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

Rhad: A program for the evaluation of the hadronic R-ratio in the perturbative regime of QCD

This paper describes the fortran program rhad which performs a numerical evaluation of the photon-induced hadronic R-ratio, R(s), related to the cross section for electron-positron annihilation, for a given center-of-mass energy \sqrt{s}. In rhad the state-of-the-art perturbative corrections to R(s) are implemented and the running and decoupling of the strong coupling constant and the quark masses is automatically treated consistently. Several options allow for a flexible use of the program.Comment: 40 pages, LaTeX. 18 ps-files included. Typos fixed, references updated. The program and this paper are available from http://www.rhad.de

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

Multi-Loop Results, Charm- and Bottom-Quark Masses and the Strong Coupling Constant

The impact of recent multi-loop calculations on precise determinations of charm- and bottom-quark masses and the strong coupling constant is discussed.Comment: ICHEP08 proceedin

Moments of heavy-light current correlators up to three loops

We consider moments of the non-diagonal vector, axial-vector, scalar and pseudo-scalar current correlators involving two different massive quark flavours up to three-loop accuracy. Expansions around the limits where one mass is zero and the equal-mass case are computed. These results are used to construct approximations valid for arbitrary mass values.Comment: 21 page

Beta functions and anomalous dimensions up to three loops

We derive an algorithm for automatic calculation of perturbative $\beta$-functions and anomalous dimensions in any local quantum field theory with canonical kinetic terms. The infrared rearrangement is performed by introducing a common mass parameter in all the propagator denominators. We provide a set of explicit formulae for all the necessary scalar integrals up to three loops.Comment: 22 pages, 4 figures, uses epsf.st

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

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

Heavy Quark Masses from Sum Rules in Four-Loop Approximation

New data for the total cross section $\sigma(e^+e^-\to{hadrons})$ in the charm and bottom threshold region are combined with an improved theoretical analysis, which includes recent four-loop calculations, to determine the short distance $\bar{\rm MS}$ charm and bottom quark masses. A detailed discussion of the theoretical and experimental uncertainties is presented. The final result for the $\bar{\rm MS}$-masses, $m_c(3 {GeV})=0.986(13)$ GeV and $m_b(10 {GeV})=3.609(25)$ GeV, can be translated into $m_c(m_c)=1.286(13)$ GeV and $m_b(m_b)=4.164(25)$ GeV. This analysis is consistent with but significantly more precise than a similar previous study.Comment: 29 page