We apply the strategy of regions within dimensional regularization to find functions involved in evolution equations which govern the asymptotic dynamics of the Abelian form factor and four-fermion amplitude in the SU (N ) gauge theory in the Sudakov limit up to the next-to-leading logarithmic approximation. The results are used for the analysis of the dominant electroweak corrections to the fermion-antifermion pair production in the e + e − annihilation at high energy.

The next-to-next-to-next-to-leading order (N 3 LO) Hamiltonian of potential nonrelativistic QCD is derived. The complete matching of the Hamiltonian and the contribution from the ultrasoft dynamical gluons relevant for perturbative boundstate calculations is performed including one-, two-, and three-loop contributions. The threshold expansion is used to disentangle and match contributions of different scales in the effective-theory calculations. As a physical application, the heavyquarkonium spectrum is obtained at N 3 LO for the case of vanishing QCD beta function. Our results set the stage for a full N 3 LO analysis of the heavy-quarkonium system.

In the framework of nonrelativistic QCD, we consider a new class of radiative corrections, which are generated at next-to-next-to-next-to-leading order through the chromoelectric dipole interaction of heavy quarkonium with ultrasoft virtual gluons. We provide analytical formulae from which the resulting shifts in the quarkonium energy levels and the wave functions at the origin may be calculated. We discuss the phenomenological implications for the top-antitop and Υ systems and point out some limitations of describing charmonium using a Coulomb potential.

We present the achievements of the last years of the experimental and theoretical groups working on hadronic cross section measurements at the low-energy e + e − colliders in Beijing, Frascati, Ithaca, Novosibirsk, Stanford and Tsukuba and on τ decays. We sketch the prospects in these fields for the years to come. We emphasise the status and the precision of the Monte Carlo generators used to analyse the hadronic cross section measurements obtained as well with energy scans as with radiative return, to determine luminosities and τ decays. The radiative corrections fully or approximately implemented in the various codes and the contribution of the vacuum polarisation are discussed.