Here is another example of how we can use the rotation matrices to compute the angular distribution in a decay process. Let's try another similar example. Consider a spin one particle, polarized with its angular momentum along the ±z-axis, with equal probabilities. Suppose it decays to two spin-1/2 particles, e.g., an electron and a positron.
(a) Suppose the decay occurs with no orbital angular momentum. What is the angular distribution of the decay products, in the frame of the decaying particle?
(b) If this is an electromagnetic decay to e+e−, and the mass of the decaying particle is much larger than the electron mass, the situation is altered, according to relativistic QED. In this case, the final state spins will be oriented in such a way as to give either m=1 or m=−1 along the decay axis, where m is the total projected angular momentum. What is the angular distribution of the decay products in this case?