quantum field theory - Relation of $Q^2$ with the distance of interaction

In a process with only one Feynmann diagram at leading order such as $e^- \mu ^-$ scattering:

the photon propagator is

$$\begin{equation} \frac{-i g_{\mu \nu}}{q^2}, \end{equation}$$ with $q^2 = (p_3 - p_1)^2$. Since $q^2 <0$, we sometimes define the positive value $Q^2 = -q^2$. Apparently, it seems ok to relate $Q^2$ just as a quantity related to the exchange of energy and momentum between the particles.

But when reading about the running coupling constants in Halzen & Martin's book, they show that the running coupling constant of QCD has a small value for increasing $Q^2$, and the author relates high $Q^2$ to small distance interactions (i.e. asymptotically freedom) and small $Q^2$ to long distance interactions.

I cannot understand how the value of the exchanged 4-momentum relates to the interaction distance. Could someone shed some light in the subject?

Answer

In a sense it is based on the heisenberg uncertainty principle, HUP

In every interaction the four momentum transfer is made up of the three momentum transfer and the energy transfer. Looking at large Δp of the Q^2 transfer within the limits of the HUP the Δx gets smaller.