= Relativistic production of a massive particle and a photon
{title2=$E_B=(\mathcal E^2+m^2c^4)/(2\mathcal E),\quad E_\gamma=(\mathcal E^2-m^2c^4)/(2\mathcal E)$}
In the <centre-of-momentum frame> with total energy $\mathcal E$, <four-momentum conservation> for a final massive particle of rest mass $m>0$ and one <photon> gives equal and opposite three-momenta. The <energy–momentum relation> and $|\mathbf p_\gamma|=E_\gamma/c$ give the displayed energies, and
$$
\frac{v_B}c=\frac{\mathcal E^2-m^2c^4}{\mathcal E^2+m^2c^4}.
$$
The photon has positive energy when $\mathcal E>mc^2$. Kinematics fixes the speed and the opposition of the two final directions, while an angular distribution requires information about the interaction.
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