[QUE/EPP-01007]

For a two particle reaction  \[ A + B \longrightarrow C + D\]  define variables \(s,t,u\) by \begin{equation}    s= (p_1+p_2)^2; \quad t= (p_1-p_3)^2; \quad u = (p_1-p_4)^2,  \end{equation} where \(p_1, p_2,p_3,p_4\) denote the four momenta of the particles \(A,B,C\) and \(D\).

• Show that \[ s+ t + u = \sum_{k=1}^4 m_k^2\] where \(m_k, k=1,..,4\) are the masses of the four particles in the reaction.
• Find the allowed range of variables \(t\) and \(u\) in terms of the masses of the particles.