Resummation in (F)APT

Abstract

We present new results on the summation of nonpower-series expansions in QCD Analytic Perturbation Theory (APT) in the one-loop approximation. We show how to generalize the approach suggested by one of us earlier to the cases of APT and Fractional APT (FAPT) with heavy-quark thresholds. Using this approach we analyze the Higgs boson decay $H^0\to \bar{b}b$. We produce estimations of the higher-order corrections importance in (F)APT and present a very transparent interpretation of the resummation results in terms of ${\Lambda }_{\text{QCD}}$ shifts.

Written version of the talk given at the Memorial Igor Solovtsov Seminar, held on January 17--18, 2008, at the Bogoliubov Laboratory of Theoretical Physics, JINR (Dubna). 15 pages, 1 figure, 1 table. Misprints are corrected and style of proceedings is reproduced

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