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

Composite operator and condensate in the $SU(N)$ Yang-Mills theory with $U(N-1)$ stability group