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Relativistic two-body decay

For a rest-frame decay

1 \to 2 + 3

,

E_{2} = \frac{m _{1}^{2} + m _{2}^{2} - m _{3}^{2}}{2 m _{1}} c^{2}, E_{3} = \frac{m _{1}^{2} + m _{3}^{2} - m _{2}^{2}}{2 m _{1}} c^{2} .

The decay is allowed exactly when

m_{1} \geq m_{2} + m_{3}

.

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Solution