Section 9.6 The Eightfold Way and Quarks
In the 1960's, newer and bigger accelerators came on line, and the proliferation of newly created particles continued. There are now literally hundreds of so-called elementary particles. A classification scheme was needed, and in 1962 Murray Gell-Mann and Yuval Ne'eman proposed the Eightfold Way. Shortly thereafter, Gell-Mann suggested that the various hadrons were actually composed of yet smaller entities called quarks.
Gell-Mann and Ne'eman studied the relationships among various groups of particles. They were looking especially for ways to organize the hadrons into groups with common dynamical properties. For instance, particles that differ only in charge (and slightly in mass) are already given the same symbol (like \(\Sigma^+\text{,}\) \(\Sigma^0\text{,}\) and \(\Sigma^-\)). Experimental evidence indicates that these particles behave identically during strong interactions. There is also good evidence from nuclear physics that the strong interaction does not depend on a particle's charge. Another way to describe this independence is to say that the strong interaction possesses charge symmetry.
Another common dynamical property among hadrons seems to be strangeness. Particles differing only in strangeness (and slightly in mass) are observed to behave identically during strong interactions. Thus, the strong interaction also possesses strangeness symmetry.
Let's see how Gell-Mann and Ne'eman used these symmetry ideas to group the hadrons. The classification scheme they devised, called the Eightfold Way, grouped together hadrons having the same spin and baryon number but different charge and strangeness. Because of charge and strangeness symmetry, the particles within one group should be interchangeable with respect to their behavior in strong interactions and have masses in a fairly small range.
As an example, let's look at the eight known spin 1/2 baryons. The upper part of Table 9.3 lists their properties. They all have the same spin and baryon number, and their masses are in a fairly small range (about 0.940 to \(1.340\Xunits{GeV/ c^2 }\)). They do differ in charge and strangeness however. When one plots the particles on a strangeness versus charge plot, a distinctive hexagonal pattern emerges. See Figure 9.4.
Gell-Mann and Ne'eman noticed that this hexagonal pattern is the same as that which arises in the mathematical group of \(3\times 3\) matrices called \(\mathrm{SU}(3)\text{.}\) An important property of these matrices is that they can all be expressed in terms of eight special basis matrices. Although a detailed explanation of the theory of groups is far beyond the scope of this text, some development of the correspondence between particle plots and matrices is in order.
If we look at the strangeness versus charge plot, we find that there are certain motions that go from one particle to another. One can move along any of the three directions parallel to the sides of the hexagon. The two horizontal motions (left or right) correspond to the symmetry that increases or decreases the charge by one unit. The two vertical motions (up or down) correspond to increasing or decreasing the strangeness by one unit. Finally, the diagonal motions will change both charge and strangeness by one unit. These six operations, plus one for measuring a particle's charge and another for measuring strangeness, correspond to the eight basis matrices for the group of \(3\times 3\) matrices, and lead to the name Eightfold Way. The Eightfold Way is also a term from Eastern philosophy and refers to the steps along the Buddhist path to enlightenment. But don't read too much into the name: Gell-Mann was just having fun with it.
Let's see how the Eightfold Way gives some structure to a different set of particles, the nine known spin zero mesons. Again, locating the particles on a strangeness versus charge plot shows the hexagonal pattern. The operations that change or measure charge and strangeness are similar to those for the baryons.
It turns out that all the known particles fit into similar patterns. In fact, Gell-Mann was so convinced that his patterns were correct that, when he found a hole in the spin 3/2 baryons' pattern, he predicted the existence of a new particle and described its properties. Within weeks of his 1962 prediction, the \(\Omega^-\) particle, with the correct properties, was discovered in bubble chamber photographs at Brookhaven National Laboratory, providing strong experimental confirmation of Gell-Mann's theory.