Using as ingredients the non-perturbative solutions of various QCD Green'sfunction obtained from Schwinger-Dyson equations (SDEs), we study two versionsof the QCD effective charge. The first one obtained from the pinch techniquegluon self-energy, and the second from the ghost-gluon vertex. Despite thedistinct nature of their buildings blocks, the two effectives charges arealmost identical in the entire range of momenta, due to a fundamental identityrelating the ghost dressing function with the two form factors of Green'sfunction, which is of central importance in the PT-BFM formalism. In this talk,we outline how to derive this crucial identity from the SDEs of theaforementioned Green's functions. The renormalization procedure that preservesthe validity of this identity is discussed in detail. Most importantly, we showthat due to the infrared finiteness of the gluon propagator, the QCD chargeobtained with either definition freezes in the deep infrared, in agreement withtheoretical and phenomenological expectations.
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