All Combinations are Possible

All quark combinations are possible. This table lists some of these combinations. When Gell-Mann and Zweig proposed the original three quark flavors, particles corresponding to all combinations of those three had not been observed. The pattern was there, but it was incomplete—much as had been the case in the periodic table of the elements and the chart of nuclides. The \({\Omega }^{-}\) particle, in particular, had not been discovered but was predicted by quark theory.

Its combination of three strange quarks, \(\text{sss}\), gives it a strangeness of \(-3\) (see this table) and other predictable characteristics, such as spin, charge, approximate mass, and lifetime. If the quark picture is complete, the \({\Omega }^{-}\) should exist. It was first observed in 1964 at Brookhaven National Laboratory and had the predicted characteristics as seen in this figure. The discovery of the \({\Omega }^{-}\) was convincing indirect evidence for the existence of the three original quark flavors and boosted theoretical and experimental efforts to further explore particle physics in terms of quarks.

Patterns and Puzzles: Atoms, Nuclei, and Quarks

Patterns in the properties of atoms allowed the periodic table to be developed. From it, previously unknown elements were predicted and observed. Similarly, patterns were observed in the properties of nuclei, leading to the chart of nuclides and successful predictions of previously unknown nuclides. Now with particle physics, patterns imply a quark substructure that, if taken literally, predicts previously unknown particles. These have now been observed in another triumph of underlying unity.

The figure shows a trace of a bubble chamber picture that shows the first observation of an omega minus particle. The trace looks like the branch of a small bush. There is a stem at the bottom labeled K minus, then a vertex from which comes a short arched segment labeled omega minus. This segment branches into a dashed line labeled xi zero and an arched line labeled pie minus. Various other solid and dashed lines continue upwards with various labels, such as lambda zero, gamma, K plus, and so on. From the scale bar in the figure, the sigma minus segment is about five centimeters long, which is much shorter than most of the other segments.

The image relates to the discovery of the \({\Omega }^{-}\). It is a secondary reaction in which an accelerator-produced \({K}^{-}\) collides with a proton via the strong force and conserves strangeness to produce the \({\Omega }^{-}\) with characteristics predicted by the quark model. As with other predictions of previously unobserved particles, this gave a tremendous boost to quark theory. (credit: Brookhaven National Laboratory)

Example: Quantum Numbers From Quark Composition

Verify the quantum numbers given for the \({\text{Ξ}}^{0}\) particle in this table by adding the quantum numbers for its quark composition as given in this table.

Strategy

The composition of the \({\text{Ξ}}^{0}\) is given as \(\text{uss}\) in this table. The quantum numbers for the constituent quarks are given in this table. We will not consider spin, because that is not given for the \({\text{Ξ}}^{0}\). But we can check on charge and the other quantum numbers given for the quarks.

Solution

The total charge of uss is \(+\left(\cfrac{2}{3}\right){q}_{e}-\left(\cfrac{1}{3}\right){q}_{e}-\left(\cfrac{1}{3}\right){q}_{e}=0\), which is correct for the \({\text{Ξ}}^{0}\). The baryon number is \(+\left(\cfrac{1}{3}\right)+\left(\cfrac{1}{3}\right)+\left(\cfrac{1}{3}\right)=1\), also correct since the \({\text{Ξ}}^{0}\) is a matter baryon and has \(B=1\), as listed in this table. Its strangeness is \(S=0-1-1=-2\), also as expected from this table. Its charm, bottomness, and topness are 0, as are its lepton family numbers (it is not a lepton).

Discussion

This procedure is similar to what the inventors of the quark hypothesis did when checking to see if their solution to the puzzle of particle patterns was correct. They also checked to see if all combinations were known, thereby predicting the previously unobserved \({\Omega }^{-}\) as the completion of a pattern.

All Combinations are Possible