  Recently, some reformulations of the Yang-Mills theory inspired by the
Cho-Faddeev-Niemi decomposition have been developed in order to understand
confinement from the viewpoint of the dual superconductivity. In this paper we
focus on the reformulated $SU(N)$ Yang-Mills theory in the minimal option with
$U(N-1)$ stability group. Despite existing numerical simulations on the lattice
we perform the perturbative analysis to one-loop level as a first step towards
the non-perturbative analytical treatment. First, we give the Feynman rules and
calculate all renormalization factors to obtain the standard renormalization
group functions to one-loop level in light of the renormalizability of this
theory. Then we introduce a mixed gluon ghost composite operator of mass
dimension two and show the BRST invariance and the multiplicative
renormalizability. Armed with these results, we argue the existence of the
mixed gluon-ghost condensate by means of the so-called local composite operator
formalism, which leads to various interesting implications for confinement as
shown in preceding works.
