EPP-Problem --- Id QUE/EPP-01001

Consider the two body decay in an arbitrary frame

1. Show that the angle \(\theta\) between the decay products is given by\begin{equation}\label{EQ01} \cos \theta =\frac{2\omega_1\omega_2-2m_1m_2}{2k_1k_2} + \frac{(m_1+m_2)^2-M^2}{2k_1k_2}\end{equation}
2. Use this result to prove that for pion decay \( \pi^0 \longrightarrow 2 \gamma\) in flight having velocity \(v\), the angle between the two photons is given by \[\cos (\theta/2) = v/2 .\]
3. Derive the condition \(M \ge m_1+m_2\) for a massive particle of mass \(M\) to decay in two particles.
4. Use the above result in \eqref{EQ01} to show that a massless particle cannot decay into two massive particles, even though the energy considerations appear to allow the decay.