QB_PH_SEC9_022: Particle Physics & Fundamental Interactions

What is the strangeness quantum number $S$ of the neutral cascade hyperon $\Xi^0$ consisting of valence quarks $(u s s)$?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Quark Quantum Numbers**: - Up quark ($u$): $Q = +2/3, \; B = 1/3, \; S = 0$ - Down quark ($d$): $Q = -1/3, \; B = 1/3, \; S = 0$ - Strange quark ($s$): $Q = -1/3, \; B = 1/3, \; S = -1$ 2. **Baryon Composition**: $\Xi^0$ is a member of the $J^P = 1/2^+$ baryon octet with quark structure $u s s$. 3. **Summation of Strangeness**: $S = S_u + S_s + S_s = 0 + (-1) + (-1) = -2$ 4. **Official Integer Value**: -2.