## The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics - Robert Oerter (2006)

### Appendix A. Quarks and the Eightfold Way

**T**he quark model, invented by Gell-Mann and independently by Zweig, shed light on the earlier Eightfold Way classification of particles. The mysterious patterns of SU(3) symmetry were suddenly seen to be a result of the internal structure of subatomic particles.

The mesons, in the new scheme, are those particles consisting of one quark and one antiquark. The pions (π^{+} and π^{-}), for instance, look like this:

What about the pi-zero (π^{0})? There are actually *two* ways to combine the up and down quarks to make a particle with zero electric charge: either combine up with antiup, or down with antidown. Which of these is the pi-zero? The answer, oddly enough, is “both.” Quantum mechanics tells us that it is possible to put a particle in a superposition state, where it has, say, a 50 percent probability of being behind Door Number 1 and a 50 percent probability of being behind Door Number 2. According to quantum field theory and the quark model, the pi-zero is a superposition of the two possibilities uu and *d*, with 50 percent probability of each. Resist the temptation to ask, “Well, which one is it *really?”:* the quantum nature of the pi-zero doesn’t allow that question to be answered. “Obviously,” you object, “that’s nonsense! The up quark has electric charge 2/3, while the down quark has charge -1/3. All we need to do to find out what the pi-zero is *really* made of is to measure the charges of the quarks inside it.” Well, what do we find if we attempt this? The experiment has never been done, because the pi-zero doesn’t last long enough to do it—the quark (whichever one it is) and the antiquark annihilate rapidly, releasing their energy in the form of photons. But, if we could do the experiment, the rules of quantum field theory tell us that half the time we would measure charges of +2/3 and -2/3 (corresponding to the up-antiup possibility) and half the time we would measure them as -1/3 and +1/3 (corresponding to down-antidown) —just like the house in Chapter 4 that was red on some days and blue on others. The reactions involving the pi-zero that we *can* measure completely support this surprising conclusion.

The property of strangeness, which seemed like an arbitrary invention, has a very natural interpretation in terms of quarks. A particle containing one strange quark has strangeness -1, a particle with two strange quarks has strangeness -2, a particle with one antistrange quark has strangeness +1, and so forth. This rule, together with the electric charge assignments of the quarks, allows us to disentangle the Eightfold Way multiplets in terms of their quark content. The lightest meson octet looks like this:

The two particles at the center of the diagram are the pi-zero, discussed already, and the eta-zero (n°), which is a superposition of *uū*, *d*, and *s*.

The lightest baryons also form an octet:

In this case, the two particles at the center of the diagram actually have the same quark composition. However, the arrangement of the quarks is different in the two cases. Since the arrangements have different energy, the two particles have different masses and so can be distinguished in experiments.

As a final example, here is the quark composition of the decuplet containing the famous omega-minus:

These are all spin -3/2 particles, so all of the quark spins must be aligned. Here again, it is the arrangement of the quarks that distinguishes, for instance, the delta-zero (A^{o}) from the neutron *(n)* of the octet previous. Both particles are composed of one up quark and two down quarks, but the delta-zero has all three quark spins aligned, while the neutron, a spin -1/2 particle, has two quarks with spin up and one with spin down (or vice versa).

The patterns of the Eightfold Way arise from SU(3) symmetry. In the quark model, this symmetry is a result of the three quark flavors: up, down, and strange. This is a different symmetry than the color SU(3) symmetry of QCD, which is a result of the fact that each quark flavor exists in three different colors. Color symmetry is an exact symmetry, while the Eightfold Way is only approximate, since the three quark flavors have different masses. We now know that there are actually six quark flavors, not three. Clearly, the Eightfold Way will be of no assistance in classifying particles containing charm, bottom, or top quarks. We could contemplate an extended symmetry that includes all six quark flavors, but the wide range in mass of the quarks means such a symmetry is very inexact, and so of limited usefulness.