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

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

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 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

MATAD: a program package for the computation of MAssive TADpoles

In the recent years there has been an enormous development in the evaluation of higher order quantum corrections. An essential ingredient in the practical calculations is provided by vacuum diagrams, i.e. integrals without external momenta. In this paper a program package is described which can deal with one-, two- and three-loop vacuum integrals with one non-zero mass parameter. The principle structure is introduced and the main parts of the package are described in detail. Explicit examples demonstrate the fields of application.Comment: 37 pages, to be published in Comp. Phys. Commu

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

Moments of heavy quark correlators with two masses: exact mass dependence to three loops

We compute moments of non-diagonal correlators with two massive quarks. Results are obtained where no restriction on the ratio of the masses is assumed. Both analytical and numerical methods are applied in order to evaluate the two-scale master integrals at three loops. We provide explicit results for the latter which are useful for other calculations. As a by-product we obtain results for the electroweak $\rho$ parameter up to three loops which can be applied to a fourth generation of quarks with arbitrary masses.Comment: 22 pages, 9 figure

RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses

In this paper the formulae are collected which are needed for the computation of the strong coupling constant and quark masses at different energy scales and for different number of active flavours. All equations contain the state-of-the-art QCD corrections up to three- and sometimes even four-loop order. For the practical implementation {\tt Mathematica} is used and a package containing useful procedures is provided.Comment: 32 pages, ps figures included, accepted for publication in Computer Physics Communication

Reconstruction of heavy quark current correlators at O(\alpha_s^3)

We construct approximate formulas for the O(\alpha_s^3) QCD contributions to vector, axial-vector, scalar and pseudo-scalar quark current correlators, which are valid for arbitrary values of momenta and masses. The derivation is based on conformal mapping and the Pade approximation procedure and incorporates known expansions in the low energy, threshold and high energy regions. We use our results to estimate additional terms in these expansions.Comment: 24 pages, 4 figure