GATE 2024 PH – Question 49

Nuclear and Particle Physics · conservation laws, isospin symmetry, charge conjugation, parity and time-reversal invariance. · 2 marks · Multiple select

Decays of mesons and baryons can be categorized as weak, strong and electromagnetic decays depending upon the interactions involved in the processes. Which of the following option is/are true?

$\pi^0\to\gamma\gamma$ is weak
$\Lambda^0\to\pi^0+p$ is electromagnetic
$K^0\to\pi^++\pi^-$ is weak
$\Delta^{++}\to p+\pi^+$ is strong

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Correct answer: (C) $K^0\to\pi^++\pi^-$ is weak; (D) $\Delta^{++}\to p+\pi^+$ is strong

Explanation

Classify the decay by the interaction responsible. Strong decays conserve strangeness and are fast ($\sim10^{-23}$ s). Electromagnetic decays involve photons ($\sim10^{-16}$ s). Weak decays change strangeness and are slow.

**A. $\pi^0\to\gamma\gamma$ is weak.** False. It involves photons, so it is **electromagnetic**.
**B. $\Lambda^0\to\pi^0+p$ is electromagnetic.** False. The charge is not conserved ($\Lambda^0$ is neutral, but $\pi^0+p$ has charge +1), so the reaction cannot occur. The real decay is $\Lambda^0\to\pi^-+p$, which is weak.
**C. $K^0\to\pi^++\pi^-$ is weak.** True. The strangeness changes from $\pm1$ to 0. ✓
**D. $\Delta^{++}\to p+\pi^+$ is strong.** True. Strangeness is conserved, the lifetime is very short, and this is a decay of a resonance. ✓

Answer **C and D**.