Asymptotic solution of Schwinger-Dyson equation for the gluon propagator in the infrared region

The equation for the gluon propagator in the approach of Baker-Ball-Zachariasen is considered. The possibility of non-integer power infrared behaviour is studied, D(q) \sim (q^2)^{-c}, q^2 \rightarrow 0. It is shown that the characteristic equation for the exponent has no solutions at -1\leq c\leq 3. The approximations made to obtain the closed integral equation are analysed and the conclusion on the infrared behaviour of the gluon propagator D(q) \sim 1/(q^2)^2, q^2 \rightarrow 0 is made when the transverse part of the triple gluon vertex is taken into account