Infrared asymptotics of gluon Green's functions in covariant gauge

It is considered whether the singular infrared behavior $D(k)\sim M^2/k^4$ of the gluon propagator and thecorresponding asymptotic behavior of the gluon vertices are compatible with the Schwinger–Dyson equation in a covariantgauge. For the investigated asymptotic behaviors, the two-loop terms most singular in the infrared region are calculated. It is shown that there exists a distinguished covariant gauge in which one can find a self-consistent description of the lowest gluon and ghost Green's functions in the infrared region of QCD.