The QCD analytic running coupling and chiral symmetry breaking

The basic idea behind the analytic approach to Quantum Field Theory is to supplement the perturbative treatment of the renormalization group (RG) formalism with the nonperturbative information encoded in the corresponding dispersion relations [1]. The latter, being based on the “first principles” of the theory, provide one with the definite analytic properties in the kinematic variable of a physical quantity at hand [2,3]. In practice the analytization procedure [2] amounts to the restoration of the correct analytic properties for a given quantity A(q) by imposing the Källén–Lehmann representation