Why Are There No 3 Up Quark Nucleons?

[Kurret]

There are four Delta particles made up of down and up quarks and having spin 3/2, but there are only two nucleons, the proton and the neutron. Why are there no particles made up of three up (or down) quarks and having spin 1/2??

 

[Bill_K]

Can't satisfy the Fermi statistics. (1) Three up quarks means the isospin part of the wavefunction is totally symmetric. (2) Must have three different colors red, green, blue, so the color part is totally antisymmetric. Conclusion: the spin part (3) must be totally symmetric. That requires it to be spin 3/2.

 

[Kurret]

Can't satisfy the Fermi statistics. (1) Three up quarks means the isospin part of the wavefunction is totally symmetric. (2) Must have three different colors red, green, blue, so the color part is totally antisymmetric. Conclusion: the spin part (3) must be totally symmetric. That requires it to be spin 3/2.

okey I see. This might be a really stupid question to you, but why can't we have a symmetric color wave function? The antisymmetric one is

RGB+BRG+GBR-RBG-BGR-GRB

why can't we have

RGB+BRG+GBR+RBG+BGR+GRB ?

 

[Bill_K]

Thanks, The requirement is that a hadron must be colorless, which is a stronger condition than what I said. Not only must the colors of the three quarks be different, they must form a singlet under the SU(3) color group, which requires them to be in the totally antisymmetric state. The totally symmetric color state on the other hand belongs to the 10 representation of color SU(3), and is not invariant, i.e. not "colorless".