Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 4 / 12B / a

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- Solution a

Solution

Two-body energy-momentum conservation in the pion rest frame gives

E_{e} = (m_{π}^{2} + m_{e}^{2}) c^{2} / (2 m_{π})

and

p_{e} = (m_{π}^{2} - m_{e}^{2}) c / (2 m_{π})

. Thus

v_{e} = c (m_{π}^{2} - m_{e}^{2}) / (m_{π}^{2} + m_{e}^{2})

.

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