Infrared behavior of the ghost propagator in the Landau gauge Yang-Mills theory

Understand

We prove that the Faddeev-Popov ghost dressing function in the Yang-Mills theory is non-zero and finite in the limit of vanishing momenta and hence the ghost propagator behaves like free in the deep infrared regime, within the Gribov-Zwanziger framework of the $D$-dimensional SU(N) Yang-Mills theory in the Landau gauge for any $D>2$.

• This result implies that the Kugo-Ojima color confinement criterion is not satisfied in its original form.
• We point out that the result crucially depends on the explicit form of the non-local horizon term adopted.
• The original Gribov prediction in the Landau gauge should be reconsidered in connection with color confinement.