In a previous paper we have shown that in quantum chromodynamics the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole. These results were obtained after angular averaging, but in the current paper we go beyond this approximation and perform an exact calculation of the angular integrals. The powers of the infrared behaviour of the propagators are changed substantially. We ﬁnd the very intriguing result that the gluon propagator vanish…

Read moreIn a previous paper we have shown that in quantum chromodynamics the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole. These results were obtained after angular averaging, but in the current paper we go beyond this approximation and perform an exact calculation of the angular integrals. The powers of the infrared behaviour of the propagators are changed substantially. We ﬁnd the very intriguing result that the gluon propagator vanishes in the infrared exactly like p2, whilst the ghost propagator is exactly as singular as 1/p4. We also ﬁnd that the value of the infrared ﬁxed point of the QCD coupling is much decreased from the y-max estimate: it is now equal to 4π/3. Following a recent study by von Smekal et al.[1], we analyzed in Ref.[2] the coupled Dyson- Schwinger equations for the gluon and ghost form factors F and G. The approximations were two-fold: ﬁrstly the vertices were taken bare, and secondly angular averaging was introduced (the so-called y-max approximation). Deferring to later work an improvement of the vertices.