On a renormalizable class of gauge fixings for the gauge invariant operator Amin2

The dimension two gauge invariant non-local operator Amin2, obtained through the minimization of ∫d4xA2 along the gauge orbit, allows to introduce a non-local gauge invariant configuration Aμh which can be employed to built up a class of Euclidean massive Yang-Mills models useful to investigate non-perturbative infrared effects of confining theories. A fully local setup for both Amin2 and Aμh can be achieved, resulting in a local and BRST invariant action which shares similarities with the Stueckelberg formalism. Though, unlike the case of the Stueckelberg action, the use of Amin2 gives rise to an all orders renormalizable action, a feature which will be illustrated by means of a class of covariant gauge fixings which, as much as 't Hooft's Rζ-gauge of spontaneously broken gauge theories, provide a mass for the Stueckelberg field.