The full gluon propagator in light-cone gauge and the transversality problem of the polarization operator in infrared region. II

A three-gluon vertex that depends on a gauge vectorn $n_\mu$ and is free of kinematic and spurion $(np)^{-1}$ singularities in the physical region is constructed. It is shown that in the case of integer power-law asymptotic behavior of the gluon propagator there is separation of the singular contributions of the single- and two-loop diagrams in the Dyson–Schwinger equation. Necessary conditions for realization of $p^{-4}$ asymptotic behavior are obtained, and it is shown that an important role in their fulfillment is played by the parts of the three-gluon vertex that depend on the gauge vector. A solution of these conditions is found; when they are fulfilled, they lead to infrared asymptotic behaviors of the complete Dyson–Schwinger equation and its single-loop approximation that are mutually compatible.