Question

Why are spin 1/2 baryons less massive/energetic than spin 3/2 ones?

Answer 1

I am just wondering why the lower spin state multiplets for both baryons (when looking at L=0L=0 and considering only the u d and s quarks) are lower in energy i.e. the 1/2+ multiplet is lower than the 3/2+ multiplet. This might well be obvious but I can't seem to come up with an argument for why it is the higher spin state that is the excited state. It is the same situation with mesons and the 0- and 1- multiplets.

When I look for an analogy with the two electron helium atom in atomic physics the differences in energy of different spin states arrises due to differences in symmetry in the spatial part of the wave function which in turn alters the electromagnetic potential and hence alters the energy but I can't really see a similar argument here.

Answer 2

 we have two identical quarks present the spin part of the wavefunction changes from antisymmetric to symmetric between the ½+ and 3/2+ groups. Since identical fermions are antisymmetric on exchange this makes the flavour (or isospin) part change from antisymmetric in the ½+ group to symmetric in the 3/2+ group (the spatial and colour parts remaining unaffected). This difference will lead to a change in strong potential of the two states and a mass difference.