Attempting to describe QCD observables in the IR region

by Dmitry Shirkov (Bogoliubov Laboratory, Dubna)

Thursday 1 Apr 2004, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

Non-perturbative results for QCD effective coupling obtained by lattice simulations and from Dyson--Schwinger equations reveal quantitative variety in the IR behaviour of differently defined \\bar{α}_s(Q). We study the relation between coupling-constant transformations and thereby induced transformations of effective couplings α_i → α_j = f_j (α_i) → \\bar{α}_i (Q; α_i) → \\bar{α}_j (Q; α_j), as well as with integral transformations of the invariant coupling \\bar{α}(Q;α) and of its powers [\\bar{α}(Q; α)]ⁿ → α_X ^[n] (x; α) = x∫ K(xQ)[\\bar{α}(Q; α)]ⁿ dQ. The last transformations change the form of functional expansion for an observable. In particular, they transform the power one, i.e., in powers of \\bar{α}(Q; α), into a non-power functional expansion. Also, they transform regular -- in α variable -- expressions into non-regular ones. Hence, the issue of "strong-coupling perturbative" QCD description in hadronization and IR regions is not only the problem of defining an effective coupling but of an adequate non-power expansion as well.