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Mesons any free quarks. There was another problem with the original theory. Quarks have the same spin as electrons. Therefore, they should also obey the Pauli exclusion principle. However, some particles are observed which are clearly combinations of identical quarks, uuu for example, all in the ground state. This appears to be a violation of the exclusion principle.

The solution was to postulate an additional quark property that could be different for each of the three quarks in a baryon. This property is called color. This is just a convenient name, and has nothing to do with real color that we see. The color property is more like electric charge, except that it has three possible values (plus three anti-values) instead of one. (Electric charge is thought of as having one value and one antivalue.) Quark colors can be red (R), green (G) and blue (B). These colors relate to the ways in which quarks combine, and not to the properties of the particles they make up. To distinguish them from colors, we call the six quark types (u, d, s, c, t, b) flavors.

Proton Neutron

Antipion

Pion

### Fig 21.21.

(a) Allowed quark combinations.These are the allowed color (and anticolor) combinations. Remember that each quark comes in six possible flavors (and each antiquark in six antiflavors) that give the particles their basic properties. In the top row, we see the combinations of three colors (or three anticolors) that give the baryons (and antibaryons). In the bottom row we see combinations of a color and anticolor that give the mesons. (b) Quark combinations for familiar particles.The proton is uud and the neutron is udd. In each case there is one quark of each color. (It doesn't matter whether the u or d is any particular color.) The pion is ud (with the u being some color and the d being the corresponding anticolor).The antipion is ud (with the d being some color and the u being the corresponding anticolor).

antiquark with the corresponding anticolor. For example, a pion is ud, where the possible color combinations are RR, GG, or BB. This explains the mesons. The other possibility is to have one quark of each color. So for a proton (uud), the possible colors for three quarks are RBG, RGB, BGR, BRG, GRB, or GBR. We can see from this that a free quark would not be colorless, and is therefore not allowed by the theory. So the introduction of color has solved the three major problems mentioned above.

The properties involving color are more than a set of ad hoc rules. They have actually been derived from a mathematical theory, derived only on the assumptions of the types of symmetry that the theory should have. This theory is called quantum chromodynamics, or QCD. It is an analog to QED. In this theory, the strong force between hadrons is no longer a fundamental force. The real force is called the color force, acting between the quarks. Just as electric charge is a measure of the ability of particles to exert and feel the electromagnetic force, color measures the ability of particles to exert or feel the color force.

There are other analogies between the electric force and the color force. The requirement that particles be colorless is analogous to the statement that matter should be electrically neutral. For the most part, matter is neutral unless we provide a lot of energy to ionize atoms. As we will see below, the color force is so strong that the analogous process is not possible for quarks. There is another similarity. In the 19th century physicists thought that the force between neutral molecules, called the van der Waals force, was a fundamental force. After the development of the atomic theory in the early 20th century, it became clear that this was nothing more than the residual force between electrons and protons within the molecules. In the same way particle physicists now realize that the strong force between two particles is the residual of the color force among the quarks making up the particles.

We have seen that quantum mechanical theories of forces require carrier particles. QCD is no different. In fact, the mathematical theory predicts the existence of a group of eight particles carrying the force. These particles are called glu-ons. There is a major difference between QED and

QCD. While the photons that carry the electromagnetic force have no electric charge themselves, the gluons that carry the color force have a color charge. This means that the gluons can interact with each other and with quarks. They can also change the colors of the quarks they interact with. This makes the theory very difficult mathematically. The detailed calculations that have characterized the success of QED have not yet been possible for QCD.

Another interesting feature comes out of QCD. The force between two quarks does not fall off with distance between the quarks. This means that the complete separation of two quarks requires an infinite amount of energy. Even if we had the energy available to drive two quarks far apart, we could not isolate a quark. This is illustrated in Fig. 21.22. As you pulled the two quarks apart, you would put enough energy into the system that you would simply create quark-antiquark pairs out of the energy. The new quark and antiquark would bind with the two quarks you were trying to pull

H Quark confinement.The figure shows a quark and antiquark in a meson, as we try to separate them. In each part, the yellow arrows show the force between the quark and antiquark (which doesn't weaken as they get farther apart). (a) We just have the normal separation. (b) We are pulling them apart, doing work against the attractive force. (c) We have done so much work that we have created a new quark-antiquark pair, and now have two mesons instead of two free quarks.

apart, creating new combinations, but no free quarks. This leads to quark confinement, and tells us that we should not see any free quarks. Pulling quarks apart is like cutting a piece of string. Each piece will always have two ends. You can never get a piece with one end.

### 21.3.5 The unification of forces

Following his general theory of relativity, Einstein spent the latter part of his life attempting to 'unify' the forces of gravity and electromagnet-ism. By 'unify' we mean that we would like to explain all of the forces as really being manifestations of one larger force. The search is not new. After all, Maxwell unified the previously distinct forces of electricity and magnetism. Einstein's search for unification was not successful, and some thought that he was wasting his time because the problem had no solution. However, during the 1980s and 90s we have seen amazing progress towards this goal. This progress is based on mathematical theories, which are, in turn, based on the expectation that nature will obey certain symmetries. The progress in the unification of the forces is shown in Fig. 21.23.

The first of the recent successes was the unification of the electromagnetic and weak forces into one force, called the electroweak force. (For this work, Sheldon Glashow, Abdus Salaam and Steven Weinberg shared the Nobel Prize for Physics in 1979.) A major test of that theory was the prediction of the masses of the W and Z particles, carriers of the weak force, before their discovery.

Increasing energy

Electricity & Magnetism

Electroweak

Weak

Strong

Gravity

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