Baryon singlet representation for SU(3) flavour symmetry

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Discussion Overview

The discussion revolves around the baryon singlet representation within the context of SU(3) flavour symmetry. Participants explore the properties and existence of the singlet state, particularly focusing on its relationship with the octet and decuplet representations, as well as the implications of Fermi statistics and angular momentum.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes the decomposition of the 27-dimensional representation into 10 + 8 + 8 + 1, seeking information about the singlet representation.
  • Another participant claims that the singlet particle is a uds combination (Lambda) but asserts it does not exist in the ground state due to Fermi statistics.
  • A different participant agrees that the SU(3) baryon flavor singlet is an isospin 0 uds combination and adds that it would have angular momentum of 1/2, clarifying that it lacks orbital angular momentum.
  • Another participant mentions the existence of an excited SU(3) singlet, suggesting the Lambda(1890) as a candidate.
  • One participant points out that there is a uds spin 1/2 state that corresponds to the Lambda particle in the baryon octet, which does exist in the octet ground state.
  • A participant seeks clarification on why the singlet does not exist, prompting further discussion about the antisymmetry requirement of fermions and the implications for the total wave function.
  • Another participant explains that the spin addition leads to a mixed symmetry state, necessitating a flavor octet rather than a singlet.

Areas of Agreement / Disagreement

Participants generally agree that the SU(3) baryon flavor singlet is an isospin 0 uds combination and that it does not exist in the ground state. However, there is disagreement regarding the implications of this non-existence and the nature of the associated states, particularly concerning the relationship between the singlet and octet representations.

Contextual Notes

The discussion includes assumptions about the properties of fermions and the requirements for antisymmetry in wave functions, which are not fully resolved. There are also references to specific particle states and their characteristics that may depend on further definitions or contexts.

Pietjuh
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Hi there!

As most people already might know, we can decompose the 27 dimensional representation for the baryons under SU(3) flavour symmetry as 27 = 10 + 8 + 8 + 1. I can find a lot of information about the particles that lie in the decuplet and in the octet, but nothing about which particle is associated to the singlet representation. Can anyone give me some information about this? :)

Thanks in advance!
 
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the singlet particle is uds (lambda) and it does not exist in the ground state (angular momentum zero) due to Fermi statistics.
 
Hamster is right that the SU(3) baryon flavor singlet is an isospin 0 uds combination. He's also right that it doesn't exist: however, it still possesses (or would possess) angular momentum of 1/2, because the three quarks each have spin 1/2. I think he means there is no orbital angular momentum.

There is an excited SU(3) singlet. It must have T=0, J=3/2, and a quick look in the PDG suggests to me that the best candidate is the Lambda(1890).
 
There is a uds spin 1/2 state that is the Lambda particle of the baryon octet.
It does exist in the octet ground state.
 
Vanadium 50 said:
Hamster is right that the SU(3) baryon flavor singlet is an isospin 0 uds combination. He's also right that it doesn't exist

Could you explain to me why it doesn't exist? I've also been wondering about this question.
 
It's a fermion so it's total wave function has to be antisymmetric. If I make it symmetric in color, under SU(3) and spatially, it's total wave function isn't antisymmetric.
 
petergreat said:
Could you explain to me why it doesn't exist? I've also been wondering about this question.
The spin addition 1/2+1/2+1/2=1/2 leads to a spin state of mixed symmetry (not completely symmetric or antisymmetric). This means the flavor state must also be mixed, which requires a flavor octet, and not a singlet.
 

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