Spin direction of quarks in a baryon

[bsaucer]

If all three quarks in a baryon have the same flavor, they all spin the same direction, causing the baryon to have 3/2 spin. In a proton, do both up-quarks spin in the same direction (with the down-quark spinning opposite)? Or can the two up-quarks spin in opposite directions?

 

[jambaugh]

Normally they, as spin 1/2 particles would be in some superposition of correlated and anti-correlated spin combinations. The composite of three spin-1/2 particles would resolve into three irreducible spin representations two with total spin of 1/2 and one with total spin of 3/2. With spin coupling through the magnetic moment the lower spin states for the composite would be lower energy and thus you should see states in the higher total spin state decay into the lower energy state.

Note the total dimension is 2x2x2=8 = 4 + 2 + 2.

And since the baryons must be color neutral the color charge of the three quarks should be distinct and they would be treated statistically as distinguishable particles (M-B statistics) with respect to their spins. The extra variable distinguishing the two spin-1/2 states would be some quantity defined by combining spin and the index variable we use to distinguish the particles (su(3) color here).

You can think of the two spin-1/2 cases as say red and green quark in a spin singlet and all the spin 1/2 is accounted for by the blue quark, times the two other equivalent cases modulo two of those six states being co-opted by the spin 3/2 irrep.