Two-loop Resummation in Fractional Analytic Perturbation Theory

Abstract

This talk describes the resummation approach in (Fractional) Analytic Perturbation Theory (FAPT) in QCD. First, we make a short historical review of the (F)APT approach and then shortly describe the global scheme of FAPT which allows one to take into account heavy-quark thresholds. After that we show how it is possible to resum a non-power series in (F)APT both in the one- and two-loop approximations. As an application we suggest our analysis of the Higgs boson decay $H^0\to b\bar{b}$, important for the LHC program, and of the vector-current Adler function.

Comments: 11 pages; 3 figures; invited talk given at the 16th International Seminar "Quarks-2010", Kolomna (Russia), June 6--12, 2010