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The nonlocal gauge invariant mass operator $\mathrm{Tr} \int d^{4}xF_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ is investigated in Yang-Mills theories in themaximal Abelian gauge. By means of the introduction of auxiliary fields a localaction is achieved, enabling us to use the algebraic renormalization in orderto prove the renormalizability of the resulting local model to all orders ofperturbation theory.

Study of the nonlocal gauge invariant mass operator $\mathrm{Tr} \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ in the maximal Abelian gauge