Infrared Behavior of Ghost and Gluon Propagators Compatible with Color Confinement in Yang-Mills Theory with the Gribov Horizon

We discuss how the existence of the Gribov horizon affects the deep infrared behavior of ghost and gluon propagators of the D-dimensional SU(N) Yang-Mills theory in the Landau gauge. If we use a horizon function in the Gribov-Zwanziger framework to restrict the functional integral to the first Gribov region for avoiding Gribov copies, we can show that the ghost propagator behaves like free, while the gluon propagator is non-vanishing in deep infrared region (the decoupling solution) in harmony with recent results obtained from numerical simulations on lattice, the Schwinger-Dyson equation and the functional renormalization group. This result should be compared with the Gribov prediction that such a restriction leads to the vanishing gluon propagator and enhanced ghost propagator (the scaling solution). We raise some questions on current understanding on the ghost propagator and its implications for quark confinement à la Wilson and color confinement à la Kugo-Ojima.