My question is: Does angular momentum conservation considerations alone forbid a spin-1/2 particle from decaying into two spin-1/2 particles?

According to this Phys.SE post, the answer seems to argue that you cannot add two spin-1/2 particles and get a spin-1/2 particle. Yes, I understand that the tensor product of two spin-1/2 particles can be re-organised as a direct sum of a spin-1 space and spin-0 space. However, I disagree that this forbids the decay, because orbital angular momentum could change such that spin+orbital angular momentum ends up being conserved. Hence I believe that under angular momentum conservation considerations alone, it is still possible to for the decay to happen. Is this reasoning correct?


1 Answer 1


No. The total orbital angular momentum is always an integer. Adding the orbital and spin angular momenta for a spin-$\frac{1}{2}$ particle will produce another half-integer value, $j=\frac{1}{2},\frac{3}{2},\frac{5}{2},\ldots$. In contrast, the total angular momentum of two fermions (orbital, plus the first spin-$\frac{1}{2}$, plus the second spin-$\frac{1}{2}$) is necessarily an integer. So the total angular momentum cannot be the same between the two arrangements. It is impossible to transition from a state with an odd number of spin-$\frac{1}{2}$ particles to a state with an even number.


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