  We discuss phenomenological tests for the frozen infrared behavior of the
running coupling constant and gluon propagators found in some solutions of
Schwinger-Dyson equations of the gluonic sector of QCD. We verify that several
observables can be used in order to select the different expressions of alpha_s
found in the literature. We test the effect of the nonperturbative coupling in
the tau-lepton decay rate into nonstrange hadrons, in the rho vector meson
helicity density matrix that are produced in the chi_{c2} --> rho rho decay, in
the photon to pion transition form factor, and compute the cross sections for
elastic proton-proton scattering and exclusive rho production in deep inelastic
scattering. These quantities depend on the infrared behavior of the coupling
constant at different levels, we discuss the reasons for this dependence and
argue that the existent and future data can be used to test the approximations
performed to solve the Schwinger-Dyson equations and they already seems to
select one specific infrared behavior of the coupling.
