The Leptons — Question 2

Question 2

Charge conjugation fixes the neutrinos in positive-muon decay

A positive muon decays into a positron and two neutral leptons through the charge-conjugate channel of ordinary negative-muon decay. Use family number +1 for leptons and -1 for antileptons.

1. Identify both neutral leptons and verify family bookkeeping.

2. For $\tau^-\to\mu^-+$ two neutral leptons, identify the analogous flavor assignment.

Question 2 - Solution

Charge conjugation fixes the neutrinos in positive-muon decay

(a) Method and calculation

$$\boxed{\mu^+\to e^++\nu_e+\bar\nu_\mu}.$$$$L_e:\ 0=-1+1,\quad L_\mu:\ -1=-1;\quad\boxed{Q:\ +1=+1}.$$

(b) Interpretation and further calculation

$$\boxed{\tau^-\to\mu^-+\bar\nu_\mu+\nu_\tau}.$$$$L_\mu:\ 0=1-1,\quad L_\tau:\ 1=1;\quad\boxed{L_{\mathrm{total}}:\ 1=1}.$$

Physical check

Neutrality alone cannot distinguish neutrinos from antineutrinos. The charged-lepton flavor and sign fix the corresponding assignments in these channels.