The criterion of irreducibility of multi-loop Feynman integrals

The integration by parts recurrence relations allow to reduce some Feynman integrals to more simple ones (with some lines missing). Nevertheless the possibility of such reduction for the given particular integral was unclear. The recently proposed technique for studying the recurrence relations as by-product provides with simple criterion of the irreducibility.Comment: LaTeX, 6 pages, no figures, the complete paper, including figures, is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ttp99/ttp99-52/ or via www at http://www-ttp.physik.uni-karlsruhe.de/Preprints

Quark Mass and Field Anomalous Dimensions to O(αs5){\cal O}(\alpha_s^5)

We present the results of the first complete analytic calculation of the quark mass and field anomalous dimensions to ${\cal O}(\alpha_s^5)$ in QCD

QCD Corrections to Hadronic Z and tau Decays

We present a brief (mainly bibliographical) report on recently performed calculations of terms of order O(\alpha_s^4 n_f^2) and O(\alpha_s^4 n_f^2 m_q^2) for hadronic Z and \tau decay rates. A few details about the analytical evaluation of the masters integrals appearing in the course of calculations are presented.Comment: revised version (some references corrected); 3 pages, talk given at International Europhysics Conference on High Energy Physics, Aachen, Germany, 17-23 July 200

Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators

We extend the ${\cal O}(\alpha_s^5)$ result of the analytic calculation of the quark mass anomalous dimension in pQCD [1] to the case of a generic gauge group. We present explicit formulas which express the relevant renormalization constants in terms of four-loop massless propagators. We also use our result to shed new light on the old puzzle of the absence of even zetas in results of perturbative calculations for a class of physical observables.Comment: An important reference [47] is correcte

Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses

We compute, for the first time, the absorptive part of the massless correlator of two quark scalar currents in five loops. As physical applications we consider the O(alpha_s^4) corrections to the decay rate of the Standard Model Higgs boson into quarks, as well as the constraints on the strange quark mass following from QCD sum rules.Comment: 5 pages, REVTeX4. Few references updated. The final version, accepted for publication. The complete paper is also available via the www at http://www-ttp.physik.uni-karlsruhe.de/Preprints

Hadronic Z- and tau-Decays in Order alpha_s^4

Using recently developed methods for the evaluation of five-loop amplitudes in perturbative QCD, corrections of order alpha_s^4 for the cross section of electron-positron annihilation into hadrons and for the decay rates of the Z-boson and the tau-lepton into hadrons are evaluated. The new terms lead to a significant stabilization of the perturbative series, to a reduction of the theory uncertainly in the strong coupling constant alpha_s, as extracted from these measurements, and to a small shift of the central value, moving two central values closer together. The agreement between two values of alpha_s measured at vastly different energies constitutes a striking test of asymptotic freedom. Combining the results from Z and tau decays we find alpha_s(M_Z)=0.1198 \pm 0.0015 as one of the most precise and presently only result for the strong coupling constant in order alpha_s^4.Comment: few citations added, final published versio