[en] We present the scheme-invariant unpolarized and polarized flavor non-singlet evolution equation to N${}^3$LO for the structure functions F${}_2$(x,Q${}^2$) and g${}_1$(x,Q${}^2$) including the charm- and bottom quark effects in the asymptotic representation. The corresponding evolution is based on the experimental measurement of the non-singlet structure functions at a starting scale Q${}_0^2$. In this way the evolution does only depend on the strong coupling constant α${}_s$(M${}_Z$) or the QCD scale Λ${}_{QCD}$ and the charm and bottom quark masses m${}_c$ and m${}_b$ and provides one of the cleanest ways to measure the strong coupling constant in future high luminosity deep-inelastic scattering experiments. The yet unknown parts of the 4-loop anomalous dimensions introduce only a marginal error in this analysis.

[en] A brief review on the status of unpolarized parton densities and the determination of the QCD scale Λ_QCD from deep-inelastic scattering data is presented. (orig.)

[en] The k _{perpendicularto} dependent gluon distribution for protons, pions and photons is calculated numerically accounting for the resummation of small x effects due to the Lipatov equation. It is represented by a convolution of a gluon density in the collinear limit and a universal function G(x, k², μ) for which an analytic expression is derived. (orig.)

[en] Relevant QED and QCD radiative corrections are calculated for the pair production cross section of leptoquarks in e⁺e^- annihilation. The corrections for the production near threshold are found to be large. For β = 0.1 the QED corrections of -30 to -45% are obtained, while QCD corrections may reach O(+100%). (orig.)

[en] We describe the structural relations between nested harmonic sums emerging in the description of physical single scale quantities up to the 3-loop level in renormalizable gauge field theories. These are weight w=6 harmonic sums. We identify universal basic functions which allow to describe a large class of physical quantities and derive their complex analysis. For the 3-loop QCD Wilson coefficients 35 basic functions are required, whereas a subset of 15 describes the 3-loop anomalous dimensions. (orig.)

[en] A program is described calculating leading log radiative corrections to deep inelastic neutral and charged current ep scattering. Due to the factorization of the leading logs also lepton bremsstrahlung for exclusive ep processes can be calculated. The package includes access to different choices of parton distributions, descriptions of the low-Q² behaviour and the different choices of kinematical variables. (orig.)

[en] The possibilities to measure structure functions, to extract parton distributions, and to measure α_s and Λ_QCD in current and future high energy deep inelastic scattering experiments are reviewed. A comparison is given for experiments at HERA, an ep option at LEP xLHC, and a high energy neutrino experiment. (orig.)

[en] The QED radiative corrections are calculated in the leading log approximation up to O(α²) for different definitions of the kinematical variables using jet measurement, the 'mixed' variables, the double angle method, and a measurement based on θ_e and y_JB. Higher order contributions due to exponentiation of soft radiation are included. (orig.)

[en] We compute the static contribution to the gravitational interaction potential of two point masses in the velocity-independent five-loop (and 5th post-Newtonian) approximation to the harmonic coordinates effective action in a direct calculation. The computation is performed using effective field methods based on Feynman diagrams in momentum-space in d=3-2$\mathrm{ϵ<!--\; ??\; -->}$ space dimensions. We also reproduce the previous results including the 4th post-Newtonian order.

[en] The nucleon structure functions probed in deep-inelastic scattering at large virtualities form an important tool to test Quantum Chromdynamics (QCD) through precision measurements of the strong coupling constant α_s(M_Z²) and the different parton distribution functions. The exact knowledge of these quantities is also of importance for all precision measurements at hadron colliders. During the last two decades very significant progress has been made in performing precision calculations. We review the theoretical status reached for both unpolarized and polarized lepton-hadron scattering based on perturbative QCD. (orig.)