This post mostly serves to describe a few preliminary concepts in quantum chromodynamics as an introduction to a few more in-depth QCD posts that I have planned. Later on in this series I’ll aim to illustrate analogues between a few phenomena from gauge theory in the context of condensed matter and other low energy phenomena.
Introduction
Electrical charge is a reasonably simple concept to understand: electrons have a charge of $-e$, positrons (anti-electrons) and protons have a charge of $+e$, and the charge of a composite object is simply equal to the algebraic sum of the charges of its constituent particles. Photons, constituting electromagnetic radiation, can interact with electrically charged particles but are themselves uncharged. The theory with quantum fields corresponding to only fundamental, electrically charged particles (electrons, positrons, muons, antimuons, etc.) and photons is called quantum electrodynamics, and has been very successful indeed since its inception in the 1930s.
The photon is not, however, the only massless gauge boson (read: “force mediator”) in the Standard Model. It is assisted by the gluon, which mediates the strong force between quarks. Due to the magical properties of the theory describing them at low energies, the strong force is not a simple $1/r^2$ law. Instead, at short distances it is far stronger than the electromagnetic force, but its strength begins to drop very rapidly with increasing distance. The theory of quarks and gluons and how they interact is called quantum chromodynamics (QCD).
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Consider ordinary electric attraction, albeit described with quantum diction. The charge on a particle determines its coupling with the photon, and so determines the strength of the electric force with other electrically charged particles. Analogously in QCD, the nature and strength of the interaction between two quarks is determined by their charge - but this charge is not a simple, additive number! Instead, it’s a more complicated object that generalises the idea of charge being a real number.
Hadrons
One peculiar feature of QCD, though nobody has managed to prove this rigorously from first principles ($1 million awaits you if you do), is that a solitary quark cannot be observed. The internal state of a quark, determining the nature of its interaction with other quarks, cannot be probed directly (at least at ordinary energies)! You may well wonder why electric charge is observable then, given the similarity in their underlying description, and the crux of the answer lies in the fact that, contrary to popular belief, electric charge is not the analogue of color charge. I go into this in another blog post here.
We can have composite particles made of multiple quarks/antiquarks of course - provided that they are colorless (“color singlets”). These are known as hadrons. The simplest example is a bound state of a quark and an anti-quark, known as a meson. For instance, the $\pi^+$ meson comprises the quarks $u\bar d$ - an up quark and a down anti-quark. If the quark has a color of red, and the antiquark has a color of antired, then the resulting combination is effectively colorless, and is allowed to exist.
This is in contrast to a combination of two quarks, which can never be colorless. That said, three quarks can form a colorless combination, known as a baryon. The ubiquitous proton and neutron are examples of this, having composition $uud$ and $udd$ respectively. Further combinations of certain quarks and antiquarks - tetraquarks, pentaquarks, and so on - are theoretically colourless, but are too heavy to see at ordinary energies. The LHC does manage to get a glimpse of them though: see here.
Confinement
All right, but nature can be tricked, you say. You can grab hold of a meson and cunningly begin to separate the quark and the antiquark, thus freeing them, can’t you? Nope, nature wins again. In the confining phase of QCD (when only color singlets are observable), there is a characteristic linear energy cost of separating a quark and an antiquark, i.e. $V(r)=\sigma r$, for some constant sigma. We say that the quark and antiquark are connected by a flux tube. Note that this flux tube is not like an ordinary spring, which stores an energy proportional to $r^2$ rather than $r$.
As $F(r) = -\frac{\mathrm d}{\mathrm dr}V(r)$, the force between two quarks is independent of distance. But as you increase the separation $r$, the energy stored in this “rubber band” increases linearly, eventually becoming high enough to excite a new quark-antiquark pair out of the QCD vacuum! It’s sort of like trying to cut a bar magnet into its separate poles.
If you’d like to learn more, I invite you to read a series on Matt Strassler’s website about particle physics.