Infrared asymptotics of power type for the gluon propagator in the axial gauge

In a gauge theory of Yang–Mills type with zero mass, a study is made of the possibility of having a power-law infrared asymptotic behavior of the total gtuon propagator: $D(k)\sim1/(k^2)^{\beta+1}$, $k^2\to0$. The axial gauge is used, and an equation for the exponent of the infrared asymptotic behavior is obtained as a consequence of the Schwinger–Dyson equation and the Ward–Slavnov identity; dimensional regularization is used. Under certain assumptions, it is shown that there exists a spectrum of discrete values of the exponent of the infrared behavior that are asymptotically consistent in the limit $k^2\to0$ with the Sehwiager–Dyson equation and the Ward–Slavnov identity. The values of the exponent are found by numerical analysis.