authors: PJ Deschenes and John Burke
We all learned in first year physics or chemistry that some strong force holds protons and neutrons together in the nucleus of an atom. This force is actually the result of another binding interaction that occurs within the protons and neutrons themselves. Protons and neutrons are members of a family of particles called baryons. Baryons are composed of three quarks, fermions with 1/2 spin and fractional charges. The charges of quarks add up to give the characteristic charges of protons and neutrons. However, they appear to violate Pauli's exclusion principle, which states that no two 1/2 spin particles can possess the same set of quantum numbers. To remedy this, a new quantum state is introduced: color.
Three colors must exist to preserve the exclusion principle in quarks, since baryons are made up of three quarks. The three colors are represented by the three primary colors red (r), blue (b), and green (g), but have nothing to do with color of visible light. Just as all particles have antiparticles, each color has its own anticolor. The anticolors are usually referred to as antired (~r), antiblue (~b), and antigreen (~g). Neither quarks nor color charges have never been isolated. They are only known to exist as compound particles called hadrons. The first type of hadron, the baryon, consists of three quarks with different colors. The baryon's color, which is determined by the sum of the colors of the three quarks, or r + b + g = white, is therefore a singlet, which means it has no observable color. The other group of hadrons, called mesons, consist of a quark and an antiquark. Even though each meson could be either r + ~r, b + ~b, or g + ~g, the two colors will always form a color singlet.
The well established theory of quantum electrodynamics (QED) is a gauge theory in which local symmetry is preserved. Local symmetry occurs when an operation can be performed on a system (like an electron or a quark) and the system remains consistent with respects to a theory without having to change every other system in the same manner. In QED the phase shift in an electron is communicated locally by the emission of a virtual photon (a photon that cannot be observed but can exist by the uncertainty principle) that can be absorbed by another electron. Due to the success of QED it is logical to try to fit a similar gauge theory to color, which is called quantum chromodynamics (QCD).
Just as electrons are able to undergo phase shifts, quarks can undergo color shifts. As proof of this, consider the three possible proton color states. Protons consist of two up quarks (u) and one down quark (d). The proton must be white, so the three possible quark/color combinations are urugdb, uburdg, and ugubdr. A proton must be able to exist in any of these three states (all protons are the same), so let's consider what must happen to allow one such conversions: urugdb -> uburdg. Effectively, the down quark changes from blue to green (db -> dg), and the green up quark changes to blue (ug -> ub). It is necessary that the two quarks communicate so that both color transformations occur, otherwise the proton would have a net color and the local symmetry would be violated. This inter-quark communication is accomplished via a particle called a gluon, which is massless and consists only of a color and an anticolor. The gluon is the QCD equivalent of the photon from QED, but there are nine possible gluons (r~g, r~b, g~r, g~b, b~r, b~g, r~r, g~g, b~b), whereas there is only one photon. The first six of these produce color changes when emitted or absorbed and so they must exist, but only two of the last three are required. The third one is the superposition of some of the other gluons. Therefore there are a total of eight gluons.
The quarks in a hadron are constantly emitting and absorbing gluons. Because there are eight different gluons, and because these gluons carry a color charge, the gluons are able to interact with each other. Theoretically, two or more gluons can interact in such a way two form a color singlet that is an observable particle called a glueball (click here for a recent article on the glueball theory). These gluon interactions contribute to one of the major differences between QED and QCD. In QED, the field lines between two test charges spread out as the charges separation increases, which corresponds to a weakening electric field. In QCD, the gluons that make up the color field lines interact with each other, causing the field to remain concentrated along the line which connects the two quarks as they are separated. With separation, the field lines of color connecting two quarks become increasingly more concentrated than the electromagnetic field lines connecting two test charges.
According to Heisenberg's uncertainty principle (dEdt >> h/2pi), as we investigate quarks more closely, the uncertainly of their energy becomes quite large. As a result, it is possible for a quark to emit virtual gluons and quark-antiquark pairs, particles that are not observed but can exist within the confines of the quark's energy. Analogously, electrons emit virtual photon and electron-positron pair production occur in QED. Virtual electron-positron pairs align themselves with the negatively charged electron pointing producing a screening of the electron's charge. The charge of the electron measured from inside the cloud of virtual particles becomes increasingly large the closer we probe, but at a distance (<10-13 m) it decreases dramatically. A similar effect occurs for quarks in QCD. However, in QCD the virtual particles produce the opposite effect on the color charge of the quark (the physical explanation, though very complicated, is based on the fact that gluons carry color charge whereas photons from QED were uncharged). The color charge of the quark is enhanced by the charged virtual particles and increases without bound as we move away from it. This is known as anti-screening. When quarks are brought together to produce color singlets, these infinite color fields cancel. At a very close distance the color charge becomes asymptotically small, so quarks existing together within a hadron, which is a color singlet, are free to move about; they have asymptotic freedom. If we try to pull the quarks apart, the color fields become large and pull the quarks back into their asymptotic region. This effect is called infrared slavery because it only occurs at (relatively) large distances. As a result, color is confined to particles with a color singlet.
Now we return to the origin of the forces between nucleons. Recall that atoms are electrically neutral structures, the negative charges of their electrons canceling the positive charges of their protons. Yet at short distances (< 10-10 m) collisions can disrupt the electron clouds of atoms creating slight polarities. These polarities bring about attractions between atoms called dispersion or Van der Waals forces. The strong force that binds nucleons is analogous to electrodynamic dispersion forces. Color neutral hadrons, such as protons and neutrons, can attract each other at short distances (<10-15 m) from a residual of the color force that binds their quarks together. Recall that the color force increases with increasing distance. As a result, the strong force between nucleons is not as week relative to the corresponding inter-quark forces as the feeble electrodynamic dispersion forces are relative to the electrostatic attraction of electrons and protons.
