QCD in the Infrared with Exact Angular Integrations

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 vanishes in the infrared exactly like p, whilst the ghost propagator is exactly as singular as 1/p. 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 DysonSchwinger 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, in this paper we seek to remove the deficiency of the y-max approximation. On the one hand the results might be regarded simply as quantitative adjustments to the y-max calculations; but on the other hand they are far from negligible. The numerical value of the infrared fixed point is reduced by a factor of almost three; and the finding that the gluon propagator has a simple zero, while the ghost propagator has a double pole, might perhaps be deemed a qualitatively new result. As an improvement on the y-max approximation used in Ref.[2], we now solve the coupled integral equations for the gluon and ghost propagators with an exact treatment of the angular [email protected] [email protected]