On the gauge-invariant operator $A^2_{\min}$ in Euclidean Yang-Mills   theories
  We review our recent work on the gauge-invariant non-local dimension-two operator $A^2_{\rm min}$, whose minimization is defined along the gauge orbit. Albeit non-local, the operator $A^2_{\rm min}$ can be cast in local form through the introduction of an auxiliary Stueckelberg field. The whole procedure results into a local action which turns out to be renormalizable to all orders. 
M.A.L.Capri, D.Fiorentini, M.S.Guimaraes, B.W.Mintz, L.F.Palhares, S.   P. Sorella
hep-th hep-lat hep-ph