Baryon Multiplets and quark content

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Discussion Overview

The discussion revolves around the properties of baryon multiplets in particle physics, specifically focusing on the J=3/2 and J=1/2 multiplets and their quark content. Participants explore the implications of quantum numbers and statistics on the existence of baryons with identical quark flavors.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that the J=3/2 multiplet contains baryons made of uuu, ddd, and sss quarks, while the J=1/2 multiplet lacks baryons with three identical quarks, questioning the underlying reasons related to quantum numbers.
  • Another participant explains that the three quarks are antisymmetric in color and must obey effective Bose statistics, suggesting that three identical quarks cannot form a spin 1/2 state due to symmetry requirements.
  • A further contribution reiterates the initial question and expands on the reasoning, stating that the wavefunction of three quarks must be totally antisymmetric, involving considerations of space, spin, flavor, and color, leading to the conclusion that the spin must be totally symmetric for the J=3/2 state.

Areas of Agreement / Disagreement

Participants express differing views on the implications of quantum statistics and the symmetry requirements for baryon states, indicating that the discussion remains unresolved regarding the complete understanding of these properties.

Contextual Notes

Participants reference Fermi-Dirac statistics and the symmetry of wavefunctions, but the discussion does not resolve the complexities involved in the interplay of these factors.

Who May Find This Useful

This discussion may be of interest to students and researchers in particle physics, particularly those studying baryon properties and quantum statistics.

Naz93
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I'm learning about particle physics at the moment, and have read that the J=3/2 multiplet contains baryons comprised of uuu, ddd, sss quarks. But the J=1/2 multiplet contains no baryons consisting of three quarks of the same flavour. Is there a reason for this? Is it something to do with quantum numbers the three quarks can take? (That doesn't really make sense to me, as the J=3/2 requires all spins of quarks aligned, so has even less "freedom" than than the J=1/2...)
 
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Because the 3 quarks are antisymmetric in the color degree of freedom, they obey effective Bose statistics.
Three identical quarks cannot be in a spin 1/2+1/2+1/2=1/2 state because this spin state is not fully symmetric.
 
Naz93 said:
I'm learning about particle physics at the moment, and have read that the J=3/2 multiplet contains baryons comprised of uuu, ddd, sss quarks. But the J=1/2 multiplet contains no baryons consisting of three quarks of the same flavour. Is there a reason for this? Is it something to do with quantum numbers the three quarks can take? (That doesn't really make sense to me, as the J=3/2 requires all spins of quarks aligned, so has even less "freedom" than than the J=1/2...)
It arises from Fermi-Dirac statistics. The wavefunction of the three quarks must be totally antisymmetric. It consists of parts: space, spin, flavor and color. The space part, assuming L=0, is symmetric. The flavor part, assuming three identical quarks, is symmetric. The color part, assuming the baryon will be colorless is totally antisymmetric. That leaves just the spin, and it must be totally symmetric. The totally symmetric coupling of three spin-1/2's is J=3/2.
 
Thanks both! :smile:
 

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