Question

Which of the following processes are allowed by the strong interaction, the electromagnetic interaction, the weak interaction, or no interaction at all?
(a)$$\pi^- + p \rightarrow 2\eta$$ (b) $$K^- +n \rightarrow \wedge^0 +\pi^-$$
(c)$$K^- \rightarrow \pi^- + \pi^0$$ (d) $$\eta \rightarrow 2\gamma$$

Answer 1

(a) $$\pi^- + p \rightarrow 2\eta$$
Baryon number: $$0 + 1\rightarrow 0$$
It is not allowed because the baryon number is not conserved.
(b) $$K^- +n \rightarrow \wedge^0 +\pi^-$$
Baryon number: $$0 + 1 \rightarrow 1 + 0$$
Charge: $$−1 + 0 \rightarrow 0 − 1$$
Strangeness: $$−1 + 0 \rightarrow −1 + 0$$
Lepton number: $$0 \rightarrow 0 $$
The interaction may occur via the strong interaction since all
are conserved.
(c) $$K^- \rightarrow \pi^- + \pi^0$$
Strangeness: $$−1 \rightarrow 0 + 0 $$
Baryon number: $$0 \rightarrow 0$$
Lepton number: $$0 \rightarrow 0 $$
Charge: $$−1\rightarrow −1 + 0 $$
(d) $$\eta \rightarrow 2\gamma$$
Baryon number: $$0 \rightarrow 0$$
Lepton number: $$0 \rightarrow 0$$
Charge: $$0 \rightarrow 0$$
Strangeness: $$0 \rightarrow 0$$
No conservation laws are violated, but photons are the mediators of the electromagnetic interaction. Also, the lifetime of the η is consistent with the electromagnetic interaction. Strangeness conservation is violated by one unit, but everything else is conserved. Thus, the reaction can occur via the
weak interaction, but not the strong or electromagnetic interaction.