Why Are There No 3 Up Quark Nucleons?

In summary, there are four types of Delta particles that are made up of down and up quarks and have a spin of 3/2. However, there are only two nucleons, the proton and the neutron, and no particles made up of three up or down quarks with a spin of 1/2. This is because having three up quarks would result in a totally symmetric isospin part of the wavefunction, which contradicts the requirement of total antisymmetry for the color part. Therefore, the spin part must be totally symmetric, leading to a spin of 3/2 for these particles.
  • #1
Kurret
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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??
 
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  • #2
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.
 
  • #3
Bill_K said:
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 ?
 
  • #4
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".
 
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Likes Naeem Anwar

1. Why is there no 3 up quark nucleon?

The reason for this is due to the principle of baryon number conservation, which states that the total number of quarks in a system must remain constant. Since an up quark has a baryon number of +1/3 and a nucleon must have a baryon number of +1, it is not possible to have 3 up quarks in a nucleon without violating this principle.

2. Can there ever be a nucleon with 3 up quarks?

No, according to our current understanding of baryon number conservation, a nucleon cannot have 3 up quarks. However, there are theoretical models, such as quark-diquark models, that propose the existence of exotic particles called pentaquarks that contain 3 up quarks and 2 down quarks.

3. Are there any other particles that contain 3 up quarks?

Yes, there are other particles known as baryons that contain 3 up quarks, such as the Delta baryon (Δ++) which has a baryon number of +2. These particles are not nucleons, however, as they are not the fundamental building blocks of atomic nuclei.

4. Why do nucleons only contain up and down quarks?

This is due to the fact that up and down quarks are the lightest and most stable quarks, making them the most abundant in the universe. In addition, the strong nuclear force, which binds quarks together to form nucleons, is stronger between up and down quarks than other combinations of quarks.

5. How does the absence of 3 up quark nucleons affect matter?

The absence of 3 up quark nucleons does not have a significant impact on matter as we know it. Nucleons with a combination of up and down quarks are stable and make up the majority of the matter in the universe. The presence of other particles, such as mesons, which contain a combination of quarks and anti-quarks, also helps to balance out the overall composition of matter.

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