Analytic Invariant Charge: Non-perturbative Aspects

Theoretical analysis of hadron dynamics in main part relies upon the renormalization group (RG) method. However, construction of exact solutions to the RG equation is still far from being feasible. Usually, in order to describe the strong interaction processes in asymptotical ultraviolet (UV) region, one applies the RG method together with perturbative calculations. The relevant approximate solutions to the renormalization group equation are used for quantitative analysis of high-energy experimental data. However, such solutions contain unphysical peculiarities in the infrared (IR) domain. An effective way to overcome such difficulties consists in invoking into consideration the analyticity requirement, which follows from the general principles of local Quantum Field Theory (QFT). This idea became the basis of the so-called analytic approach to QFT, which was first formulated in late 1950’s [1]. Recently this approach has been extended to Quantum Chromodynamics (QCD) [2, 3].