We investigate the dimension two condensate $⟨{\overline{\varphi }}_i^{ab}{\varphi }_i^{ab}-{\overline{\omega }}_i^{ab}{\omega }_i^{ab}⟩$ within the Gribov-Zwanziger approach to Euclidean Yang-Mills theories in the Coulomb gauge, in both 3 and 4 dimensions. An explicit calculation shows that, at the first order, the condensate $⟨{\overline{\varphi }}_i^{ab}{\varphi }_i^{ab}-{\overline{\omega }}_i^{ab}{\omega }_i^{ab}⟩$ is plagued by a nonintegrable IR divergence in $3D$, while in $4D$ it exhibits a logarithmic UV divergence, being proportional to the Gribov parameter ${\gamma }^2$. These results indicate that in 3D the transverse spatial Coulomb gluon two-point correlation function exhibits a scaling behavior, in agreement with Gribov’s expression. In 4D, however, they suggest that, next to the scaling behavior, a decoupling solution might emerge too.

• Received 16 March 2015

DOI:https://doi.org/10.1103/PhysRevD.91.121701