Still Another Conservation Law — Question 2

Question 2

A strange baryon can decay weakly even when strong decay is excluded

For $\Lambda\to p+\pi^-$ take rest energies 1116, 938 and 140 MeV. The Lambda has S=-1 and both daughters have S=0. Baryon number and charge are conserved.

1. Find Q and strangeness change, and identify the required interaction class.

2. Estimate daughter momentum using the nonrelativistic relative-energy relation $Q=p^2/(2\mu)$, with reduced mass $\mu=m_pm_\pi/(m_p+m_\pi)$. Check the approximation.

Question 2 - Solution

A strange baryon can decay weakly even when strong decay is excluded

(a) Method and calculation

$$\boxed{Q=1116-938-140=38\,\mathrm{MeV},\quad\Delta S=+1}.$$$$\boxed{\text{weak decay required}}\quad\text{despite positive }Q.$$

(b) Interpretation and further calculation

$$\mu c^2=\frac{938(140)}{1078}=121.818\,\mathrm{MeV},\quad\boxed{pc\simeq\sqrt{2\mu c^2Q}=96.219\,\mathrm{MeV}}.$$$$\boxed{pc/(m_\pi c^2)\simeq.687}\quad\text{so the pion is not deeply nonrelativistic}.$$

Physical check

The momentum is explicitly a rough estimate, not an accurate decay prediction. Positive energy release alone does not determine the decay mechanism.