Anomalous dimension of gluonic operator in polarized deep inelastic scattering at O(1/N_f)

We compute the O(1/N_f) correction to the predominantly gluonic flavour singlet twist-2 anomalous dimension used in polarized deep inelastic scattering. It is consistent with known two loop perturbation theory and we determine the three loop contribution at O(1/N_f). The treatment of the epsilon-tensor in the large N_f d-dimensional critical point formalism is also discussed.Comment: 8 Latex pages, 1 postscript figur

The method of expansion of Feynman integrals

The method of expansion of integrals in external parameters is suggested. It is quite universal and works for Feynman integrals both in Euclidean and Minkowski regions of momenta.Comment: 6 pages, latex, no figure

Higher derivative relativistic quantum gravity

Relativistic quantum gravity with the action including terms quadratic in the curvture tensor is analyzed. We derive new expressions for the corresponding Lagrangian and the graviton propagator within dimensional regularization. We argue that the considered model is a good candidate for the fundamental quantum theory of gravitation.Comment: 7 page

The 4-loop quark mass anomalous dimension and the invariant quark mass

We present the analytical calculation of the four-loop quark mass anomalous dimension in Quantum Chromodynamics within the minimal subtraction scheme. On the basis of this result we find that the so-called invariant quark mass is a very good reference mass for the accurate evolution of the running MS-bar quark mass in phenomenological applications. We also obtain for the first time a complete 4-th order perturbative QCD expression for a physical quantity, the total Higgs boson decay rate into hadrons, and analyze the infrared fixed point for this case.Comment: 11 pages, Late

On the role of the quark mass thresholds in extrapolations of the running \alpha_s

The accuracy of the conventional treatment of quark mass thresholds in the QCD running coupling constant $\alpha_s$, based on the step approximation to the $\beta$--function, is investigated. The errors of extrapolating \ase(\mu) from low energies to $\mu=M_Z$, implied by this approximation, are shown to be of the same magnitude as the typical next--to--next--to--leading order contributions to \as and tend to increase the resulting \as. The importance of the proper choice of matching points is emphasized.Comment: latex, 7 pages, 2 uuencoded figure

Matching QCD and HQET at three loops

QCD/HQET matching for the heavy-quark field and heavy-light quark currents with three-loop accuracy is discussed.Comment: Talk at Loops and Legs 2010, Woerlitz, 25-30 April, 7 pages; v2: references adde

Structure function evolution at next-to-leading order and beyond

Results are presented of two studies addressing the scaling violations of deep-inelastic structure functions. Factorization-scheme independent fits to all ep and mu p data on F_2 are performed at next-to-leading order (NLO), yielding alpha_s(M_Z) = 0.114 +- 0.002_exp (+0.006-0.004)_th . In order to reduce the theoretical error dominated by the renormalization-scale dependence, the next-higher order (NNLO) needs to be included. For the flavour non-singlet sector, it is shown that available calculations provide sufficient information for this purpose at x > 10^-2.Comment: 3 pages LaTeX including 4 eps-figures, uses npb.sty. Talk presented at DIS'99, DESY-Zeuthen, April 1999. To appear in the proceeding

The next-to-leading QCD approximation to the Ellis-Jaffe sum rule

The \alpha_s^2 correction to the Ellis-Jaffe sum rule for the structure function g_1 of polarized deep inelastic lepton-nucleon scattering is calculated.Comment: 9 pages, latex, CERN-TH.7208/9

Next-to-next-to-leading logarithmic threshold resummation for deep-inelastic scattering and the Drell-Yan process

The soft-gluon resummation exponents G^N in moment space are investigated for the quark coefficient functions in deep-inelastic structure functions and the quark-antiquark contribution to the Drell-Yan cross section dsigma/dM. Employing results from two- and three-loop calculations we obtain the next-to-next-to-leading logarithmic terms alpha_s (alpha_s ln N)^n of G^N to all orders in the strong coupling constant alpha_s. These new contributions facilitate a reliable assessment of the numerical effect and the stability of the large-N expansion.Comment: 9 pages, LaTeX, 2 eps-figure