the critical exponents $\alpha,\beta,\gamma$ ([*cf.*]{} [Eq. (\[df\])]{}) we have instead compared $V_C$ to the phenomenological, Wilson potential [@as1]. In what follows we will use the larger value of the string tension, to be in agreement with Ref. [@goz].

If the two exponents $\alpha$ and $\beta$, which determine the infrared behavior of $d(p)$ and $f(p)$ respectively, satisfy $2\alpha + \beta > 2$, then the self energy in [Eq. (\[sigma\])]{} is divergent and so is the [*rhs*]{} of [Eq. (\[vc\])]{}. This reflects the long-range behavior of the effective confining potential generated by self-interactions between the gluons that make up the Coulomb operator. For the colorless $Q\bar Q$ system the total energy which is the sum of $V_C$ and $\Sigma$, is finite as it should be. For a colored system, [*e.g.*]{} a quark-quark source, the sign of $V_C$ changes, there is no cancellation between the infrared singularities, and in the confined phase the system would be un-physical with infinite energy. The integral determining the self energy also becomes divergent in the UV, since for $p\to \infty$ the product $d^2(p)f(p)$ only falls-off logarithmically. Modulo these logarithmic corrections this UV divergence is the same as in the Abelian theory and can be removed by renormalizing 