QB_PH_SEC9_005: Particle Physics & Fundamental Interactions

Consider the proposed reaction: $\pi^- + p \to K^0 + \Lambda^0$. Which of the following fundamental conservation laws is/are strictly obeyed by this strong interaction?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Particle Quantum Numbers Tabulation**: - $\pi^-$: $Q = -1, \; B = 0, \; S = 0, \; I = 1, \; I_3 = -1$ - $p$: $Q = +1, \; B = 1, \; S = 0, \; I = 1/2, \; I_3 = +1/2$ - $K^0$ ($d\bar{s}$): $Q = 0, \; B = 0, \; S = +1, \; I = 1/2, \; I_3 = -1/2$ - $\Lambda^0$ ($uds$): $Q = 0, \; B = 1, \; S = -1, \; I = 0, \; I_3 = 0$ 2. **Conservation Checks**: - **Electric Charge ($Q$)**: Initial $= -1 + 1 = 0$; Final $= 0 + 0 = 0$ (CONSERVED) - **Baryon Number ($B$)**: Initial $= 0 + 1 = 1$; Final $= 0 + 1 = 1$ (CONSERVED) - **Strangeness ($S$)**: Initial $= 0 + 0 = 0$; Final $= +1 + (-1) = 0$ (CONSERVED) - **Isospin $I_3$**: Initial $= -1 + 1/2 = -1/2$; Final $= -1/2 + 0 = -1/2$ (CONSERVED) 3. **Conclusion**: Baryon number, electric charge, and strangeness are all conserved (exemplifying associated production). Option (B) is correct.