The Qcd Analytic Effective Charge and Its Dependence on the Pion Mass

The description of the infrared hadron dynamics remains a crucial challenge for elementary particle physics. Whereas perturbative calculations allow for a detailed study of the strong interaction processes at high energies, to date there is no reliable theoretical method which would enable one to handle the hadron dynamics at low energies. However, many physical phenomena are tightly bound to the intrinsically nonperturbative aspects of the strong interaction. The renormalization group (RG) method plays a fundamental role in the framework of Quantum Field Theory (QFT) and its applications. Usually, in order to describe Quantum Chromodynamics (QCD) in the ultraviolet region, one applies the RG method together with perturbative calculations. Eventually, this leads to approximate solutions of the RG equations, which are commonly used in the quantitative analysis of high energy processes. However, such solutions possess unphysical singularities in the infrared domain, a fact that contradicts the general principles of local QFT and complicates the theoretical description of the intermediate and low energy experimental data. Nevertheless, these difficulties can be avoided if one complements the perturbative results with a proper nonperturbative insight. For this purpose the relevant dispersion relations can be used. The idea of employing the information “stored” in such integral representations together with per-