We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in SUN Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with the algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is possible to connect the vacuum energy, due to the mass dimension-two condensate discussed here, with the nontrivial vacuum energy originating from the condensate hA 2 i, which has attracted much attention in the Landau gauge.

The nonlocal mass operator Tr R d 4 xF D 2 ÿ1 F is considered in Yang-Mills theories in Euclidean space-time. It is shown that the operator Tr R d 4 xF D 2 ÿ1 F can be cast in local form through the introduction of a set of additional fields. A local and polynomial action is thus identified. Its multiplicative renormalizability is proven by means of the algebraic renormalization in the class of linear covariant gauges. The anomalous dimensions of the fields and of the mass operator are computed at one-loop order. A few remarks on the possible role of this operator for the issue of the gauge invariance of the dimension two condensates are outlined.

The effects of the Gribov copies on the gluon and ghost propagators are investigated in SU (2) Euclidean Yang-Mills theory quantized in the maximal Abelian gauge. The diagonal component of the gluon propagator displays the characteristic Gribov type behavior. The off-diagonal component of the gluon propagator is found to be of the Yukawa type, with a dynamical mass originating from the dimension two condensate A a µ A a µ , which is also taken into account. Finally, the off-diagonal ghost propagator exhibits infrared enhancement. * marcio@dft.if.uerj.br † vitor@dft.if.uerj.br ‡ sobreiro@uerj.br § sorella@uerj.br ¶ Work supported by FAPERJ, Fundação de Amparoà Pesquisa do Estado do Rio de Janeiro, under the program Cientista do Nosso Estado, E-26/151.947/2004. thibes@dft.if.uerj.br

We construct the multiplicatively renormalizable effective potential for the mass dimension two local composite operator A a µ A µa in linear covariant gauges. We show that the formation of A a µ A µa is energetically favoured and that the gluons acquire a dynamical mass due to this gluon condensate. We also discuss the gauge parameter independence of the resultant vacuum energy.

A BRST perturbative analysis of SU (N ) Yang-Mills theory in a class of maximal Abelian gauges is presented. We point out the existence of a new nonintegrated renormalizable Ward identity which allows to control the dependence of the theory from the diagonal ghosts. This identity, called the diagonal ghost equation, plays a crucial role for the stability of the model under radiative corrections implying, in particular, the vanishing of the anomalous dimension of the diagonal ghosts. Moreover, the Ward identity corresponding to the Abelian Cartan subgroup is easily derived from the diagonal ghost equation. Finally, a simple proof of the fact that the beta function of the gauge coupling can be obtained from the vacuum polarization tensor with diagonal gauge fields as external legs is given. A possible mechanism for the decoupling of the diagonal ghosts at low energy is also suggested.