Question 31.3: Checking Lepton Numbers A Use the law of conservation of ele...
Checking Lepton Numbers
A Use the law of conservation of electron-lepton number to determine if the decay scheme \mu^{-} \rightarrow e ^{-}+\bar{\nu}_{e}+\nu_{\mu} can occur.
B Use the law of conservation of electron-lepton number to determine if the decay scheme \pi^{+} \rightarrow \mu^{+}+\nu_{\mu}+\nu_{e} can occur.
A:
Because this decay involves a muon and an electron, L_{\mu} \text { and } L_{e} must both be conserved. Before the decay, L_{\mu}=+1 \text { and } L_{e}=0 . After the decay, L_{\mu}= 0+0+1=+1 \text { and } L_{e}=+1+(-1)+0=0 .
Therefore, both numbers are conserved, and on this basis the decay is possible.
B:
Before the decay, L_{\mu}=0 \text { and } L_{e}=0 . After the decay, L_{\mu}=-1+1+0=0, \text { but } L_{e}=0+0+1=1 .
Therefore, the decay is not possible because electronlepton number is not conserved.