On the QCD coupling behavior in the infrared region
  The summary of nonperturbative results for the QCD invariant coupling bar{alpha}_s obtained by lattice simulations for functional integral and by solution of approximate Dyson--Schwinger equations reveals a puzzling variety of IR behavior of bar{alpha}_s(Q^2) even on a qualitative level. This, in turn, rises a question of correspondence between the results obtained so far by different groups.   We analyze this issue in terms of mass-dependent coupling constant transformations and conclude that the question of the IR behavior of effective QCD coupling and of propagators is not a well--defined one and needs to be more specified. 
D.V. Shirkov