Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2009-02-27
Physics
High Energy Physics
High Energy Physics - Phenomenology
20 pages, 6 figures, Invited topical article prepared for the Modern Encyclopedia of Mathematical Physics (MEMPhys), Springer
Scientific paper
The aim of this topical article is to outline the fundamental ideas underlying the recently developed Fractional Analytic Perturbation Theory (FAPT) of QCD and present its main calculational tools. For this, it is first necessary to review previous methods to apply QCD perturbation theory at low spacelike momentum scales, where the influence of the Landau singularities becomes inevitable. Several concepts are considered and their limitations are pointed out. The usefulness of FAPT is discussed in terms of two characteristic hadronic quantities: the perturbatively calculable part of the pion's electromagnetic form factor in the spacelike region and the Higgs-boson decay into a b\bar b pair in the timelike region. In the first case, the focus is on the optimization of the prediction with respect to the choice of the renormalization scheme and the dependence on the renormalization and the factorization scales. The second case serves to show that the application of FAPT to this reaction reaches already at the four-loop level an accuracy of the order of 1%, avoiding difficulties inherent in the standard perturbative expansion.
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