What makes the (non-abelian) strong interaction so special that it leads to confinement?

Question

The strong interaction has a coupling constant of $\alpha_s(91GeV)\approx 0.1$ whereas the weak interaction has a much lower coupling constant $\alpha_w \approx 10^{-6}$. Both theories are non-abelian gauge theories, the strong interaction is based on SU(3) gauge symmetry, whereas the electroweak interaction is based on $U(1)\times SU(2)$ gauge symmetry.

What makes the strong interaction so special that it leads to confinement, whereas for the electroweak interaction it is not the case? It is certainly related with the $\beta$-function of the corresponding interaction, but why is the $\beta$-function of the electroweak interaction positive and the $\beta$-function of the strong interaction negative? Actually, I am not very familiar with use of renormalisation group arguments, so I would prefer a not too formal answer based on essentially on physics arguments.

Answer 1

Just to state the result for the beta-function associated to QCD
\begin{equation} \beta = -\frac{g^2}{32 \pi^2} \left(\frac{11}{3}N_c - \frac{2}{3}N_f \right) \end{equation} in which $N_c$ is the amount of colours and $N_f$ is the amount of flavours.

Essentially, both terms boil down to antiscreening and screening respectively.
A single quark can be surrounded by quark-antiquark pairs which tend to screen it from effects of the environment (much like in QED with electron-positron pairs).
However, the important piece is now the antiscreening effect due to the self-interaction of the gluons (because of the non-Abelian gauge symmetry). This tends to make the quark more susceptible to its environment.

Filling in the constants gives a negative beta-function. In other words, if we probe quarks at higher energies, the coupling constant decreases sufficiently such that we may regard them as being free (eg. a quark-gluon plasma). At small energies, the coupling constant becomes enormous and quarks are effectively bound together into hadrons - confinement.