Mass Corrections to the Vector Current Correlator

Three-loop QCD corrections to the vector current correlator are considered. The large momentum procedure is applied in order to evaluate mass corrections up to order $(m^2/q^2)^6$. The inclusion of the first seven terms to the ratio $R=\sigma(e^+e^- \to hadrons)/\sigma(e^+e^- \to \mu^+\mu^-)$ leads to reliable predictions from the high energy region down to relatively close to threshold.Comment: 16 pages, LaTeX, 11 postscript 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

Four-Loop Decoupling Relations for the Strong Coupling

We compute the matching relation for the strong coupling constant within the framework of QCD up to four-loop order. This allows a consistent five-loop running (once the $\beta$ function is available to this order) taking into account threshold effects. As a side product we obtain the effective coupling of a Higgs boson to gluons with five-loop accuracy.Comment: 11 page

Threshold expansion for heavy-light systems and flavor off-diagonal current-current correlators

An expansion scheme is developed for Feynman diagrams describing the production of one massive and one massless particle near the threshold. As an example application, we compute the correlators of heavy-light quark currents, (\bar b gamma_mu u) and (\bar b gamma_5 u), through O(alpha_s^2).Comment: 4 pages, revtex

R(s) and hadronic tau-Decays in Order alpha_s^4: technical aspects

We report on some technical aspects of our calculation of alpha_s^4 corrections to R(s) and the semi-leptonic tau decay width [1-3]. We discuss the inner structure of the result as well as the issue of its correctness. We demonstrate recently appeared independent evidence positively testing one of two components of the full result

Quartic Mass Corrections to RhadR_{had}

The influence of nonvanishing quark masses on the total cross section in electron positron collisions and on the $Z$ decay rate is calculated. The corrections are expanded in $m^2/s$ and \as. Methods similar to those applied for the quadratic mass terms allow to derive the corrections of order \as m^4/s^2 and \as^2m^4/s^2. Coefficients which depend logarithmically on $m^2/s$ and which cannot be absorbed in a running quark mass arise in order \as^2. The implications of these results on electron positron annihilation cross sections at LEP and at lower energies in particular between the charm and the bottom threshold and for energies several GeV above the $b\bar b$ threshold are discussed.Comment: 17 pages, LaTex (uses epsf.sty, figures appended as uuencoded ps- and eps-files). A complete postscript file, including figures, is available via anonymous ftp at ttpux2.physik.uni-karlsruhe.de (129.13.102.139) as /pub/ttp94-08/ttp94-08.ps, Local preprint# TTP94-0

Higher Moments of Heavy Quark Vacuum Polarization

We present analytical calculation of the first seven moments of the heavy quark vacuum polarization function in the three-loop order. The obtained results are compared against the asymptotic formulas following from the threshold singularities. We also discuss the $\mu$ dependence of the moments within the BLM procedure.Comment: 9 pages, LaTeX, no figures, sprocl.sty provided (To appear in the Proceedings of the Second Workshop on Continuous Advances in QCD, Minneapolis, U.S.A., March 1996). Postscript also available at ftp://www-ttp.physik.uni-karlsruhe.de/ttp96-22/ttp96-22.ps or at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints

Hoelder Inequalities and QCD Sum-Rule Bounds on the Masses of Light Quarks

QCD Laplace Sum-Rules must satisfy a fundamental Hoelder inequality if they are to consistently represent an integrated hadronic spectral function. The Laplace sum-rules of pion currents is shown to violate this inequality unless the $u$ and $d$ quark masses are sufficiently large, placing a lower bound on $m_u+m_d$, the SU(2)-invariant combination of the light-quark masses.Comment: 3 pages, latex, write-up of talk presented at DPF 200

Recent progress in computing four-loop massive correlators

We report about recent progress in computing four-loop massive correlators. The expansion of these correlators in the external momentum leads to vacuum integrals. The calculation of these vacuum integrals can be used to determine Taylor expansion coefficients of the vacuum polarization function and decoupling functions in perturbative Quantum chromodynamics. New results at four-loop order for the lowest Taylor expansion coefficient of the vacuum polarization function and for the decoupling relation are presented.Comment: 4 pages, talk given at the 12th International Conference on Quantum Chromodynamics, Montpellier, 4-8th July 200

Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions

The anomalous dimensions of the gluon and ghost fields as well as the ghost-ghost-gluon and quark-quark-gluon vertexes are analytically computed in pQCD. Taken together with already available anomalous dimensions of the coupling constant, the quark field and the mass the results lead to complete knowledge of all renormalization constant entering into the renormalization of the QCD Lagrangian at the four-loop level. As a by-product we get scale and scheme invariant gluon and ghost propagators at NNNLO. Using a theorem due to Dudal, Verschelde and Sorella, we also construct the four-loop anomalous dimension of the ``gluon mass operator'', A^2, in the Landau gauge.Comment: a reference added. Final version accepted for publication in Nucl. Phys. B. Full list of the results can be found (in a computer-readable form) in http://www-ttp.physik.uni-karlsruhe.de/Progdata/ttp04/ttp04-08

Double Bubble Corrections to Heavy Quark Production

Second order ${\cal O}(\alpha_s^2)$ corrections to the heavy quark production cross-section due to massless quarks and coloured scalars are calculated for all energies above threshold. Based on the method introduced in this letter also the gauge non-invariant second order corrections due to the pure gluonic selfenergy insertion and a certain class of ${\cal{O}}(\alpha_s^3)$ and ${\cal{O}}(\alpha_s^4)$ corrections are determined. For the special choice of the gauge parameter, $\xi=4$, the leading threshold and high energy behaviour of the pure second order gluonic corrections to the cross-section are governed by the gluonic self energy insertion.Comment: 9 pages, latex, 17 figures, the complete postscript file of this preprint, including figures, is available via anonymous ftp at ftp://www-ttp.physik.uni-karlsruhe.de/ttp96-04/ttp96-04.ps (129.13.102.139) or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints