Problem 6.302

A relativistic particle with rest mass $m$ collides with a stationary particle of mass $M$ and activates a reaction leading to formation of new particles: $m+M \rightarrow m_{1}+m_{2}+\ldots,$ where the rest masses of newly formed particles are written on the right-hand side. Making use of the invariance of the quantity $E^{2}-p^{2} c^{2},$ demonstrate that the threshold kinetic energy of the particle $m$ required for this reaction is defined by Eq. (6.7c).