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Two general rules for combining quarks to form hadrons are:

  1. Baryons are composed of three quarks, and antibaryons are composed of three antiquarks.
  2. Mesons are combinations of a quark and an antiquark.

One of the clever things about this scheme is that only integral charges result, even though the quarks have fractional charge.

All combinations are possible

All quark combinations are possible. [link] 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 Ω size 12{ %OMEGA rSup { size 8{ - {}} } } {} particle, in particular, had not been discovered but was predicted by quark theory. Its combination of three strange quarks, sss size 12{ ital "sss"} {} , gives it a strangeness of 3 size 12{ - 3} {} (see [link] ) and other predictable characteristics, such as spin, charge, approximate mass, and lifetime. If the quark picture is complete, the Ω size 12{ %OMEGA rSup { size 8{ - {}} } } {} should exist. It was first observed in 1964 at Brookhaven National Laboratory and had the predicted characteristics as seen in [link] . The discovery of the Ω size 12{ %OMEGA rSup { size 8{ - {}} } } {} 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 Ω size 12{ %OMEGA rSup { size 8{ - {}} } } {} . It is a secondary reaction in which an accelerator-produced K size 12{K rSup { size 8{ - {}} } } {} collides with a proton via the strong force and conserves strangeness to produce the Ω size 12{ %OMEGA rSup { size 8{ - {}} } } {} 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)

Quantum numbers from quark composition

Verify the quantum numbers given for the Ξ 0 size 12{Ξ rSup { size 8{0} } } {} particle in [link] by adding the quantum numbers for its quark composition as given in [link] .

Strategy

The composition of the Ξ 0 size 12{Ξ rSup { size 8{0} } } {} is given as uss size 12{ ital "uss"} {} in [link] . The quantum numbers for the constituent quarks are given in [link] . We will not consider spin, because that is not given for the Ξ 0 size 12{Ξ rSup { size 8{0} } } {} . But we can check on charge and the other quantum numbers given for the quarks.

Solution

The total charge of uss is + 2 3 q e 1 3 q e 1 3 q e = 0 size 12{+ left ( { {2} over {3} } right )q rSub { size 8{e} } - left ( { {1} over {3} } right )q rSub { size 8{e} } - left ( { {1} over {3} } right )q rSub { size 8{e} } =0} {} , which is correct for the Ξ 0 size 12{Ξ rSup { size 8{0} } } {} . The baryon number is + 1 3 + 1 3 + 1 3 = 1 size 12{+ left ( { {1} over {3} } right )+ left ( { {1} over {3} } right )+ left ( { {1} over {3} } right )=1} {} , also correct since the Ξ 0 size 12{Ξ rSup { size 8{0} } } {} is a matter baryon and has B = 1 size 12{B=1} {} , as listed in [link] . Its strangeness is S = 0 1 1 = 2 size 12{S=0 - 1 - 1= - 2} {} , also as expected from [link] . 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 Ω size 12{ %OMEGA rSup { size 8{ - {}} } } {} as the completion of a pattern.

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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