Why Can't UUU & DDD Show on Spinhalf Diagrams?

  • Thread starter barnflakes
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In summary, the exclusion principle, based on the Pauli principle and the addition of spins, prevents the construction of a spin 1/2 state with three identical u quarks due to the requirement of complete antisymmetry in (color)(space)(spin). This can be explained through group theory and the decomposition of the direct product of three fundamental '3's of SU(3).
  • #1
barnflakes
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Can anyone explain to me why you can't have uuu and ddd on the first (spinhalf.gif) diagrams I have uploaded please?
 

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  • #3
The answers in that thread were completely beyond me. Can somebody explain in a single sentence for me? I'm only studying very elementary particle physics..
 
  • #4
The short answer is the exclusion principle. But to see that you need to know a bit about groups and their representations. Specifically that the direct product of 3 fundamental '3's of SU(3) decomposes like 3 * 3 * 3 = 10 + 8 + 8 + 1. The decuplet (which contains uuu) is necessarily spin 3/2 and completely symmetric.
 
  • #5
The attempt to construct a spin 1/2 state |uuu> results in a violation of the Pauli exclusion principle.

As far as I remember from my QCD lectures (~ two decades ago!) the explanation in the other thread misses the spatial part of the wave function. One must take into account
|color> * |spin> * |isospin> * |space>
Ofcourse this doesn't make things easier ...
 
  • #6
yes the most basic answer is to combine the two of haelfix and tom.stoer
 
  • #7
The ground state L=0 is space-symmetric in the constituent quark model.
 
  • #8
The answer is simpler than group theory, but is based on the Pauli principle (Fermi-Dirac statistics) and the addition of spins. The combined state of (color)(space)(spin) must be completely antisymmetric for three identical u quarks. The wave function is antisymmetric in color. The spin addition 1/2+1/2+1/2=1/2 is of mixed symmetry, and so cannot combine with the presumed symmetry spatial ground state and antisymmetric color state to form a completely antisymmetric state. Spin 1/2 for three quarks is only possible if they are not all identical, for instance uud.
 

Related to Why Can't UUU & DDD Show on Spinhalf Diagrams?

1. Why do some spin states, such as UUU and DDD, not show on spinhalf diagrams?

Spinhalf diagrams show the spin states of particles with half-integer spin values, such as electrons. UUU and DDD represent spin states that have integer spin values, and therefore cannot be shown on spinhalf diagrams.

2. Can spinhalf diagrams be used to represent all types of particles?

No, spinhalf diagrams are specifically designed to represent particles with half-integer spin values. Other types of particles, such as photons and gluons, have different spin values and require different diagrams for representation.

3. Is there a reason why spinhalf diagrams only show spin states along one axis?

Spinhalf diagrams only show spin states along one axis, usually the z-axis, because this is the axis along which spin measurements are typically made. Showing spin states along multiple axes would make the diagrams more complex and difficult to interpret.

4. How can we use spinhalf diagrams to understand spin interactions between particles?

Spinhalf diagrams can be used to visualize the possible spin states of two or more particles and how they may interact with each other. By comparing the spin states of different particles, we can predict how they will behave in certain interactions.

5. Are there any limitations to using spinhalf diagrams in particle physics research?

While spinhalf diagrams are a useful tool for understanding spin states, they have limitations. They cannot accurately represent particles with spin values greater than 1/2, and they do not account for other important properties of particles, such as mass and charge. Therefore, spinhalf diagrams should be used in conjunction with other tools and techniques in particle physics research.

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