- #1
geoduck
- 258
- 2
The uuu hadron doesn't violate Pauli's exclusion principle presumably because there is color.
But even without color, can't the uuu exist if spatial wavefunctions are different? Suppose one u quark is located at r1, another at r2, and another at r3, and say that all three u quarks have spin up.
Then you can construct the antisymmetric wavefunction:
$$(|r_1 r_2 r_3 \rangle - |r_2 r_1 r_3 \rangle+...)\otimes |\uparrow \uparrow \uparrow \rangle
\otimes | u u u \rangle
$$
where r1, r2, and r3 are permuted with negative sign if the permutation is odd.
If you swap any two particles, you get a negative sign.
Also in general, must we assume that the wavefunction is a direct product? This seems to say that spin is uncorrelated with flavor. If a baryon is made of a u, d, and s quark, why must each of these different quarks have the same amplitude of being found spin up or spin down (as implied by a direct product)?
But even without color, can't the uuu exist if spatial wavefunctions are different? Suppose one u quark is located at r1, another at r2, and another at r3, and say that all three u quarks have spin up.
Then you can construct the antisymmetric wavefunction:
$$(|r_1 r_2 r_3 \rangle - |r_2 r_1 r_3 \rangle+...)\otimes |\uparrow \uparrow \uparrow \rangle
\otimes | u u u \rangle
$$
where r1, r2, and r3 are permuted with negative sign if the permutation is odd.
If you swap any two particles, you get a negative sign.
Also in general, must we assume that the wavefunction is a direct product? This seems to say that spin is uncorrelated with flavor. If a baryon is made of a u, d, and s quark, why must each of these different quarks have the same amplitude of being found spin up or spin down (as implied by a direct product)?