When a muon decays from rest, typically what fraction of the energy is carried off by the electron? I tried looking into some papers, but I wasn't sure how to interpret the graphs they displayed.
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There are two neutrinos involved, so there is a spectrum. Both the maximum and the minimum are easy to get.
The most energetic case involves the two neutrinos being emitted in the same direction and the electron recoiling. By treating the neutrinos as massless (an acceptable approximation) we get
$$ pc + \sqrt{m_e^2 c^4 + p^2 c^2} = m_\mu c^2 \,,$$
which can be solved for $p$ and the electron energy found directly.
The minimum would be $\frac{m_e}{m_\mu}$. The two neutrinos are emitted back-to-back and the electron is left at rest.
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A (somewhat idealized plot) is shown on page 6 of this paper. In a three body decay, the energy peaks close to the maximum due to phase space. The maximum is $53$ MeV and the peak looks to be around $45-48$ MeV
Ross Millikan
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