Taming Landau singularities in QCD perturbation theory: The analytic approach 2.0

TL;DR

This paper discusses the development and application of Fractional Analytic Perturbation Theory (FAPT) in QCD to address Landau singularities, improving predictions for hadronic processes at low energies.

Contribution

It introduces FAPT as a novel method to handle Landau singularities in QCD and demonstrates its effectiveness in precise calculations of hadronic quantities.

Findings

FAPT improves the accuracy of QCD predictions at low energies.

Application of FAPT achieves about 1% accuracy at four-loop level.

Predicted Higgs decay width into b-quarks aligns with experimental data.

Abstract

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 together with key applications. 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. The obtained results are compared with estimates from fixed-order and contour-improved QCD perturbation theory. Using the brand-new Higgs mass value of about 125 GeV, measured at the Large Hadron Collider (CERN), a prediction for $\Gamma_{H\to b\bar{b}}=2.4 \pm 0.15 {\rm MeV}$ is extracted.