 Solution

ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2017-resit/4/solution

In the pion rest frame, momentum conservation makes the muon and neutrino momenta opposite, with common magnitude

p

. For a massless neutrino,

E_{ν} = p c

E_{μ} + p c = m_{π} c^{2}, E_{μ}^{2} - p^{2} c^{2} = m_{μ}^{2} c^{4} .

Substitute

p c = m_{π} c^{2} - E_{μ}

into the second equation. The

E_{μ}^{2}

terms cancel, leaving

E_{μ} = \frac{m _{π}^{2} + m _{μ}^{2}}{2 m _{π}} c^{2} .

E_{ν} = (m_{π}^{2} - m_{μ}^{2}) c^{2} / (2 m_{π})

. The result is a total energy, including the muon rest energy, rather than its kinetic energy.

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