EPP-Problem --- Id:: QUE/EPP-01002

A particle of mass \(M\) decays into three particles of masses \(m_1,m_2,m_3\):     \[A \longrightarrow B + C  + D \]  Considering the decay process in the rest frame of the particle \(A\), determine the angle between the momenta of \(B\) and \(C\) and hence show that the energies \(E_1\) and \(E_2\) must lie in a region of \(E_1,E_2\) plane bounded by the curve

\[ 4(E_1^2-m_1^2)(E_2^2-m_2^2) = (M^2-2m_1(E_1+E_2) +2E_1E_2 - m_3^2 + m_1^2 + m_2^2)^2\]