1. The problem statement, all variables and given/known data I have a question regarding exercise 48.4-b in Srednicki's QFT book (the chapter is related to Yukawa theories). I have the official solution + explanation to the problem but I still do not fully understand the reasoning used in it, so perhaps you can help me. In the excersise we are asked to calculate the probability amplitude for decay of a scalar into an electron-positron pair, focusing on the conditions that make the amplitude zero. The pair's three momentum goes along the Z axis and spin is quantized on the X axis. According to the solution, we get zero when the two fermion spins are opposite. The reason for this would be that parity forces the orbital angular momentum "l" of the pair to be odd (l=1): since the original particle had zero spin then necessarily the particles must have spins aligned on X to overcome the non-zero orbital angular momentum. 2. Relevant equations 3. The attempt at a solution What I do not understand about that answer is that, as far as I know, the orbital angular momentum refered to in the problem is the quantum number "l" and not the value of angular momentun on the X direction. This means that theoretically the electron-positron pair could be in a |l,m_l> = |1,0> orbital, have spins in opposite directions and produce a zero spin value in the X direction. In fact, the resulting state after the decay should be a combination of states with orbital numbers |l,m_l> = |1,-1>,|1,0>,|1,1> to preserve total angular momentum. That would include the aforementioned case where |l,m_l> = |1,0> and |s,m_s> = |1,0> (the latter representing the overall spin state of both particles). My only guess is that perhaps the |l,m_l> = |1,0> orbital, when expressed in momentum space, has no momentum aligned in the Z axis and so for the purposes of this problem we should only focus on |l,m_l> = |1,-1>,|1,1>. Unfortunately, I have not been able to find useful information on the momentum space properties of orbitals and so I cannot verify this idea.