Color Interactions of Quarks

Peter Kim

Upon its discovery, the quark seemed to contradict many of the established principles of quantum mechanics. Quarks combine in groups of three to form hadrons, but have never been observed to exist as independent particles. In addition, scientists have observed the ++ particle which consists of three up quarks whose spins point in the same direction. This violates the Pauli exclusion principle which exludes that two or more particles with spin in the same direction can occupy the same quantum system. The peculiar properties of quarks led to the introduction of the quantum chromodynamics theory (QCD) which explains the strong force acting between quarks.

The strong force acts between color charges of quarks and does not affect particles without color charges, called colorless particles. Color charges can be broken into three basic groups: red minus green (R - G), green minus blue (G - B), and blue minus red (B - R). Each quark can have a value of -1/2, 0, or +1/2 for each of the three charges. For example, the charge configurations for red, green, and blue quarks are shown below.

(R - G) (G - B) (B - R)

Red + 1 / 2 0 - 1 / 2

Green - 1 / 2 + 1 / 2 0

Blue 0 - 1 / 2 + 1 / 2

The antiquarks are formed by reversing the signs of the three charges. These are the only three types of quarks that have been observed in nature. These three quarks and three antiquarks have the property that they have the only combinations of non-zero charges for which the total charge equals zero. Furthermore, since the color charges of a quark add up to zero, the values of any two of the charges uniquely determines the vlue of the third. This allows mathematicians / theoretical physicists to consider only two charrges and exclude the third when analyzing the properties of quarks.

The quarks combine to form color neutral particles, whose color charges are all zero in two ways: one red, one white, one blue, or quark and an antiquark. The first combination forms a baryon, and the second combination forms a meson. The mechanism that has been proposed to explain these interactions is the gluon. The gluon is a massless particle that transmits the strong force between quarks. The gluons are charged particles, unlike the photon, and come in nine different types according to their color-carrying properties: R to G, R to B, G to R, G to B, B to R, B to G, R to R, G to G, B to B. The superposition of the last three gluons, (R to R) + (G to G) + (B to B) does not change the color configuration of a quantum system. So, mathematicians / theoretical physicists can disregard this superposition, and only two independent gluons of the last three are needed in the quark model, making a total of eight gluons.

Since the gluons are charged, quark and gluon interactions can cause the quark to change color. For example, a Red quark could emit a (R to G) gluon and thus be transformed into a Green quark. The three color charges of a gluon can be determined by applying the law of conservation of color charges e.g. the color charges of the Red quark plus the color charges of the (R to G) gluon must equal the charges of the Green quark.

The fact that gluons are charged limits the quark - gluon interactions. For example, a red quark can only emit (R to G), (R to B), and (R to R) gluons, and it can only absorb (G to R), (B to R), and (R to R) gluons.

When a quark is placed alone in a vacuum, it becomes immediately surrounded by a cloud of virtual quarks and antiquarks and gluons. The antiquarks become polarlized such that the antiquarks cluster nearer to the true quark than the virtual quarks. Hence, the actual color charge of the quark is shielded by the antiquark cloud. However, gluons act oppositely such that opposite charges repel and like charges attract, and the quark becomes surrounded by a cloud of virtual gluons of the same charge. Since there are far more virtual gluons than virtual antiquarks, the net result is that the apparent charge of the quark is spread out over the area around it. As a result, the true quark plus the cloud of virtual gluons exerts a greater force on the surrounding area than the true quark alone. Thus, more and more virtual gluons are attracted to the cloud, making it stronger and stronger. Eventually, the whole universe would be filled with a cloud of virtual gluons. The simplest solution to prevent the destruction of the order of the universe is to assume that there are no isolated quarks. They exist only in configurations that form baryons and mesons.

Observations show that the strong force between two quarks does not decrease as distance increases, but actually remains the same. This means that it would take huge amounts of energy to separate quarks and afterwards to keep them separated. Asymptotic freedom refers to the fact that strong forces become weak at very short distances, and quarks are free to move independently as long as they stay very close to each other. This provides evidence supporting that quarks do not exist independently in nature, since an isolated quark would be very unstable.

The QCD theory is new and has not had the chance to be tested out very much. Scientists are, however, fairly certain that the color force model of strong forces correctly describes quark-quark interactions. This theory is beautiful in its simplicity and mathematical symmetry and will lead to advancements in the understanding of the secret of matter.