  In this paper, we discuss non-perturbative infrared features of Yang-Mills
theory in Euclidean space-time dimensions greater than four in the Landau gauge
and within the Refined Gribov-Zwanziger framework, which enables us to take
into account the existence of gauge copies by restricting the domain of
integration in the path integral to the Gribov region. Evidences for a
decoupling/massive solution for the gluon propagator in higher dimensions are
provided. This behavior is strengthened the bigger the dimension is. Further,
we show that, by a dimensional reduction of the Refined Gribov-Zwanziger action
from five to four dimensions, a non-perturbative coupling between the inverse
of the Faddeev-Popov operator and the scalar field corresponding to the fifth
component of the gauge field naturally arises, being in agreement with the
recently proposed mechanism \cite{Capri:2014bsa} to generalize the Refined
Gribov-Zwanziger construction to the matter sector.
