main motivation of this thesis was the optimization of GoeGrid perfor- mance by efficient monitoring. The goal has been achieved by means of the GoeGrid monitoring information analysis. The data analysis approach was based on the adaptive-network-based fuzzy inference system (ANFIS) and machine learning algorithm such as Linear Support Vector Machine (SVM). The main object of the research was the digital service, since availability, reliability and ser- viceability of the computing platform can be measured according to the constant and stable provisioning of the services. Due to the widely used concept of the service oriented architecture (SOA) for large computing facilities, in advance knowing of the service state as well as the quick and accurate detection of its disability allows to perform the proactive management of the com- puting facility. The proactive management is considered as a core component of the computing facility management automation concept, such as Autonomic Computing. Thus in time as well as in advance and accurate identification of the provided service status can be considered as a contribution to the computing facility management automation, which is directly related to the provisioning of the stable and reliable computing resources. Based on the case studies, performed using the GoeGrid monitoring data, consideration of the approaches as generalized methods for the accurate and fast identification and prediction of the service status is reasonable. Simplicity and low consumption of the computing resources allow to consider the methods in the scope of the Autonomic Computing component

Complete Renormalization Group Improvement-Avoiding Factorization and Renormalization Scale Dependence in QCD Predictions

For moments of leptoproduction structure functions we show that all dependence on the renormalization and factorization scales disappears, provided that all the ultraviolet logarithms involving the physical energy scale Q are completely resummed. The approach is closely related to Grunberg's method of Effective Charges. A direct and simple method for extracting the universal dimensional transmutation parameter of QCD from experimental data is advocated.Comment: 16 pages, no figure

FAPT: a Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory

We provide here all the procedures in \texttt{Mathematica} which are needed for the computation of the analytic images of the strong coupling constant powers in Minkowski (${\bar{\mathfrak A}_{\nu}(s;n_f)}$ and ${\mathfrak A_{\nu}^\text{glob}(s)}$) and Euclidean (${\bar{\mathcal A}_{\nu}(Q^2;n_f)}$ and ${\mathcal A_{\nu}^\text{glob}(Q^2)}$) domains at arbitrary energy scales (${s}$ and ${Q^2}$, correspondingly) for both schemes --- with fixed number of active flavours ${n_f=3, 4, 5, 6}$ and the global one with taking into account all heavy-quark thresholds. These singularity-free couplings are inevitable elements of Analytic Perturbation Theory (APT) in QCD and its generalization --- Fractional APT, needed to apply the APT imperative for renormalization-group improved hadronic observables.Comment: 23 pages, 6 figures. Citations added. Now it matches version approved for publication in Comp. Phys. Commu