Taming Landau singularities in QCD perturbation theory: The analytic approach 2.0
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aming Landau Singularities in QCD Perturbation Theory: The Analytic Approach 2.01, 2 N. G. Stefanis Institut für Theoretische Physik II, RuhrUniversität Bochum, D44780 Bochum, Germany email: [email protected]unibochum.de Abstract—The aim of this topical article is to outline the fundamental ideas underlying the recently devel oped Fractional Analytic Perturbation Theory (FAPT) of QCD and present its main calculational tools together with key applications. For this, it is first necessary to review previous methods to apply QCD pertur bation 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 Higgsboson decay into a b 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 fourloop level an accuracy of the order of 1%, avoiding difficulties inherent in the standard perturbative expansion. The obtained results are compared with estimates from fixedorder and contourimproved QCD perturbation theory. Using the brandnew Higgs mass value of about 125 GeV, measured at the Large Hadron Collider (CERN), a prediction for Γ H → bb = 2.4 ± 0.15 MeV is extracted. Keywords: General properties of perturbation theory, Perturbative calculations in QCD, Summation of per turbation theory, Renormalization group evolution, Electromagnetic form factors DOI: 10.1134/S1063779613030155 21
1. INTRODUCTION
In writing this article, I have two main objectives. The first is to chart the evolution of the analytic approach to Quantum Chromodynamics (QCD) per turbation theory, focusing on the key turning points in its theoretical development. The second is to demon strate how this approach works in terms of selected applications. Of course, I am forced to leave out many interesting applications and aspects of the approach, which in turn means that my presentation will not be complete. I would refer the reader to the original ref erences for further reading and in order to study the subject in more technical detail. The sorts of ideas and issues to be discussed in this presentation include the following benchmarks: —“Ultraviolet (UV) freedom”, “infrared (IR) sla very”, and Landau singularity. —Renormalizability, analyticity (in Q2 and g2), causality, and summability. 1 This
is an extended and updated version of an invited plenary talk at the International Conference Renormalization Group and Related Topics (RG 2008), Dubna, Russia, September 1–5, 2008. 2 The article is published in the original.
—First remedies in the infrared: Color saturation
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