The reason for the fact that baryons have spin 1 2 or 3 2 , and mesons have a spin 0 or 1.

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Chapter 43, Problem 14Q

To determine

The reason for the fact that baryons have spin 12 or 32, and mesons have a spin 0 or 1.

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You have entered a graduate program in particle physics and are learning about the use of symmetry. You begin by repeating the analysis that led to the prediction of the Ω- particle. Nine of the spin- 3/2 baryons are four ∆ particles, each with mass 1232 MeV/c2 , strangeness 0, and charges +2e, +e, 0, and -e; three Σ* particles, each with mass 1385 Me/c2 , strangeness -1, and charges +e, 0, and -e; and two Ξ* particles, each with mass 1530 MeV/c2 , strangeness -2, and charges 0 and -e. (a) Place these particles on a plot of S versus Q. Deduce the Q and S values of the tenth spin- 3/2 baryon, the Ω- particle, and place it on your diagram. Also label the particles with their masses. The mass of the Ω- is 1672 MeV/c2 ; is this value consistent with your diagram? (b) Deduce the three-quark combinations (of u, d, and s) that make up each of these ten particles. Redraw the plot of S versus Q from part (a) with each particle labeled by its quark content. What regularities do you see?