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## GR0877 Problem 98

PROBLEM STATEMENT: Which of the following is the principal decay mode of the positive muon $\mu^{+}$?

(A) $\mu^{+} \to e^{+} + \nu_e$

(B) $\mu^{+} \to p + \nu_{\mu}$

(C) $\mu^{+} \to n + e^{+} + \nu_e$

(D) $\mu^{+} \to e^{+} + \nu_e + \overline{\nu_{\mu}}$

(E) $\mu^{+} \to \pi^{+} + \overline{\nu_e} + \nu_{\mu}$

SOLUTION: (D) Lepton number $L_e$ is conserved only for (D). Remember, $L_e = +1$ for the electron, the muon, and the neutrino, and $L_e = -1$ for the positron, the positive muon and the antineutrino (all other particles are given a lepton number of zero).

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