[Source: Siegfried Bethke, Experimental Tests of Asymptotic Freedom, arXiv:hep-ex/0606035, Fig. 17.]
Life without interaction is boring. If quarks would not interact, there would be no protons, no neutrons, no atoms, no readers of blogs. In quantum chromodynamics (QCD), the theory that in principle explains how quarks bind to protons, this interaction between quarks is described by the exchange of gluons - particles that glue together the quarks. The very naive idea is the following: two quarks exchange a gluon with momentum Q, and depending on the colour charge of the quarks, this exchange results in an attraction or a repulsion between both quarks.
The strength of the interaction depends of a factor which is called the "coupling constant", which for quarks and gluons is usually denoted as αs. Here, the index "s" stands for "strong", since the interaction between quarks and gluons had been called the "strong interaction" for reasons that show up nicely in the plot above, as we will see in a second. The exchange of one gluon is proportional to a factor g² = 4παs - in the diagram, each on of the two vertices where the gluon and the quark get in touch contributes a factor of g, the square root of 4παs.
This is completely analogous to quantum electrodynamics, where the exchange of a photon between two electrons is proportional to e², the product of the electrical charges of the two interacting particles - the very same factor that has been known since a long time from Coulomb's law for the force between charges. In electrodynamics, the constant α = e²/4π is called the fine structure constant - it's a pure number, without dimensions of length or mass, and has the value α ≈ 1/137. Moreover, it has the nice property to be more or less independent of the momentum Q of the photon that is exchanged. The smallness and the constancy of α in QED allow all kinds of calculations that are in pretty good agreement with experiment.
In QCD, alas, things are more complicated, and the main reason for this is encoded in the plot above. It shows a compilation of the values for αs, derived from many different experiments, and for different momenta Q of the exchanged gluons. Gluon momentum is measured in GeV/c (and c, the speed of light, is set to 1), and a logarithmic scale has been used to allow to show a bigger range of values.
There are two features of the curve which correspond to two main characteristics of quantum chromodynamics:
The "coupling constant" αs is not a constant at all - it decreases with increasing momentum. Moreover, it lies in the range 0.1 - 0.3 at values of Q that can be probed in experiment, which means that it's about 50 times larger than the fine structure constant of electrodynamics - that's why the "strong interactions" are strong -, and the factor g² = 4παs is on the order of 1, and bigger than 1 for small momenta.
This second feature is called "asymptotic freedom", and it means that quarks are nearly free, or non-interacting, when the exchange momentum is very big. As a result, the computational tools which are so successful for electrons and photons can be applied to quarks and gluons at very high energies.
The other side of the coin, however, is that phenomena at lower energies are much harder to calculate. And, for example, in the regime where quarks bind together to protons or other hadrons, αs is too big to use the recipes of quantum electrodynamics. So far, there are only numerical methods available to solve the full equations of QCD for hadrons, and many different analytic approximation schemes.
Which makes, on the other hand, the question of how quarks interact to build a proton as challenging as interesting.
More than you ever wanted to know about the running coupling of QCD can you find, e.g., in the paper by Siegfried Bethke: Experimental Tests of Asymptotic Freedom, arXiv:hep-ex/0606035, and Progress in Particle and Nuclear Physics 58 (2007) 351-386, and in the review Quantum Chromodynamics and its coupling by I. Hinchliffe for the Particle Data Group (PDF file).
On asymptotic freedom, and QCD in general, you can check out QCD Made Simple (Physics Today) and Asymptotic Freedom: From Paradox to Paradigm (arXiv: hep-ph/0502113) by Frank Wilczek, who together with David Gross and David Politzer was awarded the Nobel Prize in Physics 2004 for the discovery of asymptotic freedom in QCD.
This post is part of our 2007 advent calendar A Plottl A Day.