Question

The $\Xi^{0*}$ particle is a member of the Baryon decuplet with isospin state \[ | I, I_3 \rangle = \left| \tfrac{1}{2}, \tfrac{1}{2} \right\rangle \] and strangeness quantum number $-2$. In the quark model, which one of the following is the flavour part of the $\Xi^{0*}$ wavefunction?

• A. \(\frac{1}{\sqrt{2}}(uss - ssu)\)
• B. \(\frac{1}{\sqrt{3}}(uss + sus + ssu)\)
• C. \(\frac{1}{\sqrt{2}}(uss + ssu)\)
• D. \(\frac{1}{\sqrt{3}}(uss - sus + ssu)\)

Hint:

In baryon wavefunctions, the flavour part is a linear combination of quark states, and the coefficients are chosen to ensure proper symmetry under particle exchange.

Answer 1

The Correct Option is B

- In the quark model for baryons, the $\Xi^{0*}$ particle has two up quarks and one strange quark. - The wavefunction for the $\Xi^{0*}$ particle will involve a linear combination of quark flavour states. Since the isospin quantum number \(I = \frac{1}{2}\) and strangeness is \(-2\), the flavour part of the wavefunction involves combinations of $uss$, $sus$, and $ssu$ states.
- The correct choice is a normalized combination: \[ \frac{1}{\sqrt{3}}(uss + sus + ssu) \] - This is the flavour wavefunction for the $\Xi^{0*}$ particle.