= Diphoton opening-angle distribution
{title2=$p(A)=\cos(A/2)/(2\beta\gamma\sin^2(A/2)\sqrt{\gamma^2\sin^2(A/2)-1})$}
An <isotropic> two-<photon> decay of a massive parent with laboratory <Lorentz factor> $\gamma>1$ has the displayed normalized opening-angle <probability density>, with $\beta=\sqrt{1-\gamma^{-2}}$ and $2\arcsin(1/\gamma)<A<\pi$. To derive it in units $c=1$, the laboratory <photon> <energies> are $E_{1,2}=\gamma M(1\pm\beta z)/2$, where $z$ is uniform on $[-1,1]$. The <diphoton invariant mass> gives $\sin^2(A/2)=1/[\gamma^2(1-\beta^2z^2)]$. Apply the <change of variables for probability densities> to both signs of $z$. Its minimum-angle peak is an <inverse-square-root singularity>. At $\gamma=1$, the <probability distribution> is concentrated at $A=\pi$.
Back to article page
