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What maintains quark spin alignments in baryons?

The $uud$ proton and $udd$ neutron are both spin 1/2, implying that two of their spin 1/2 quarks are always parallel and the other is always opposed.

In contrast, the $\Delta^+$ particle (which like the proton is $uud$) and the $\Delta^0$ particle (which like the neutron is $udd$) are both spin 3/2, implying presumably that the same principle keeps their internal quark spins all parallel.

What principle keeps trios of quarks aligned or anti-aligned in such specific ways?

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2 Answers 2

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The question is "what maintains the orientation". What maintains it is simply the angular momentum conservation. If the total angular momentum has $J^2=j(j+1)\hbar^2$ for $j=1/2$ or $j=3/2$, it obviously can't change because the whole vector $\vec J$ (including its length) is conserved. An up-spin may not spontaneously change to a down-spin and there is no value in between.

The quantum mechanical problem for the bound state of quarks has, much like similar problems for atoms, some solutions with various values of the spin. Just like in atomic physics, the symmetry or antisymmetry of the orbital part of the wave function is correlated with the wave function for the spins, and therefore with the total spin, in various ways to guarantee that the overall wave function is antisymmetric. Some of these solutions have $j=1/2$, others have $j=3/2$. There are no other values of spins one may get by combining three $j=1/2$ spins.

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Nice clean answer, thanks Luboš! –  Terry Bollinger Nov 29 '12 at 12:08

I can only imagine that the anti-symmetry of the wave-function maintains that order. Thus is one takes into account all the quantum numbers of the baryons, since the baryons are fermions, they obey the Fermi-Dirac statistics, and the wave-function must be anti-symmetric.

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