 Solution

ID: past-exam-of-the-nuclear-and-particle-physics-course-of-the-university-of-oxford/2022/4/c/solution

u d s

1

- 1

and isospin projection zero. Their total isospins differ:

Σ^{0} : I = 1, I_{z} = 0; Λ^{0} : I = 0, I_{z} = 0.

The

u d

flavor part is symmetric for the Sigma baryon and antisymmetric for the Lambda baryon. In the usual ground state coupling, the associated

u d

pair has spin one for

Σ^{0}

and spin zero for

Λ^{0}

, with the strange quark giving total spin

1/2

in both cases. Distinct total isospin makes these orthogonal states despite their coincident position in the weight diagram.

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