Resummation in Fractional APT: How many loops do we need to take into account?

Abstract

We give a short introduction to the Analytic Perturbation Theory (APT) and its generalization to Fractional powers -- FAPT. We describe how to treat heavy-quark thresholds in FAPT and then show how to resum perturbative series in both the one-loop APT and FAPT. As an application we consider FAPT description of the Higgs boson decay $H^0\to b\bar{b}$.

Comments: 7 pages, 1 figure, talk presented at the International Meeting "Excited QCD", February 8--14, 2009, Zakopane (Poland), misprints corrected