The and quark contents give the octet states and (measured ) and the decuplet states…
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model
Symmetry and Flavour, Ch The constituent quark model: wave functions, magnetic moments and hyperfine masses
Problem
The uss and dss quark contents give the octet states Ξ0 and Ξ− (measured JP=21+) and the decuplet states Ξ∗0 and Ξ∗− (measured JP=23+).
((a)) For three identical fermions with L=0 and colour in the unique antisymmetric singlet, the spin and flavour parts together must be totally symmetric. List the symmetry types available to three-quark SU(3) flavour states and to three-spin-half states.
((b)) Show that a totally symmetric spin-flavour state can only be built as (symmetric flavour)×(symmetric spin) or as (ϕMSχMS+ϕMAχMA)/2, and that no totally symmetric combination exists pairing a decuplet flavour state with a spin doublet, or an octet flavour state with the spin quartet.
((c)) Hence explain why the Ξ family has an octet member with J=21 and a decuplet member with J=23, but neither a decuplet member with J=21 nor an octet member with J=23, and verify the total ground-state count 10×4+8×2=56.