Fig. 1. The upper panel show the total field distribution and the lower the distribution from mutual interaction (no self-energies) only. ](Fig3.eps){width="2.5in"}

Finally, to study the effects of $f_L(p)$, in Fig. 5 we show the predictions for the $Q{\bar Q}$ field distribution given by [Eq. (\[vc\])]{} where we use $d(p)$ and $f(p)$ in the form given by [Eq. (\[df\])]{} with $\alpha = 1/2$ and $\beta=1$ and normalized such that $V(R) \to bR$ at large distances. Furthermore, to remove the oscillations introduced by the momentum space cutoff, we now cut the small $x$ region in coordinate space, by i) extending the upper limits of integration in Eqs. (\[dpl\]) and (\[fl\]) to infinity and ii) cutting off the position space functions at short distances, $$d'_L(r) = {2\over {\pi\alpha}} \sin(\pi\alpha/2)
 \Gamma(2 -\alpha) \theta(r\mu - 1)
  { {\mu^2} \over {(\mu r)^{2-\alpha}}}$$ $$f_L(r) = {1\over {2\pi^2}} \sin(\pi\beta/2)  
  \Gamma(2-\beta) \theta(r \mu - 1)
  { {\mu^3} \over {(\mu r)^{3-\beta}}}.$$

Comparing Fig. 3 and Fig. 5 we observe a narrowing of the flux tube. This is to be expected as the action of $f(p)$ is to introduce additional gluonic correlations. That said, there is no major qualitative change in the field distribution.

![\[fig4\] $R^2 \langle \E^2(x) \rangle$ for 