Resummation in QCD Fractional Analytic Perturbation Theory

Abstract

We describe the generalization of Analytic Perturbation Theory (APT) for QCD observables, initiated by Radyushkin, Krasnikov, Pivovarov, Shirkov and Solovtsov, to fractional powers of coupling -- Fractional APT (FAPT). The basic aspects of FAPT is shortly summarized. 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 $H^0\to b\bar{b}$. The main conclusion is: To achieve an accuracy of the order of 1% it is enough to take into account up to the third correction.

4 pages, 2 figures, invited talk at the Bogolyubov Kyiv Conference on Modern Problems of Theoretical and Mathematical Physics, Sept. 15--18, 2009, Kyiv, Ukraine; improved citations

References in corpus (5)

• Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses
• QCD Analytic Perturbation Theory. From integer powers to any power of the running coupling
• Global Fractional Analytic Perturbation Theory in QCD with Selected Applications
• Generalization of the BLM procedure and its scales in any order of pQCD
• Analyticity properties of three-point functions in QCD beyond leading order