A Gauge-Invariant Stueckelberg Extension of Yang–Mills Theory

We investigate a non-Abelian Yang--Mills theory coupled to a group-valued Stueckelberg field that provides a gauge-invariant mechanism for introducing a mass scale while preserving local gauge symmetry. Using the BRST formalism in a covariant $R_\xi$ gauge, we construct the gauge-fixed quantum action and derive the complete set of perturbative Feynman rules, including the vertices generated by the non-polynomial Stueckelberg sector. The one-loop renormalization structure is analyzed within dimensional regularization and the $\overline{\mathrm{MS}}$ scheme. We compute explicitly the individual loop contributions to the gluon self-energy, demonstrate that Stueckelberg scalar loops contribute only to the longitudinal tensor structure and therefore do not modify the transverse ultraviolet divergence, and verify that a Slavnov--Taylor consistency relation among renormalization constants is satisfied at one loop. The resulting one-loop beta function coincides with that of ordinary Yang--Mills theory, establishing that the two theories share the same ultraviolet universality class and that asymptotic freedom is preserved. While non-perturbative phenomena such as confinement and the Yang--Mills mass gap lie beyond the scope of the present analysis, the framework provides a controlled perturbative setting in which gauge-invariant mass generation in non-Abelian gauge theories can be systematically explored.