Asymptotic Freedom

This is a scary name for a relatively simple, but crucial effect that demonstrates part of the vast difference between the QED behind electromagnetic phenomena and the QCD behind the strong phenomena of the nucleon.

In QED, we learn that the sum total of all Feynman diagrams that can describe a process contribute to the end result.  This means that all the crazy diagrams you can draw with the same external lines, no matter how many vertices creating and destroying any number of virtual particles, must go into the calculation of the process.  The saving grace is the fine structure constant , which gives the coupling strength of the vertex, is .  This means that each additional vertex of higher and higher order terms contributes less and less to the final result by orders of magnitude, and can be ignored.

Things get more complicated when we apply this method to QCD.  The coupling constant here  is determined by experiment to be greater than 1.  This means each successive order contributes more and more!  Now the solution for calculability instead comes from the dependence of the coupling on distance, the "reach" of the strong force, which is mediated by a massless gauge boson that carries charge and can thus couple to itself.

The key to understanding this puzzle lies within charge screening.  In E&M, a charge q in a dielectric medium is screened by the presence of molecular dipoles whose negative end is attracted towards the positive charge, effectively lowering the charge.  The closer to the charge, the fewer molecules in the way to decrease the observed charge strength.  It turns out the vacuum acts as a dielectric as it sprouts particle/anti-particle pairs, so this always applies.  For example the effective electron charge we know and love is really lower than the value very close to an "unscreened" electron.

In QCD, the vacuum sprouts not only particle/anti-particle pairs as in QED, but also gluon loops, as the gluon can couple to itself; it has "charge."  Thus a red charged quark begets more red charged particles in its neighborhood, which creates an anti-screening.  The further away, the more particles, the larger the charge looks!  Here we have asymptotic freedom: the QCD coupling increases at distance, but decreases close together.  Quarks are free to rattle around when near each other, but can't stray too far.

Sources: Griffiths Intro to Elementary Particles p64 and Halzen and Martin's Quarks & Leptons p10