Yang-Mills two-point functions in linear covariant gauges

Understand

In this work we use two different but complementary approaches in order to study the ghost propagator of a pure SU(3) Yang-Mills theory quantized in the linear covariant gauges, focusing on its dependence on the gauge-fixing parameter $\xi$ in the deep infrared.

• In particular, we first solve the Schwinger-Dyson equation that governs the dynamics of the ghost propagator, using a set of simplifying approximations, and under the crucial assumption that the gluon propagators for $\xi>0$ are infrared finite, as is the case in the Landau gauge $(\xi=0)$.
• Then we appeal to the Nielsen identities, and express the derivative of the ghost propagator with respect to $\xi$ in terms of certain auxiliary Green's functions, which are subsequently computed under the same assumptions as before.
• Within both formalisms we find that for $\xi>0$ the ghost dressing function approaches zero in the deep infrared, in sharp contrast to what happens in the Landau gauge, where it known to saturate at a finite (non-vanishing) value.