K.G. Chetyrkin

Quark mass anomalous dimension to O (αs4)

We present the results of analytic calculation of the quark mass anomalous dimension to alpha_s**4.

Three-loop polarization function and O(αs2) corrections to the production of heavy quarks

Abstract The three-loop vacuum polarization function Π ( q 2 ) induced by a massive quark is calculated. A comprehensive description of the method is presented. From the imaginary part the O ( α s 2 ) result for the production of heavy quarks R ( s ) = σ ( e + e − → hadrons)/ σ ( e + e − → μ + μ − ) can be extracted. Explicit formulae separated into the different colour factors are given.

QCD corrections to the e+e− cross-section and the Z boson decay rate: concepts and results

Abstract QCD corrections to the electron positron annihilation cross section into hadrons and to the hadronic Z boson decay rate are reviewed. Formal developments are introduced in a form particularly suited for practical applications. These include the operator product expansion, the heavy mass expansion, the decoupling of heavy quarks and matching conditions. Exact results for the quark mass dependence are presented whenever available, and formulae valid in the limit of small bottom mass ( m b 2 ⪡ s ) or of large top mass ( m t 2 ⪢ s ) are presented. The differences between vector and axial vector induced rates as well the classification of singlet and nonsinglet rates are discussed. Handy formulae for all contributions are collected and their numerical relevance is investigated. Prescriptions for the separation of the total rate into partial rates are formulated. The applicability of the results in the low energy region, relevant for measurements around 10 GeV and below, is investigated and numerical predictions are collected for this energy region.

Correlator of the quark scalar currents and Γtot(H → hadrons) at O(αs3) in pQCD

Abstract We present the results of the analytical evaluation of the massless four-loop O(αs3) correction to the correlator of the quark scalar currents and the Higgs decay rate into hadrons. In numerical form we found (in MS scheme) that Γ(H→ b b)=( 3G F 4 2 π )M H m b 2 (M H )[1+5.667 α s π +(35.94−1.359n f ) α s π ) 2 +(164.139−25.771n f +0.259n f 2 )( α s π ) 3 ] where nf is the number of quark flavour and αs = αs(MH).

Corrections of order O(GFMt2αs2) to the ϱ parameter

The three-loop QCD corrections to the

Heavy quark current correlators to O(αs2

rho

Heavy quark vacuum polarisation to three loops

parameter from top and bottom quark loops are calculated. The result differs from the one recently calculated by Avdeev et al. As function of the pole mass the numerical value is given by

Corrections of order αs3 to Rhad in pQCD with light gluinos

drho=frac{3G_F M_t^2}{8sqrt{2}pi^2}(1- 2.8599 api - 14.594 (api)^2 )

Four loop massless propagators: An algebraic evaluation of all master integrals

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QCD corrections from the top quark to relations between electroweak parameters up to order alpha 2s.

Abstract In this paper the three-loop polarization functions Π ( q 2 ) are calculated for the cases of an external vector, axial-vector, scalar or pseudo-scalar current. Results are presented for the imaginary part which directly leads to the cross section σ ( e + e − → Z → hadrons) and to the Higgs decay rates, respectively.