In $\beta^+$ decay, a proton (consisting of 2 up and 1 down quarks) decays into a neutron (1 up and 2 down quarks), a positron and an electron neutrino.
(Image source: https://commons.wikimedia.org/wiki/File:Feynman-beta-plus-decay.svg)
If I'm not mistaken, all quarks, the positron and the neutrino each have a spin of 1/2. So in the overall process, there is a net gain of spin 1.
How is this possible? Where does the extra spin come from?
(If spin conservation didn't matter on the other hand, I wouldn't see any argument for the production of the neutrino.)
where time flows from left to right.
Best Answer
The addition of angular momenta in quantum mechanics is rather more complicated than it is in classical mechanics. In short, it is possible for two spin-1/2 particles to couple in such a way (with "opposite" angular momenta) that the system as a whole behaves as a spin-0 system. They can also couple in a way that will give total system spin 1, but that option is ruled out in this case because of the constraint you note.