Section 10.5 Quark Color
At first glance, the quark model of the hadrons as outlined by Gell-Mann is very appealing in that it seems to explain the occurrence of most of the observed particles. But several problems come forward when a closer look is taken. Consider the three up quarks that make up the \(\Delta^{++}\) on page 9.7 in Chapter 9. The \(\Delta^{++}\) is the lowest mass doubly-charged baryon, so presumably the quarks are each in the ground state. 1 But quarks are fermions (spin 1/2) and so the Pauli exclusion principle should apply! How can three identical quarks all occupy the same state?
The way around this problem is to postulate that the three up quarks in \(\Delta^{++}\) (or the three quarks in any baryon) are not identical, but are each a different “color.” Now of course they don't actually appear colored, but for the reasons described below we call this extra property of quarks color, and a quark can be red (\(R\)) or blue (\(B\)) or green (\(G\)). The antiquarks come in anti-colors: anti-red (\(\overline R\)), anti-blue (\(\overline B\)), or anti-green (\(\overline G\)). No kidding, we really use these labels.
There is a single simple rule about quark color and here it is:
The Colorless Rule: No physically observable particle ever carries net color.
By never carrying a net color, we mean that the colors of the constituent quarks in a particle must cancel out, so that the composite particle is colorless. This can happen in three ways.
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1.
A particle can contain a colored quark and an anti-quark of opposite color, i.e., \(R\overline R\text{,}\) \(B\overline B\text{,}\) or \(G\overline G\text{.}\)
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2.
A particle can contain three quarks, one of each color (i.e., \(RBG\)). The colors cancel out in much the same way as the three primary colors of light mix to give white (colorless) light. This is the reason we say quarks carry color rather than using some other name.
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3.
A particle can contain three antiquarks, one of each anti-color (i.e., \(\overline R\overline B\overline G\)).
The colorless rule automatically picks out those combinations of quarks that actually occur in nature. We never see a lone quark, or combinations such as \(qq\text{,}\) \(q\overline q\overline q\text{,}\) or \(qqq\overline q\text{,}\) because these would of necessity show net color. Furthermore, the rule automatically forbids the possibility of observing particles with fractional baryon number or fractional charge. The Rule is crafted so that we are only allowed to observe what we in fact do observe.
The colorless rule is actually a simplified way of describing a very deep symmetry in nature, color symmetry. Since net color can never be observed, it really can't matter whether we label the quarks in a proton as \(RBG\) or \(RGB\) or \(BGR\) or \(BRG\) or \(GRB\) or \(GBR\text{.}\) We'll see in the next section how the colorless rule is enforced by the exchange of gluons, the messenger particles that actually hold the quarks together and keep them confined inside hadrons.