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 Σ∗0 is the J=23 decuplet member built from one u, one d and one s quark, with L=0.
((a)) Write down the unique totally symmetric combination ϕS of the three flavour labels u,d,s, built from all six orderings and normalised to unity, and check its normalisation.
((b)) Pair ϕS with the totally symmetric spin state ∣↑↑↑⟩ (S=23,Sz=23) to build ∣Σ∗0,Sz=23⟩, and confirm that the combined state is symmetric under exchange of any two quarks, as required given the antisymmetric colour singlet and symmetric L=0 space part.
((c)) State why the octet states Λ and Σ0, which have the same quark content uds, cannot use ϕS, and instead require the mixed-symmetry flavour combinations ϕMS,ϕMA paired with the mixed-symmetry spin doublets χMS,χMA.