GATE 2023 PH – Question 27
The Ξ0∗ particle is a member of the Baryon decuplet with isospin state | I, I3〉= | 1 2 , 1 2〉 and strangeness quantum number −2. In the quark model, which one of the following is the flavour part of the Ξ0∗ wavefunction?
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Correct answer: (B) $(uss+sus+ssu)/\sqrt3$
Explanation
The $\Xi^{*0}$ is a member of the baryon **decuplet** (spin $\tfrac32$). The quark content of $\Xi^{*0}$ is $uss$: one $u$ quark and two $s$ quarks, so the charge is $\tfrac23-\tfrac13-\tfrac13=0$ and the strangeness is $-2$.
**Flavour symmetry.** All members of the decuplet have a **completely symmetric** flavour wave function (the spin part is symmetric too, and the colour part is antisymmetric to satisfy the Pauli principle). The symmetric combination of the three arrangements of $u,s,s$ is
$$\frac{1}{\sqrt3}\left(uss+sus+ssu\right)\quad(\text{option B}).$$
The other options are antisymmetric or partially symmetric, and are not decuplet states.