Two-photon decay ($E_{\gamma }^{\ast }=M{c}^2/2$)

Decay of a massive parent into exactly two photons. In its rest frame, momentum conservation requires opposite photon momenta of equal magnitude, so each photon has energy $M{c}^2/2$. A boost along their common axis gives laboratory photon energies $\gamma M{c}^2(1\pm \beta )/2$. Their product stays $(M{c}^2/2{)}^2$ in that collinear configuration; other emission angles require the corresponding angular Lorentz transformation.