In $Co\rightarrow Ni^* + e^- + \bar{v}_e$ , the Wu experiment, it is said that $J_{co}$ = 5, $J_{Ni}$ = 4 and hence J of "$e^- + \bar{v}_e$" system is 1. If orbital angular momentum is zero, its S=J=1. Because of this we say both electron and anti-neutrino has $S_z$=1/2. But I guess, if S=1, $S_z$ of this total system can also be 1,0 or -1. This leads to $S_z$ of electron and neutrino to have values $S_z$=0,1/2 or -1/2. Then, why do we take only +1/2 for both electron and anti-neutrino?