We construct an asymptotic expansion in powers of the coupling constant directly of the cross-section for pair production and decay of fundamental unstable particles. The resonant and kinematic singularities arising in the expansion we treat in the sense of distributions. This mode allows us to transform formally divergent integrals into absolutely convergent ones with keeping the asymptotic property of the expansion. The appropriate procedure is elaborated up to an arbitrary order of the expansion. The peculiarity of application of the procedure in the threshold region is analysed. The scheme of the calculations within the NNLO approximation is explicitly discussed.

The processes of production and subsequent decay of W-and Z-bosons in e + e − collisions are considered in a recently proposed modified perturbation theory (PT), based on a direct expansion of probabilities instead of amplitudes. In such an approach the non-integrable singularities in the phase space, which are intrinsic in the conventional PT, appear as singularities in the coupling constant (with subsequent compensation by the decay factors of unstable particles). In the present paper the systematic investigation of the modified PT is carried out. The results are compared with the results of the conventional approach, based on calculation of the amplitude with Dyson resummation. A solution to the problem of the loss of one-loop PT order in the resonance region is found. On the basis of this solution the proof of gauge cancellations in any order of the modified PT is given. A simple generalization of the fermion-loop scheme is proposed which provides a complete description of W-pair production in next-to-leading order approximation.

We show that Gribov diffusion of the partons in the impact parameter plane, which leads to the square-root-of-logarithmic growth of the transverse size of the hadrons, can occur only simultaneously with a similar diffusion in the transverse-momentum space. At the same time, a restriction of the partons in the transverse momenta entails an increase in their propagation in the impact parameter plane. Ultimately this leads to a logarithmic growth of the transverse size of hadrons at asymptotically high energies.

A generalization of the on-mass-shell scheme of UV renormalization (the OMS scheme) to the case of presence of unstable fundamental particles is proposed. Its basic ingredients are as follows: (i) the renormalized mass coincides with a real part of the position of the complex pole of the corresponding propagator, (ii) the imaginary part of the on-shell self-energy coincides with the imaginary part of the complex pole position. The latter property implies the gauge-invariance of the imaginary part of the on-shell self-energy in the OMS scheme and its direct connection with the width of the unstable particle. Starting with the three-loops this connection becomes nontrivial.