  Recently, a reformulation of the $SU(N)$ Yang-Mills theory inspired by the
Cho-Faddeev-Niemi decomposition has been developed in order to understand
confinement from the viewpoint of the dual superconductivity. The concept of
infrared Abelian dominance plays an important role in the realization of this
concept and through numerical simulations on the lattice, evidence was found
for example in the form of the dynamical mass generation for certain gluon
degrees of freedom. A promising analytical attempt to explain the generation of
such masses is through condensates of mass dimension two. In this talk, we want
to focus on the reformulated $SU(N)$ Yang-Mills theory in the previously
overlooked minimal option with the non-Abelian $U(N-1)$ stability group, in
contrast to the famous maximal Abelian gauge, where the decomposition
corresponds to the Abelian $U(1)^{N-1}$ stability group. We proceed with a
thorough one-loop analysis of this novel decomposition, calculating all
standard renormalization group functions at one-loop level in light of the
renormalizability of this theory. We subsequently define an appropriate mixed
gluon-ghost composite operator of mass dimension two as the candidate for the
condensate within this theory and prove its (on-shell) BRST invariance and the
multiplicative renormalizability. Finally, the existence of the condensate is
discussed within the local composite operator formalism.
