Infrared asymptotic behavior of gluon Green's functions in quantum chromodynamics

The possibility that the gluon propagator could have the infrared asymptotic behavior $D(k)\sim 1/(k^{2})^{2}$, $k^{2}\to0$, in quantum chromodynamics is considered. It is shown by means of the Schwinger–Dyson equation in the axial gauge and the Ward–Slavnov identities that such behavior can indeed be realized if the three-gluon vertex function has a definite infrared asymptotic behavior independently of the value of the gauge parameter. This result makes it possible to obtain in the infrared region an effective gauge-invariant Lagrangian containing explicitly a constant with the dimensions of mass.