I.L. Solovtsov

New expansion in QCD

Abstract We formulate a systematic, nonperturbative expansion in quantum chromodynamics using a new small parameter. The quark-gluon running coupling constant, quark masses and static quark-antiquark potential are constructed.

ß-function for the ϕ4-model in variational perturbation theory

Abstract We consider the renormalization procedure for the ϕ4-model in the variational perturbation theory. The nonperturbative s-function is derived in the framework of the proposed approach. The obtained result is in agreement with the four-loop approximation and has an asymptotic behaviour as g 3 2 for a large coupling constant.

Gaussian effective potential in variational perturbation theory

Abstract The nonperturbative Gaussian effective potential is derived in the λϕ 4 -theory as the first nontrivial order of variational perturbation theory. In the framework of the proposed approach the algorithm of calculating corrections is determined from the very beginning. Various ways of constructing the variational procedure for the action functional and questions about the convergence of the variational perturbation theory series are discussed. The series convergence for the anharmonic variational perturbation theory functional is proved.

Convergent series in variational perturbation theory

Abstract The problem of convergenof series of the variational perturbation theory isanalyzed for the λλφ 4 ( d ) -model. It is shown that there exist such methods of choosing variational additions that lead to convergent series for any values of the coupling constants.

Analytic properties of the QCD running coupling constant and τ decay

Abstract A non-perturbative expansion method which gives a well-defined analytic continuation of the running coupling constant from the spacelike to the timelike region is applied to the inclusive semileptonic decay of the τ-lepton. The method allows us to evaluate R τ by integration over the non-perturbative physical region, rather than by using Cauchys theorem, and hence to incorporate threshold effects in a very direct way. Within our framework the difference between the effective coupling constants in the timelike and spacelike domains can be substantial and is not simply a matter of the standard π 2 terms.

Nonperturbative expansion in QCD

Abstract The purpose of this article is to construct the nonperturbative expansion in quantum chromodynamics using a new small parameter and apply it to the investigation of the connection between nonperturbative and perturbative regimes of the effective coupling constant. We calculate the nonperturbative renormalization group β -function and discuss the properties of the series convergence using the two-loop approximation in this method. Based on the information from meson spectroscopy we derive the effective coupling constant in the perturbative region.

Re+e− at low energies in variational perturbation theory

Abstract We calculate R e + e − at low energies using method of variational perturbation theory in quantum chromodynamics. We apply the “smearing” method to compare the obtained theoretical prediction for R e + e − with experimental data down to lowest energies. The problem of the “freezing” of the QCD coupling constant is discussed.

A nonperturbative a-expansion technique and the Adler D-function

We show that the “experimental” D-functions corresponding to the e+e− annihilation into hadrons and the inclusive τ-decay data both are in good agreement with results obtained in the framework of the nonperturbative a-expansion method.

NONPERTURBATIVE β-FUNCTION IN QUANTUM CHROMODYNAMICS

We propose a method by which it is possible to go beyond the scope of quantum chromodynamics perturbation theory. By using a new small parameter we formulate a systematic nonperturbative expansion and derive a renormalization β-function in quantum chromodynamics.

Infrared asymptotic behavior of gauge-invariant propagator in quantum electrodynamics

A new class of gauge-invariant fields is introduced. The Dyson-Schwinger equations are obtained for the gauge-invariant generalization of the spinor propagator. On the basis of these equations, and also by means of functional methods, it is shown that the gauge-invariant spinor propagator has a singularity in the form of a simple pole in the infrared region.