How do neutrinos conserve angular momentum?

[SteveDC]

I'm learning about beta decay and as I understand in beta decay we get:

neutron → proton + electron

And since all these have spin 1/2 we have that the conservation of angular momentum is not conserved.

The neutrino with spin 1/2 is proposed to also exist in the process to solve this so that:

neutron → proton + electron + neutrino

But I don't understand how this conserves angular momentum since haven't you now gone from a spin 1/2 particle one side to three spin 1/2 particles the other side so the spin has changed by 1. Shouldn't the change in spin need to be zero to conserve angular momentum?

 

[Orodruin]

But I don't understand how this conserves angular momentum since haven't you now gone from a spin 1/2 particle one side to three spin 1/2 particles the other side so the spin has changed by 1. Shouldn't the change in spin need to be zero to conserve angular momentum?

The angular momentum has not changed. You can couple three spin 1/2 to an overall spin 1/2 (simply couple two of the spins anti-parallel).