Ten years of the analytic perturbation theory in QCD

The renormalization group method allows improving the properties of the QCD perturbative power series in the ultraviolet region. But it ultimately leads to unphysical singularities of observables in the infrared domain. The analytic perturbation theory is the next step in improving the perturbative expansions. Specifically, it involves an additional analyticity requirement based on the causality principle and implemented in the Källen–Lehmann and Jost–Lehmann representations. This approach eliminates spurious singularities of the perturbative power series and enhances the stability of the series with respect to both higher-loop corrections and the choice of the renormalization scheme. This paper is an overview of the basic stages in developing the analytic perturbation theory in QCD, including its recent applications to describing hadronic processes.