The baryon has quark content (three strange quarks)
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 Ω− baryon has quark content sss (three strange quarks), orbital angular momentum L=0, and colour wavefunction the unique antisymmetric singlet ϵijkqiqjqk.
((a)) Explain why the flavour part of the Ω− wavefunction is automatically totally symmetric under exchange of any two quarks.
((b)) Using the symmetrisation postulate and the antisymmetry of the colour singlet, show that the spin part of the Ω− must be totally symmetric under exchange of any two quarks, and identify which of the three-spin-half states (the symmetric quartet or the mixed-symmetry doublets) satisfies this.
((c)) Hence give the total spin S of the Ω− and, taking the intrinsic parity of a quark to be +1 and the orbital parity for L=0 to be +1, derive JP.