IR fixed point and low-momentum gluon propagator

Assuming the gluon propagator to be finite at $g_s^2\mathrm{/}4\pi \equiv \alpha \to {\alpha }_{\ast }$, where ${\alpha }_{\ast }=\alpha (0)$, we derive its low-momentum asymptotics. In some cases the results modify the known ones. In our work, we also establish the field-theoretical nature of a universal phenomenological parameter introduced in works \cite{Alk} and determining the behaviour of Green’s functions in the infrared region. The importance of studying the renormalization group parameters in the vicinity of the infrared stable point is emphasized.