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

Abstract

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

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