Discussion
The \(\Xi^{0*}\) particle is a member of the Baryon decuplet with isospin state \(|I, I_{3}\rangle = |\frac{1}{2}, \frac{1}{2}\rangle\) and strangeness quantum number -2. In the quark model, which one of the following is the flavour part of the \(\Xi^{0*}\) wavefunction?
Answer: B
The flavour wavefunction is \(\frac{1}{\sqrt{3}}(uss + sus + ssu)\).
Strangeness -2 means two strange quarks; with total isospin projection +1/2 the third quark is a \(u\). The baryon decuplet is the totally symmetric flavour multiplet of SU(3) (its spin part is symmetric too, and colour supplies the antisymmetry), so the state must be the symmetric sum of all distinct orderings of \(u, s, s\), normalised by \(1/\sqrt{3}\).
The two \(1/\sqrt{2}\) options leave out the \(sus\) ordering, so they are neither symmetric nor complete; \(uss - ssu\) is also antisymmetric under exchange of the first and third quarks. The option with \(-sus\) is not symmetric under exchanging neighbouring quarks.
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