Behavior of the Effective QCD Coupling in the Infrared Region

The summary of nonperturbative results for the QCD invariant coupling $\bar \alpha _s$ obtained by numerical lattice simulations for the path integral and by solution of the approximate Dyson–Schwinger equations reveals a remarkable variety of IR behaviors of $\bar \alpha _s(Q^2)$ even at the qualitative level. In turn, this raises the question of the correspondence between the results obtained by different groups. We analyze this issue in terms of mass-dependent coupling-constant transformations and conclude that the problem of the IR behavior of the effective QCD coupling and of propagators is not well defined and requires a further clarification.